An in-depth survey of the artificial gorilla troops optimizer: outcomes, variations, and applications

Abstract

A recently developed algorithm inspired by natural processes, known as the Artificial Gorilla Troops Optimizer (GTO), boasts a straightforward structure, unique stabilizing features, and notably high effectiveness. Its primary objective is to efficiently find solutions for a wide array of challenges, whether they involve constraints or not. The GTO takes its inspiration from the behavior of Gorilla Troops in the natural world. To emulate the impact of gorillas at each stage of the search process, the GTO employs a flexible weighting mechanism rooted in its concept. Its exceptional qualities, including its independence from derivatives, lack of parameters, user-friendliness, adaptability, and simplicity, have resulted in its rapid adoption for addressing various optimization challenges. This review is dedicated to the examination and discussion of the foundational research that forms the basis of the GTO. It delves into the evolution of this algorithm, drawing insights from 112 research studies that highlight its effectiveness. Additionally, it explores proposed enhancements to the GTO’s behavior, with a specific focus on aligning the geometry of the search area with real-world optimization problems. The review also introduces the GTO solver, providing details about its identification and organization, and demonstrates its application in various optimization scenarios. Furthermore, it provides a critical assessment of the convergence behavior while addressing the primary limitation of the GTO. In conclusion, this review summarizes the key findings of the study and suggests potential avenues for future advancements and adaptations related to the GTO.

1 Introduction

Optimization involves identifying the optimal choice variables to reach the objective function’s minimal or maximum value; in order to discover the best solution to a particular problem, tactics for optimization explore the search space. The optimization process starts with the aim of enhancements that rely upon the parameters, constraints, and objective function (Gharehchopogh et al. 2020; Karaboga and Akay 2009).

The underlying objective function will be utilized to guide the optimization process as it is executed to find the optimal value for the intended decision values. Various single- and multi-objective optimization problems can be solved differently (Ide and Schöbel 2016). Each optimization problem has a specific domain, constraints, and challenges that limit the desired solutions to fit the context (Alzaqebah et al. 2020, 2022; Dhal et al. 2020). Optimization problems are becoming increasingly more complicated in various domains (Traversa et al. 2018). Numerous complex real-world optimization problems with problematic structures are given to be solved using basic optimization algorithms (Dhiman and Kaur 2019). The restrictions and increasing computational complexity imposed by conventional optimization algorithms in handling complicated optimization problems have motivated researchers to discover or improve nature-inspired optimization algorithms (Hussien et al. 2023). In recent years, many researchers have been motivated to develop new optimization algorithms through various techniques of inspiration arising from the need to solve sophisticated optimization problems (Hussain et al. 2019; Abualigah et al. 2022). Among these optimization techniques, swarming and evolutionary are the most widely used. These algorithms comprise a variety of methods, such as Genetic Algorithms (GA) (Mirjalili and Mirjalili 2019), Particle Swarm Optimization (PSO) (Bansal 2019), Salp Swarm Algorithm (SSA) (Abualigah et al. 2020), Multi-Verse Optimizer (MVO) (Mirjalili et al. 2016), Harris Hawk Optimizer (HHO) (Heidari et al. 2019), and many other algorithms (Hashim and Hussien 2022; Hashim et al. 2023; Xiao et al. 2024; Cui et al. 2024).

In contrast, Abdollahzadeh et al. (2021) proposed a new metaheuristic algorithm inspired by gorilla troops’ social intelligence in nature, called Artificial Gorilla Troops Optimizer (GTO). The GTO is a population-based metaheuristic algorithm, where the random solutions form the initial population of the algorithm; then, by using the exploration and exploitation techniques, the algorithm searches for the optimal solution, which is determined according to the objective function. In the GTO, five techniques are used in the exploration and exploitation phases: migration to known and unknown locations to diversify the searching process (exploration) and movements to other gorillas to balance the exploration and exploitation phases. The silverback represents the best solution in each iteration, which the GTO aims to optimize.

The GTO algorithm was chosen as our case study due to its prominent standing as a metaheuristic algorithm, offering advantages such as robustness, flexibility, and simplicity. However, it faces challenges like low exploration ability, premature convergence, and insufficient population diversity. Despite these drawbacks, GTO demonstrates high adaptability and can be enhanced, hybridized, and customized for various problem domains. This has led to the emergence of numerous GTO variants aimed at addressing its limitations and improving its performance. Each variant has its own strengths and weaknesses, making them suitable for different problem scenarios.

Before proposing enhancements to a metaheuristic algorithm, it’s crucial to thoroughly investigate its statistical properties, performance, and structure to identify key factors influencing its effectiveness. However, there’s a noticeable lack of analytical studies on metaheuristic algorithms, including well-established ones. Therefore, experimental analysis is essential to understand a metaheuristic algorithm’s behavior before developing new variants. Despite the proliferation of GTO variants, a comprehensive review of the algorithm is lacking in the literature. Hence, this study aims to fill this gap by gathering and analyzing existing literature on GTO and its variants. This endeavor allows for systematic categorization and evaluation of GTO’s performance and its enhanced versions across various optimization problems. Additionally, the study explores practical applications of GTO in different settings and provides insights for future research in this field.

This survey paper aims to provide a comprehensive overview of the Gorilla Troops Algorithm’s core process and sources. Some basic, modified (Alsolai et al. 2022; Mostafa et al. 2023; Shaheen et al. 2023), binary (Cinar 2023), hybrid (Rawa et al. 2022; Cinar 2022), and multi-objective versions (Houssein et al. 2023; Elkholy et al. 2023) of the Gorilla Troops Algorithm exist. Groups of benchmark functions, machine learning applications, scheduling applications, image applications, engineering applications, parameter estimation applications, network applications, wireless sensor network applications, cybersecurity applications, and other applications are the applications that have used the Gorilla Troops Algorithm. Additionally, the Gorilla Troops Algorithm’s results for solving typical benchmark test functions are given and explored with those of other optimization algorithms that have been published in the literature to illustrate to researchers the algorithm’s general ability to solve problems. Eventually, the most common uses of this method, along with its significant advantages and drawbacks, will be explained through discussion and theoretical analysis.

The following points clarify the contributions of the paper:

• An overview of the primary concept of basic GTO is presented to emphasize the algorithm’s key strengths, weaknesses, and procedures.

• Conducting a thorough investigation of GTO studies within a specified timeframe to formulate a roadmap for scientists and researchers interested in related domains.

• Theoretical aspects of GTO, encompassing binary, discrete, chaotic-based, opposition-based learning, improved, hybridized-based, and multi-objective versions of GTO, are discussed.

• A comprehensive summary of all applications and fields employing GTO has been compiled and presented.

• A performance evaluation of GTO compared to well-known and recently published algorithms in the literature.

• A critical analysis is provided to unveil the primary advantages and disadvantages of GTO.

• Proposing future research directions for advancing GTO and exploring its applications.

The rest of this paper is organized as follows: Sect. 2 gives an overview of the GTO algorithm and its time complexity, while Sect. 3 presents the research methodology and GTO survey taxonomy. Section 4 shows GTO’s expansion and current trend. Section 5 presents the different variants of GTO, such as enhancement, hybrid, and multi-objective, whereas Sect. 6 discusses the applications of GTO. Section 7 presents the evaluations and analysis of GTO using GTO, while Sect. 8 discusses the advantages and disadvantages of GTO. Section 9 concludes the paper and adds some future work.

2 Research methodology and AGTO survey taxonomy

This section provides an overview of the research methods employed in this survey and outlines the various taxonomies of research topics within AGTO.

2.1 Research methodology

We began our paper collection by employing relevant search terms such as optimization algorithms, multi-objective optimization, metaheuristic algorithms, nature-inspired algorithms, and swarm-based algorithms. These terms were combined with “Artificial Gorilla Troops Optimizer” and its abbreviation “AGTO” to conduct a comprehensive search in Web of Science¹ and Scopus² databases. This search yielded a total of 433 papers. After removing duplicate papers and filtering out those unrelated to the Artificial Gorilla Troops Optimizer, we obtained 186 relevant papers. However, among these, 74 papers merely mention AGTO as a base comparison algorithm without delving into it extensively. Hence, we excluded them from our investigation. Subsequently, based on the remaining 112 papers, we propose new taxonomies for study, as detailed in the subsequent subsection. Figure 1 depicts the selection process for these research articles.

Fig. 1

Visual representation depicting the paper collection procedure

2.2 AGTO survey taxonomy

The paper examines 112 research papers on AGTO accepted between 2021 and 2023. These papers are analyzed from two angles. First, they are sorted based on various versions of AGTO, such as binary, discrete, chaotic-based, opposition-based learning, improved, hybridized-based, and multi-objective versions. Second, they are scrutinized regarding application domains, highlighting AGTO’s trends across different fields. These domains include engineering optimization, image segmentation, scheduling optimization, machine learning, deep learning, and energy optimization.

3 Overview of artificial gorilla troops optimizer

Gorilla Troops Optimizer is a swarm-inspired algorithm that mimics the social behavior of gorillas in searching for food, such as leaves, stems, and fruits. Gorillas are social animals that live in groups called troops; each group contains an adult male and several adult females and their offspring. Gorillas are the largest primates on Earth and have feelings and strong family bonds because of the silver-colored hair on the adult’s backs; they are called silverbacks. The adult male gorilla is the leader among them and is responsible for guarding the area, making decisions, guiding the other gorillas to plentiful food sources, and other duties (Abdollahzadeh et al. 2021; Wu et al. 2022).

Gorillas, both male and female, often migrate away from their birthplace. Generally, gorillas move and join new groups. Additionally, male gorillas frequently leave their groups to form new ones by attracting migratory females. On the other hand, male gorillas occasionally stay with the same group into which they were born, belonging to the silverback group. These gorillas may take control of the group if the leader dies or fights with the silverback to do so. The social life of gorillas revolves around the relationship between females and silverbacks. This link is preserved by keeping each other close and caring for one another (Abdollahzadeh et al. 2021; Bonis 2012).

There are two phases to this algorithm: exploration and exploitation. In this algorithm, the optimization operation for gorilla behavior is simulated by five distinct operators: traveling to an unknown place, approaching the other gorillas, and crossing to a familiar place are the three operators in the exploration stage. On the other hand, to enhance the effectiveness of the search during the exploitation stage, two distinct operators are used to track the silverback and compete for adult females. Figure 2 illustrates the main phases of the GTO algorithm.

Fig. 2

The main phases of the GTO

3.1 Exploration phase

Based on an investigation of gorilla behavioral patterns, we may conclude that gorillas exist in the wild in groups under the leadership of silverbacks, which must be obeyed; gorillas occasionally break away from their group. The gorillas will migrate to new natural locations after leaving the group, where they may or might not have previously come across one another. All gorillas are considered candidate solutions in the GTO algorithm, and the silverback gorilla is the best candidate solution at each stage of the optimization process. In contrast, the gorilla’s candidate position GX will be updated in each iteration according to Eq. 1. The random parameter P is defined at the beginning before starting the optimization process, which has a random value in the range $[0-1]$. It is used to determine the migration behavior to an unknown place. The first movement technique to an unknown place will be taken if the $rand < P$, while the second mechanism is chosen, and the gorilla moves towards other gorillas if the $rand \ge 0.5$. however, the gorilla moves to a known place if the $rand < 0.5$ by choosing the third mechanism.

$$\begin{aligned} GX(t+1) = {\left\{ \begin{array}{ll} (UB - LB) \times r_1 + LB, &{}rand< P\\ (r_2 - C) \times X_r(t) + L \times H, rand \ge 0.5 &{}rand \ge 0.5\\ X(i) - L \times (L \times (X(t) - GX_r(t)) + r_3 \times (X(t) - GX_r(t))) &{}rand < 0.5\\ \end{array}\right. } \end{aligned}$$

(1)

where $GX(t+1)$ represents the position’s vector of the candidate gorilla in the next iteration, while the X(t) is the current position of the gorilla, LB and UB demonstrate the lower and upper values for variables; hence, $rand,r_1,r_2,$ and $r_3$ are random variables in the range [0-1]. $X_r$ and $GX_r$ represent a randomly selected gorilla and its position vector. C, L, and H are calculated as follows:

$$\begin{aligned} C= & {} F \times \left( 1 - \frac{It}{{maxIt}}\right) \end{aligned}$$

(2)

$$\begin{aligned} F= & {} cos(2 \times r_4) + 1 \end{aligned}$$

(3)

$$\begin{aligned} L= & {} C \times l \end{aligned}$$

(4)

where

$$\begin{aligned} H= & {} Z \times X(t) \end{aligned}$$

(5)

$$\begin{aligned} Z= & {} [-C, C] \end{aligned}$$

(6)

Hence, It and MaxIt represent the current iteration and the maximum number of iterations. $r_4$ is also a random value between 0 and 1, while l has a random value between -1 and 1.

3.2 Exploitation phase

The two behaviors of Follow the Silverback and Competition for Adult Females are used in the exploitation phase of the GTO algorithm. The group is led by a silverback gorilla, who makes all the choices, chooses the group’s route, and points the gorillas toward the food sources.

All gorillas in the group obey all Silverback decisions, and it is also in charge of safeguarding the safety and well-being of the group. On the other side, the black gorilla in the group may take on a leadership role, or other male gorillas may challenge the silverback gorilla and take control of the group as it ages and weakens. For adult females, the options are Follow the Silverback or Competition, as explained with the two exploitation phase methods based on the C, which was calculated in Eq. 2. The gorillas follow the silverback in case of the $C \ge W;$ otherwise, the competition between adult females will happen.

3.2.1 Follow the silverback

The silverback and other gorillas can carry out their tasks effectively while young. Male gorillas, for example, easily follow the silverback. Each member also can influence other members. This behavior was mathematically formulated as follows:

$$\begin{aligned} GX (t + 1) = L \times M \times (X(t) - X_{Silverback}) + X(t) \end{aligned}$$

(7)

where the $X_{silverback}$ represents the optimal solution (silverback’s position vector) so far, while L is calculated using the following formula:

$$\begin{aligned} M= & {} \left( \left| \frac{1}{N} \sum _{i=1}^{N} GX_i(t)\right| ^g\right) ^{\frac{1}{g}} \end{aligned}$$

(8)

$$\begin{aligned} g= & {} 2^{L} \end{aligned}$$

(9)

The total number of gorillas is illustrated as N, where $GX_i(t)$ represents the position vector for each gorilla at iteration t.

3.2.2 Competition for adult females

One of the most essential phases of maturity for young gorillas is competing with other males for females. There is usually severe competition here, which continues for days and impacts other members.

$$\begin{aligned} GX(i)= & {} X_{Silverback} - (X_{Silverback} \times Q - X_{t} \times Q) \times A, \end{aligned}$$

(10)

$$\begin{aligned} Q= & {} 2 \times r_5 - 1, \end{aligned}$$

(11)

$$\begin{aligned} A= & {} \beta \times E, \end{aligned}$$

(12)

$$\begin{aligned} E= & {} {\left\{ \begin{array}{ll} N_1 &{}rand \le 0.5\\ N_2 &{}rand > 0.5\\ \end{array}\right. } \end{aligned}$$

(13)

The Q determines the force impact, and $r_5$ is a random value ranging from 0 to 1. A is a coefficient vector for assessing the conflict’s level of violence based on a pre-defined variable $\beta$ and E. where E mimics how violence affects the boundaries of solutions based on a threshold of 0.5; when $E \ge 0.5$, the E’s value will be equivalent to random values in the dimensions of the problem and the normal distribution; otherwise, the E’s value is equal to an arbitrary number inside the normal distribution.

In summary, Fig. 3 illustrates the flowchart of the GTO algorithm, while the pseudo-code for the GTO algorithm is demonstrated in Algorithm (1). (Abdollahzadeh et al. 2021).

Fig. 3

Flowchart of the GTO algorithm

Algorithm 1

GTO Algorithm

3.3 Pros and cons of AGTO as per the survey

The creators of AGTO asserted that it represents a potent, efficient, and attractive Swarm Intelligence Algorithm (SIA) designed for tackling global optimization challenges. Nonetheless, they acknowledged several minor drawbacks in AGTO, including the absence of a self-learning mechanism and the influence of fitness values on solution updates (Abdollahzadeh et al. 2021).In the literature, scholars have identified certain shortcomings in AGTO, including significant flaws like falling in local minima regions, expensive computational costs, and slow convergence rates, especially when employed in highly multidimensional/complex nonconvex optimization issues such as training of neural network. The lack of exploration during research phase of the AGTO algorithm contributes to the stagnation at local minima. To address this issue, a second innovation was introduced to enhance the follow the silverback of the AGTO algorithm (Mostafa et al. 2023).

3.4 Time complexity of GTO

The time complexity of the GTO algorithm can be grouped into three main phases: initialization phase, solutions evaluation, and update positions strategies (exploration and exploitation). The number of search agents (gorillas) is represented by N, T is the maximum number of iterations. In addition, the problem’s dimension D plays a crucial role in the computation complexity.

$$\begin{aligned} O(\text {GTO}) = O(\text {Initialization}) + O(\text {Evaluation}) + O(\text {Update Positions}) \end{aligned}$$

(14)

In turn, the time complexity for the initialization phase will be O(N), and in each iteration, all gorillas N will be evaluated, producing $O(T \times N)$. The update positions will take $O(T \times N \times D) \times 2$ for both exploration and exploitation. Thus, the time complexity for the GTO will be:

$$\begin{aligned} O(\text {GTO}) = O(N) + O(T \times N) + O(T \times N \times D) \times 2 = O(N \times (1 + T + TD) \times 2) \quad \end{aligned}$$

(15)

4 The expansion of artificial gorilla troops optimizer

The Artificial Gorilla Troops Optimizer (GTO) has attracted substantial attention and gained broad recognition since it was first introduced in 2021. As of Nov 1, 2023, according to Google Scholar, the initial research paper has been cited 433 times. Within these citations, 370 have appeared in reputable academic journals, 48 have been included in conference proceedings, and 15 have been featured as book chapters. The strengths and benefits of GTO have elevated the original paper’s status, resulting in its recognition as one of the top-rated papers in both Web of Science and Scopus databases.

This research adheres to a structured procedure as depicted in Fig. 4. Initially, we commence with a preliminary investigation. Subsequently, we conduct a review of papers that reference the original paper in order to identify keywords for our search. In the next step, we employ skimming and scanning methods to identify pertinent papers. Following this, we meticulously assess and scrutinize these papers to gather the essential data. Finally, we proceed to extract and systematize the data to construct a well-organized representation of the concepts and insights acquired.

Fig. 4

Review methodology

This section offers an extensive evaluation and scrutiny of the growth and development of the GTO from 2021 to October 2023. It encompasses several facets, such as the yearly count of research publications on GTO, the annual number of citations, the recognition of influential authors in the domain, and significant research institutions incorporating GTO into their studies. Furthermore, it includes a variety of other statistical data associated with GTO research.

To acquire these results, we gathered a total of 171 scientific research publications from the Scopus database. These publications encompass a range of formats, including articles, book chapters, surveys, and conference papers. As some of these works were authored in different languages, we applied several filters to refine the selection to pertinent publications for examination.

The volume and extent of research published concerning the utilization of any optimization technique, particularly in prestigious and highly-regarded journals, serves as a crucial gauge of the optimizer’s effectiveness. As illustrated in Fig. 5, we can observe the yearly total of publications related to GTO. Evidently, there is a mounting interest in the adoption of GTO, particularly in the realm of optimization challenges. The number of articles reached its peak in 2021 with just 12 publications, followed by a significant surge in 2022, with 149 papers. From 2023 up to September, approximately 180 papers have been published annually.

Figure 6 offers an overview of the main publishers that have opted to showcase GTO-related research in their journals. Remarkably, Elsevier leads the way with 221 articles, followed by Springer with 110 research papers, and MDPI with 34 publications. The remaining contributions are distributed among various other publishers, as depicted in Fig. 6.

The number of citations is a vital metric for assessing the quality of research and the degree of interest among researchers in a particular subject. Figure 7 illustrates the MPA’s citation count over the period defined by the Scopus query. Through Fig. 7, it becomes apparent that the number of citations saw a significant increase between 2021 and 2023. In 2021, there were 12 citations, but by October 2023, this number had surged to 213. This substantial increase reflects the growing interest of researchers in applying the GTO in their work.

Regarding GTO citations across various domains, computer science has garnered the most with 235 citations, followed by engineering with 195 citations, and mathematics with 121 citations. Figure 8 illustrates the leading GTO citations within each of these domains.

When it comes to the most prominent GTO authors, “Mirjalili, S.” stands out as the top author with 18 publications in GTO. Following closely is “Abualigah, L.” with 16 papers, and “Abdel-Basset, M.” with 13 papers in GTO. Figure 9 presents the remaining top GTO authors.

Within the domain of journals publishing GTO research, IEEE ACCESS takes the lead with a total of 17 research papers, as displayed in Table 1. Knowledge-based Systems hold the second position with 16 papers, while Mathematics secures the third position with 14 papers. The rankings of the remaining journals are provided in Table 1.

When evaluating GTO research, institutions play a pivotal role, as emphasized in Fig. 10. Zagazig University in Egypt stands out with its research team specializing in GTO, having published over 31 articles. Mansoura University takes the second position with 19 GTO articles, and Universiti Sains Malaysia follows in third place with 15 GTO works. Further information about other contributing institutions can be found in Fig. 10.

Fig. 5

Number of publications per year

Fig. 6

Number of publications per publisher

Fig. 7

Number of citations per year

Fig. 8

Number of publications per domain

Table 1 The top 10 journals with the largest number of papers on GTO

Fig. 9

Number of publications per author

Fig. 10

Number of publications per affiliation

5 Variants of artificial gorilla troops optimizer

In literature, there are different variants of AGTO which use hybridization techniques, or apply it to binary domain or multi-objective problems or use various operators such as OBL, chaotic, etc. Fig. 11 shows the distribution of such variants.

Fig. 11

GTO variants distributions

5.1 Binary artificial gorilla troops optimizer

Many optimization problems can be classified as binary optimization, a subfield of combinatorial optimization. Binary optimization problems involve decision variables that can take binary values, either 0 or 1. This binary representation is used to model the discrete nature of the decision variables in these problems. Well-known binary optimization problems include the knapsack problem (KP), unit commitment problems, and feature selection (FS). These problems are encountered in various real-world applications and are modeled as binary optimization problems due to their discrete decision variables.

Cinar (2023) introduced 17 binary adaptations of the GTO algorithm to solve the complex wind turbine placement problem (WTPP) on a 10x10 grid with 100 dimensions. These binary GTO variants denoted as BAGTO1 through BAGTO17, were used to identify optimal solutions to the problem. The empirical results showed that several of these binary GTO variants performed well in addressing the WTPP. BAGTO9, BAGTO10, and BAGTO16 emerged as the top three variants based on mean final rankings, and BAGTO10, BAGTO17, and BAGTO9 ranked highest according to Friedman’s test values. The convergence profiles mirrored these findings, highlighting the effectiveness of these binary GTO adaptations in successfully solving the WTPP.

5.2 Discrete artificial gorilla troops optimizer

The GTO algorithm was modified to adapt it to the discrete search spaces of various optimization problems.

Piri et al. (2022) introduced the Discrete Gorilla Troop Optimization (DAGTO) algorithm for feature selection (FS). They meticulously crafted four distinct DAGTO variants, each tailored to specific fitness criteria (number and type), making them highly suitable for FS. They also incorporated a robust initialization technique based on mutual information, facilitating expedited convergence. Among these variants, MO-DAGTO2 stood out by seamlessly integrating filter and wrapper approaches, excelling in identifying non-dominated (ND) solutions that closely resembled actual Pareto frontiers. Comparative assessments against four well-established multi-objective FS techniques authenticated the supremacy of MO-DAGTO2. It exhibited the advantages of reduced feature dimensions and heightened recognition accuracy. These remarkable results were consistently observed across diverse datasets, corroborated by multiple multi-objective performance evaluation criteria, thereby solidifying MO-DAGTO2’s position as a top-tier FS solution. Its effectiveness was further validated using a dataset related to COVID-19 patients.

El Houd et al. (2023) introduced a novel framework leveraging swarm intelligence algorithms to optimize hybrid assembly lines in the automotive industry. They developed two discrete versions of the Whale Optimization Algorithm (VNS-DWOA) and Gorilla Troops Optimizer (DGTO) for assembly line balancing. A comparative analysis of their performance against traditional metaheuristics and expert solutions demonstrated the superiority of the proposed methods. Notably, VNS-DWOA achieved significant cycle time enhancements, ranging from 7% over expert solutions to a 20% maximum improvement over other methods. These findings highlight the potential of swarm intelligence algorithms and dynamic simulation-based frameworks to accelerate and improve assembly line design optimization in industrial settings, reducing time to market.

5.3 Chaotic artificial gorilla troops optimizer

Several new versions of the GTO algorithm have been developed by integrating its search behavior with chaotic maps. This integration aims to improve the optimizer’s overall performance and search speed. Chaotic maps, a mathematical method for analyzing nonlinear dynamical systems, are instrumental in enhancing the efficiency and effectiveness of various optimization algorithms.

In their study, Sayed and Hassanien (2022) introduced an improved version of the GTO algorithm, called the chaotic Gorilla Troops Optimizer (CGTO). The CGTO incorporates chaotic maps to address the common challenges of local optima and premature convergence encountered in standard GTO. The study evaluated the CGTO’s performance on global optimization problems and multilevel thresholding tasks, employing three distinct chaotic maps: Circle, Gauss, and Tent chaotic maps. Experimental results demonstrated that the CGTO outperforms other swarm optimization algorithms. These findings were quantitatively and qualitatively substantiated, particularly in the context of fundus images, affirming the CGTO’s capability to identify dominant regions and outperform the original GTO.

To address the increasing demands of emerging services in vehicular networks (VNs), Alsolai et al. (2022) proposed an innovative approach that tackles communication challenges by integrating unmanned aerial vehicles (UAVs) into VN infrastructure. The integration of UAVs into vehicular networks offers several significant advantages, including improved mobility, higher data rates, enhanced security, and expansive 3D communication coverage. To address the challenges of UAV-assisted vehicular networks, the authors introduced the Enhanced Artificial Gorilla Troops Optimizer-based Clustering Protocol for a UAV-Assisted Intelligent Vehicular Network (EAGTOC-UIVN). EAGTOC-UIVN’s primary aim is to cluster nodes within UAV-based VNs to maximize network lifetime and energy efficiency. EAGTOC-UIVN leverages the EAGTO algorithm, incorporating circle chaotic mapping, and defines a fitness function with multiple parameters. Rigorous simulation analyses confirmed that EAGTOC-UIVN outperforms other existing methods, demonstrating its superior performance.

To address the mounting challenges of complex optimization problems, Xiao et al. (2022) developed an advanced iteration of the GTO algorithm called the Improved Gorilla Troops Optimizer (IGTO). IGTO incorporates a suite of critical enhancements to boost its overall performance, including the circle chaotic mapping for diversified initialization, lens opposition-based learning to avert local optima entrapment, and adaptive $\beta$-hill climbing to augment local search capabilities. These refinements significantly enhance IGTO’s exploration and exploitation abilities, making it a robust and versatile optimization algorithm. Comprehensive evaluations across 19 benchmark functions, engineering design problems, and multilayer perceptron training instances demonstrate IGTO’s superiority in terms of solution quality, local optima avoidance, and suitability for real-world applications. These results affirm IGTO’s potential as a powerful tool for tackling complex optimization challenges.

Chaudhary et al. (2022) introduced an enhanced optimization algorithm, the Chaotic Gorilla Troop Optimizer (CGTO), which incorporates one-dimensional chaotic maps based on ten established chaotic maps. They evaluated the CGTO’s performance on two classes of benchmark functions, unimodal and multi-modal, and applied it to optimize a 500 hp AC motor model and design a controller using the unified domain method and approximate model matching technique. Comparative analyses revealed that the CGTO outperformed various contemporary approaches in terms of optimal solutions and convergence characteristics. Assessing the standard deviation of optimal values confirmed the algorithms’ stability, reinforcing their potential for practical applications.

Ganguli (2022) introduced the Chaos-Based Gorilla Troop Optimizer (CBGTO), a novel method encompassing 50 variations of the GTO algorithm. These variations utilize one-dimensional chaotic maps to modify the parent algorithm’s regulating parameters and random variables. To evaluate the CBGTO, the study employed a fifth-order induction motor model and designed an intelligent PID controller using the same approach. The motor model was simplified using the delta operator. Statistical analyses, particularly the integral of time-weighted absolute error (ITAE), confirmed the applicability of the CBGTO, demonstrating highly positive results for a 50 hp induction motor. This research demonstrates the potential for further parameter adjustments to enhance the GTO’s performance. The PID controller implementation employed an approximate model-matching framework, with the novel methods exhibiting superior convergence speed and accuracy compared to standard and state-of-the-art methods.

Chaudhary and Ganguli (2022) introduced a chaotic variant of the Gorilla Troop Optimizer (CGTO) by modifying its position equation with one-dimensional chaotic maps from ten well-established chaotic maps. They evaluated the CGTO’s efficacy on two unimodal and three multi-modal test functions and applied it to optimize a 50 hp induction motor model and design its controller using the delta operator and approximate model matching. The results showed that the CGTO exhibited superior convergence speed and accuracy compared to conventional and contemporary methods, highlighting its potential for various applications.

Bhadoria and Marwaha (2022) proposed a novel approach to addressing the intricate Energy Generation Scheduling Problem using the Chaotic Gorilla Troop’s Optimizer (CGTO) algorithm. This bio-inspired heuristic optimizer, inspired by gorilla hierarchy and hunting behaviors, tackles complex scheduling problems in power system operational planning. The CGTO algorithm combines binary string generation and chaotic operations to identify global optima while avoiding local minima. The authors present a straightforward yet effective strategy for integrating wind power into the system, considering its chaotic behavior. Comparative analyses against existing techniques show the proposed method’s superiority, particularly when extended to wind power sharing. The convergence curve further highlights the robustness and effectiveness of this innovative algorithm.

Chaudhary et al. (2023) proposed a novel approach to modeling and controlling electric vehicle (EV) drive systems using a chaotic variant of the Gorilla Troops Optimizer (ChGTO). This adaptation integrates one-dimensional chaotic maps into the ChGTO algorithm to modify parameters, enhancing its performance on high-dimensional benchmark test functions and complex electric motor and drive models. Controllers are developed using a model-matching technique, demonstrating the promise of ChGTO in both modeling and controlling EV drive systems. This research is of great significance in optimizing EV performance and aligning with the growing importance of EV technology and sustainability goals.

Sattar and Braik (2023) addressed the challenging problem of parameter and order identification for fractional-order chaotic systems by approaching it as a multidimensional optimization task and employing five modern metaheuristic methods: Harris Hawks optimization (HHO), Coot Bird (CB), Chameleon Swarm Algorithm (CSA), Ali Baba and the Forty Thieves (AFT), and GTO algorithm. They applied these methods to the parameter identification problem across six fractional-order chaotic systems, including three newly introduced systems as well as Borah, Chen, and financial systems, using Mean Square Error as the objective function. Numerical simulations showed that the AFT method achieved higher accuracy and faster convergence for parameter identification in four selected fractional-order chaotic systems, while the GTO algorithm outperformed other methods in terms of numerical and graphical results for two fractional-order chaotic systems.

5.4 Opposition based learning artificial gorilla troops optimizer

The researchers also enhanced the capabilities of the GTO by incorporating opposition-based learning (OBL), a technique that improves the exploitation capability and convergence speed of optimization algorithms. This integration aims to balance exploration and exploitation abilities during the optimization process. The following subsection reviews and discusses various applications and use cases of the GTO with OBL.

Mostafa et al. (2023) introduced mGTO, an improved version of the GTO algorithm, designed to overcome its limitations. mGTO incorporates several enhancements, including Opposition-Based Learning (OBL), the Cauchy Inverse Cumulative Distribution (CICD) Operator, and the Tangent Flight Operator (TFO), to diversify the population and enhance the exploitation process. Experimental assessments across the CEC2020 benchmark, constraint engineering problems, and feature selection challenges demonstrated mGTO’s effectiveness. In the CEC2020 benchmark, with dimensions D = 10 and D = 20, mGTO achieved optimal values and demonstrated remarkable performance in 60% and 80% of the test functions, respectively. In engineering problems, mGTO exhibited swift convergence, reduced costs, and high stability, surpassing other methods in both mean and worst-case scenarios. Simulations consistently validated mGTO’s stability and robustness, firmly establishing its effectiveness in various optimization and problem-solving applications.

Liang et al. (2022) introduced the Opposition-Based Learning and Parallel Strategies Artificial Gorilla Troop Optimizer (OPGTO) to enhance the accuracy of node localization in wireless sensor networks (WSNs). OPGTO harnesses opposition-based learning to expand the exploration space, significantly augmenting its global exploration capability. The incorporation of parallel strategies involves segmenting the population into multiple groups for exploration, effectively increasing population diversity. These parallel strategies are fine-tuned to accommodate various types of optimization problems. Through comprehensive experimental evaluations on the CEC2013 benchmark function set, OPGTO demonstrated its superiority over other optimization algorithms, including PSO, SCA, WOA, and the original GTO, particularly on intricate multimodal and combinatorial functions. Furthermore, OPGTO was successfully applied to enhance the real 3D localization of WSNs operating in challenging terrains, resulting in a reduction of localization errors based on the Time Difference of Arrival (TDOA) method.

Si et al. (2023) addressed the significant challenge of enhancing breast cancer diagnosis via Magnetic Resonance Imaging (MRI) segmentation methodologies. They utilized Kapur’s entropy-based multilevel thresholding in tandem with the GTO technique to fine-tune the segmentation of breast Dynamic Contrast-Enhanced MRI (DCE-MRI) lesions. Notably, the researchers introduced a refined GTO variant known as GTORBL, which incorporates the concept of Rotational Opposition Based Learning (RBL). The author meticulously evaluated GTO and GTORBL using a dataset comprising T2 Weighted Sagittal DCE-MRI scans from 20 patients, with comparisons against a range of alternative optimization algorithms. The findings prominently highlighted the supremacy of the proposed GTORBL-based segmentation approach, characterized by heightened precision, sensitivity, and a remarkable Dice Similarity Coefficient (DSC).

Wu et al. (2022) proposed a Modified Gorilla Troops Optimizer (MGTO), an enhanced variant of GTO that addresses certain limitations of the original algorithm. MGTO incorporates Beetle-Antennae Search Based on Quadratic Interpolation (QIBAS) to promote diversity, integrates the teacher phase from Teaching-Learning-Based Optimization (TLBO) for behavior updates, and introduces Quasi-Reflection-Based Learning (QRBL) to generate quasi-reflection positions of the silverback. Thorough evaluations on benchmark functions and engineering problems demonstrate that MGTO consistently delivers competitive performance, indicating its potential for real-world optimization tasks.

Vashishtha et al. (2023) introduced a novel approach to optimize hyperparameters in deep learning models to enhance worm gearbox fault diagnosis performance. They proposed the Amended Gorilla Troop Optimization (AGTO) algorithm, an improved version of GTO that incorporates opposition-based learning and quantum gate rotation to adapt a Convolutional Neural Network (CNN) for feature extraction from Morlet wavelet-transformed vibration and acoustic signals. The AGTO algorithm effectively optimized hyperparameters, resulting in an impressive classification accuracy of 98.95% and a low standard deviation of 0.2145, outperforming other classifiers. This approach demonstrated its superiority in diagnosing worm gearbox defects, and the AGTO algorithm’s effectiveness was further validated on benchmark functions, confirming its potential for various optimization tasks.

Alrayes et al. (2023) proposed an innovative deep learning-enabled cybersecurity threat detection (CTD) model, the Enhanced Artificial Gorilla Troops Optimizer (EAGTO)-based Pinhole Imaging Opposition-Based Learning (PI-OBL) strategy, to address the growing cybersecurity challenges in IoT cloud networks. Facing evolving threats like malware attacks and software piracy, this model focuses on threat identification by converting binary files into color images and employing image classification techniques for malware detection. The model preprocesses data, utilizes a cascaded gated recurrent unit (CGRU) model for threat classification, and leverages EAGTO for hyperparameter optimization. Performance evaluation on a dataset with malignant and benign labels demonstrated the model’s effectiveness, achieving an impressive accuracy rate of 99.47%, promising enhanced cybersecurity in the IoT cloud environment.

5.5 Improved versions of artificial gorilla troops optimizer

Shaheen et al. (2023) introduced an enhanced version of GTO called EAGT for the precise extraction of parameters from the PV Triple-Diode Model, marking a significant development in the field of photovoltaic system optimization. EAGT balances exploration and exploitation using a fitness-based crossover method and a periodic Tangent Flight operator. Notably, rigorous testing on STM6-40/36 and KC200GT PV modules demonstrated EAGT’s superiority over contemporary algorithms and previously published parameter extraction methods. EAGT’s effectiveness was further demonstrated on the SP70 module under varying solar conditions, highlighting its potential for real-world applications.

Abdel-Basset et al. (2022) proposed the Memory-based Improved Gorilla Troops Optimizer (MIGTO) to address the challenging task of accurately extracting parameters from complex Photovoltaic (PV) models. PV models, due to their nonlinear and multi-modal nature, often pose challenges to traditional optimization algorithms, which can become trapped in local optima. Precise parameter estimation is essential for enhancing PV system efficiency in terms of current and power generation. MIGTO incorporates several enhancements, including the Explorative Gorilla with an Adaptive Mutation Mechanism (EGAMM) and the Gorilla memory-saving technique (GMS). EGAMM introduces explorative and adaptive mutation operators to facilitate the exploration of new gorilla positions in the search space, thereby reducing the risk of being stuck in local optima (probability = 0.1). Supported by GMS, MIGTO effectively extracts parameters from various PV models, consistently outperforming other well-established metaheuristic algorithms in extensive experimental evaluations.

El-Dabah et al. (2022) addressed the crucial issue of electrical power system stability, underscoring the adverse effects of disturbances. To combat instability arising from these aberrations, they introduced Power System Stabilizers (PSSs) as supplementary controllers. The research introduced a novel optimization approach, the Quantum Artificial Gorilla Troops Optimizer (QAGTO), to fine-tune PSS parameters. This optimization algorithm demonstrated its superiority by outperforming other techniques, including the standard GTO. The study explored four PSS structures: Dual Input PSS (DIPSS), Tilt-Integral-Derivative (TID-PSS), Fractional-Order Proportional-Integral-Derivative (FOPID-PSS), and the conventional Lead-Lag PSS. Among these, the TID-PSS demonstrated the lowest fitness function value, showcasing its exceptional performance, marked by minimal maximum overshoot, undershoot, and a shorter settling time.

You et al. (2023) proposed innovative strategies to enhance the performance of the GTO algorithm. First, they proposed a shrinkage control factor fusion strategy, which expands the search space and promotes global optimization by improving communication among gorillas. Second, a sine-cosine interaction fusion strategy, based on closeness, stabilizes gorilla performance and enhances convergence. Third, a strategy for identifying individual differences among gorillas reduces disparities to improve optimal solutions. The resulting modified GTO (MGTO) algorithm was rigorously tested on benchmark functions, demonstrating superior performance across 63 functions. MGTO also proved its effectiveness in solving seven practical engineering problems, highlighting its value for a wide range of optimization tasks.

Ebeed et al. (2023) introduced an enhanced version of GTO (EGTO) to tackle the complex challenge of optimal reactive power dispatch (ORPD) while incorporating renewable energy resources (RERs), considering their stochastic and time-varying characteristics. The study primarily focused on addressing the stochastic optimal reactive power dispatch (SORPD) problem, which accounts for uncertainties related to load demand, generated power, and the reactive power generation capacity of photovoltaic (PV) systems. EGTO employs a range of strategies to minimize power loss, improve voltage profiles, and enhance system stability under uncertain conditions. The algorithm’s effectiveness was evaluated on the IEEE 30-bus system, both with and without the STATCOM functionality of the PV system, and compared to other established optimization algorithms. The results highlighted a substantial improvement when incorporating the PV unit, leading to reductions in power losses, voltage deviations, and improved voltage stability in both scenarios.

Huang et al. (2023) presented a solution for the challenging Spherical Asymmetric Multiple Traveling Salesman Problem (AMTSP), an extension of the AMTSP where cities and paths are arranged on a sphere. To tackle this complex problem, they introduce the spherical vector-based Artificial Gorilla Troops Optimization (SGTO) algorithm, which uses a discrete state transition strategy. Unlike Cartesian coordinates, SGTO updates positions in spherical coordinates, enhancing population diversity and local search efficiency through swap, shift, symmetric, and substitute operators. Numerical simulations demonstrate SGTO’s superiority over the basic GTO and other classical metaheuristic algorithms in solving the spherical AMTSP, highlighting its effectiveness in addressing this complex problem.

Shaheen et al. (2023) introduced an advanced iteration of the Improved Gorilla Troops Technique (IGTT) to enhance parameter extraction for proton exchange membrane fuel cells (PEMFCs), focusing on the BCS 500W and Modular SR-12 models. IGTT incorporates a dual migration approach for enhanced exploitation and local optimum avoidance. Furthermore, the Tangent Flight Strategy (TFS) facilitates efficient search space exploration. Comparative evaluations against SDO, FFO, and RFO underscore IGTT’s superior performance. IGTT outperforms standard GTT, GWA, and PSO in most statistical indices. IGTT’s effectiveness in PEMFC stack parameter identification is confirmed by its notably low sum of squared error (SSE) values. For the studied PEMFC stacks, IGTT consistently delivers excellent performance and superior SSE objectives with minimal standard deviations (STD).

Zhang and Razmjooy (2023) proposed an approach to enhance short-term electric power price prediction in the competitive electricity market, accounting for the influence of renewable energy sources, particularly wind energy, on pricing. Their method combines an Elman neural network with an improved Gorilla Troops Optimizer to optimize wavelet decomposition and neural network architecture, addressing the challenge of power price prediction in volatile markets. Numerical testing using historical data from various regions in China demonstrated promising day-ahead price prediction results, especially when compared to other contemporary techniques. These results highlight their approach’s effectiveness in addressing the complexities of the modern electricity market, particularly regarding renewable energy sources.

Abdel-Basset et al. (2023) presented an innovative optimization strategy known as the Ranking-Based Gorilla Troops Optimizer (RGTO), strategically crafted to address intricate optimization dilemmas encountered across a spectrum of practical domains. RGTO augments the traditional GTO with the infusion of two distinct tactical approaches: the ranking-based update strategy and the convergence acceleration strategy. The former refines the local and global exploration competencies of individual gorillas, while the latter is devoted to elevating GTO’s capacity for swift convergence towards superior solutions. Rigorous evaluations of RGTO are conducted on the exacting CEC2017 benchmark, effectively showcasing its supremacy in terms of both exploratory and exploitative proficiencies. Furthermore, RGTO is successfully deployed in tackling three distinctive engineering optimization challenges, encompassing parameter inference for photovoltaic and fuel cell models, as well as engineering design quandaries, consistently outclassing rival optimization methodologies.

Bansal and Sahoo (2023) proposed a new framework to discover cancer subtypes by integrating heterogeneous and high-dimensional multi-omics data. They developed an improved sparse-joint non-negative matrix factorization (sparse-jNMF) method to improve sparse-jNMF initialization and convergence. They also introduced the adaptive gorilla troops optimizer (Ada-GTO), an improved version of GTO algorithm that incorporates adaptive weights update strategies using the Lévy flight (LF) movement in the exploration and exploitation phases. Using consensus clustering, they constructed patient-patient similarity matrices to obtain stable patient clusters. They applied the proposed framework to various real-life multi-omics cancer datasets, demonstrating improved cluster quality and significant survival differences, which can aid in tailored cancer treatments.

Gomaa et al. (2023) proposed a novel enhanced version of the GTO algorithm, to improve its efficiency and effectiveness in solving global optimization problems. The original GTO algorithm, which features separate operators for exploration and exploitation, was found to require a better balance between these processes to accurately identify the global optimum. To address this limitation, the authors introduced a dynamic controlling parameter and refined the equations of the GTO algorithm based on this parameter. Computational experiments on benchmark test functions demonstrate the superior performance of NEGTO over the standard GTO and other algorithms in terms of efficiency, effectiveness, and stability. The proposed NEGTO offers several advantages, such as improved performance on both unimodal and multimodal benchmark test functions, making it a promising approach for broader search spaces and intensification in finding global optimal solutions.

Bansal and Sahoo (2022) proposed an innovative method to address the complex challenge of integrating high-dimensional data from multiple sources during exploratory data analysis. The author focused on integrative clustering analysis through joint non-negative matrix factorization (jNMF) to uncover latent features from a diverse set of data sources. The main challenge in jNMF is initialization, a critical factor influencing the solution’s quality and convergence. Since NMF problems are non-convex and multimodal, the authors proposed utilizing the GTO algorithm for initialization. Additionally, they introduced a novel strategy called chaos-driven GTO (CD-GTO), which incorporates chaos dynamics to enhance global search capabilities. The results indicated that GTO initialization led to an average improvement of 11% in silhouette scores and a 4% enhancement in purity measures across four multi-omics cancer datasets compared to other metaheuristic and traditional initialization methods. The experimental findings validated that CD-GTO initialization further elevated clustering performance beyond traditional GTO.

Badashah et al. (2023) proposed a novel technique for assessing the surface roughness of machined products using a Taylor-Gorilla Troops Optimizer (Taylor-GTO)-based Deep Neuro-Fuzzy Network (DNFN). Surface roughness is a critical quality characteristic of machined products, and traditional measurement methods using surface profile meters with contact styluses can lead to surface degradation. The proposed method addresses this limitation by employing a Taylor-GTO-based DNFN to estimate roughness without contact. The approach involves pre-processing, data augmentation, feature extraction, feature fusion, and roughness estimation using the DNFN trained with Taylor-GTO. The developed Taylor-GTO-based DNFN model exhibited excellent performance, with minimal Mean Absolute Error (MAE), Mean Square Error (MSE), and Root Mean Square Error (RMSE) values of 0.403, 0.416, and 1.149, respectively, demonstrating its effectiveness in surface roughness estimation.

5.6 Hybridized based GTO variants

Hybrid-based methods involve combining two different metaheuristic algorithms to develop a new algorithm. This approach aims to leverage the advantages of both algorithms, resulting in an efficient solution for addressing complex optimization problems. As a result, many researchers and scholars have been actively developing a variety of hybrid approaches that incorporate the GTO algorithm. These hybrid methods aim to improve the exploration and exploitation capabilities of existing algorithms, ultimately enhancing their performance as given in Table 2.

Table 2 List of algorithms hybridized with GTO

Rawa et al. (2022) introduced two innovative hybrid optimization algorithms, Honey Badger Algorithm (HBA) and GTO, to enhance the precision of solar cell parameter estimation. The intricate and nonlinear characteristics of solar cells demand efficient optimization techniques to address this engineering challenge. In a unique approach, the study combines the strengths of HBA and GTO in two variants, with one having GTO initialize HBA and the other vice versa. These hybrid algorithms exhibit a remarkable improvement in convergence and accuracy. They were effectively applied to estimate parameters for various solar cell models and photovoltaic (PV) modules, demonstrating their superiority through lower Root Mean Square Error (RMSE) values and robust statistical tests. Furthermore, these algorithms closely align the estimated parameters with simulation data under diverse irradiance and temperature conditions, emphasizing their potential to revolutionize PV model parameter estimation.

Cinar (2022) proposed the artificial differential evolution gorilla troops optimizer (ADEGTO), a novel hybrid algorithm specifically designed to tackle high-dimensional optimization problems. ADEGTO leverages the strengths of both the traditional differential evolution (DE) algorithm and the artificial gorilla troops optimizer (AGTO) to improve solution quality. The F and CR parameters of DE are crucial for the algorithm’s performance, and this study conducts a series of experiments to determine the optimal values of these parameters for high-dimensional optimization problems. The research involves extensive experimentation in a 100-dimensional space, exploring various parameter settings. Additionally, the study investigates the optimal F and CR values for ADEGTO and compares its performance against ten state-of-the-art optimization algorithms, demonstrating its effectiveness in addressing high-dimensional optimization challenges.

Ghith and Tolba (2023) proposed a novel hybrid algorithm called the Hybrid Arithmetic Optimization and Artificial Gorilla Troop’s Optimization (HAOAGTO). They conducted a comprehensive performance comparison of HAOAGTO against four other optimization algorithms: Arithmetic Optimization Algorithm (AOA), Artificial Gorilla Troop’s Optimization (GTO), Seagull Optimization Algorithm (SOA), and Parasitism-Predation Algorithm (PPA). These algorithms were used to optimize PID controller parameters for various cost functions, including Integral Absolute Error (IAE), Integral of Time Multiplied by Square Error (ITSE), Integral Square Time Multiplied by Square Error (ISTES), Integral Square Error (ISE), Integral of Time Multiplied by Absolute Error (ITAE). The simulation results revealed that the PPA algorithm achieved the highest fitness value, while HAOAGTO outperformed other optimization methods by reducing the fitness function the most. These results demonstrate the effectiveness of the HAOAGTO algorithm in obtaining optimal PID parameters for minimizing the ISTES cost function, making it a valuable tool in controller parameter tuning.

Konakoglu et al. (2023) introduced a novel hybrid ANN-GTO model for predicting zenith wet delay (ZWD) in weather forecasting. This model combines the strengths of artificial neural networks (ANNs) and the GTO algorithm to achieve superior prediction performance. The study conducted a comprehensive performance comparison of ANN-GTO with two other training algorithms, Levenberg-Marquardt and Bayesian Regularization, as well as improved ANN methods, using various performance criteria. The model was trained and tested on three input parameters: pressure, temperature, and water vapor pressure (WVP). The results of the study revealed that all ANN models enhanced with GTO outperformed classic ANN and other hybrid ANN models in predicting ZWD. This demonstrates the effectiveness and promise of the proposed approach in the domain of weather forecasting.

Prakash et al. (2023) conducted a study on predicting the compressive strength (CS) of ultrahigh performance concrete (UHPC) using hybrid machine learning models. These hybrid models combined artificial neural networks (ANNs) with nine different optimization algorithms: Ant Lion Optimization (ALO), Grey Wolf Optimization (GWO), Slap Swarm Algorithm (SSA), Whale Optimization Algorithm (WOA), Dragonfly Algorithm (DA), Particle Swarm Optimization (PSO), Harris Hawk Optimization (HHO), Slime Mould Optimization (SMO), and GTO. The ANN-GTO model outperformed the others, achieving high accuracy in predicting CS during both the model construction and testing phases. Sensitivity analysis demonstrated that ANN-GTO accurately captured the relationship between influential variables and CS, making it a promising tool for civil engineering projects. The study’s outcomes and evaluation metrics underscore the effectiveness of the ANN-GTO model for predicting the compressive strength of ultrahigh-performance concrete.

Hatata et al. (2022) introduced an adaptive protection (AP) scheme for fault detection and location in FREEDM microgrids using a convolutional neural network (CNN) optimized with the GTO technique. The CNN processed current and voltage measurements at bus points and transformed them into multidimensional arrays for fault identification and classification. The proposed AP scheme exhibited highly accurate fault detection, classification, and location capabilities in the FREEDM microgrid system, outperforming existing methods with an overall accuracy of 99.37% for fault detection, 99% for classification, and 98.2% for location. These results demonstrate the effectiveness of the proposed approach in enhancing the reliability and resilience of FREEDM microgrids.

Alghamdi et al. (2022) proposed a novel double input single output (DISO)-AVR model for synchronous generators, departing from conventional single input single output (SISO) approaches. The DISO-AVR model considers both the generator voltage setpoint and excitation voltage disturbance as inputs, providing a more comprehensive representation of the AVR system dynamics. To derive the transfer functions and objective functions for the DISO-AVR model, the authors employed a systematic approach. They then optimized the model parameters using a hybrid algorithm combining the simulated annealing algorithm and the GTO algorithm. The proposed DISO-AVR model and parameter optimization algorithm were comprehensively evaluated against traditional approaches through practical experiments conducted on 120 MVA synchronous generators in HPP Piva, Montenegro. The results demonstrated the superior performance of the proposed approach, highlighting its efficiency and applicability in real-world generator control scenarios.

Abdel-Basset et al. (2021) tackled the challenging task of accurately estimating the unknown parameters in proton exchange membrane fuel cell (PEMFC) models. Precise parameter estimation is essential for constructing accurate PEMFC models, and it is inherently an optimization problem. However, not all optimization algorithms are equally suited for this intricate and nonlinear task. To address this challenge, the authors introduced the GTO. In their quest to enhance GTO’s performance, they proposed a modified version termed the Modified GTO (MGTO). MGTO refines both exploration and exploitation operators, with a particular emphasis on population diversity in the exploitation phase for more effective optimization. The study then applied both GTO and MGTO to estimate the unknown parameters in three widely used PEMFC stacks. Comparative analyses, encompassing metrics such as best, average, worst, standard deviation, CPU time, mean absolute percentage error (MAPE), mean absolute error (MAE), and Wilcoxon rank-sum tests, unequivocally demonstrated that MGTO outperformed other optimization algorithms across most performance metrics. This positions MGTO as a highly promising choice for addressing the intricate challenge of parameter estimation in PEMFC modeling.

Bagal et al. (2022) conducted dry turning experiments on titanium alloys using modern titanium carbonitrides chemical vapor deposition (MT-CVD) coated carbide tool inserts. They systematically investigated the impact of cutting parameters (feed rate, cutting speed, and depth of cut) on essential performance metrics (cutting forces, flank wear, and surface roughness). They combined response surface methodology (RSM) with a hybrid optimization technique that integrated the GTO Algorithm and the Dingo Optimization Algorithm to determine the optimal cutting conditions. The study revealed that the depth of cut had a pivotal role in reducing cutting forces, flank wear, and surface roughness. The results underscored the effectiveness of the hybrid optimization approach, which surpassed conventional experimentation in achieving enhanced machining efficiency and quality.

In their work, Bansal and Sahoo (2022) addressed the critical task of identifying cancer subtypes through the integrative analysis of complex multi-omics data, which encompasses a wide range of high-dimensional and diverse data types. To reveal the inherent structures and interconnections within this data, they employed integrative clustering, utilizing joint non-negative matrix factorization (jNMF) and sparse-jNMF. Since NMF exhibits inherent non-convex and non-differentiable characteristics, selecting the optimal initial point for factor matrices is of utmost importance. To address this challenge, the authors introduced an initialization method grounded in the high-dimensional Gorilla Troops Optimization encoded structure (HD-GTO). Their experimental findings, conducted on two multi-omics cancer datasets, demonstrated that the HD-GTO-guided initialization of sparse-jNMF yielded enhanced accuracy and purity when compared to other metaheuristics. This approach achieved an average increase of 3.5% in accuracy and 4.1% in purity across the two datasets compared to jNMF, highlighting its efficacy in identifying cancer subtypes.

Ali et al. (2023) proposed a new hybrid optimization algorithm, the Hybrid Multi-Population Gorilla Troops Optimizer and Beluga Whale Optimization (HMGTO-BWO), to accurately model photovoltaic (PV) generation units. HMGTO-BWO uses a multi-population approach to improve diversity and prevent stagnation, which are common problems with traditional GTO. It also leverages the exploration and exploitation capabilities of the Beluga Whale Optimization (BWO) algorithm, which is inspired by synchronized swimming and Lévy flights. HMGTO-BWO is used to minimize the root mean square error (RMSE) between simulated and measured data for PV cells and panels, which are modeled using double-diode and triple-diode models. Its effectiveness is robustly demonstrated through extensive benchmarking, demonstrating its superior performance in estimating PV module parameters.

Fan et al. (2023) proposed a new method for accurate load forecasting, essential for efficient electricity utilization, carbon emission reduction, and power system safety. Their proposed model is a bidirectional memory hybrid that combines multiple techniques. First, they use Variational Mode Decomposition (VMD) optimized with the gray wolf algorithm to decompose electricity load data into distinct modal components. They then perform multidimensional uncertainty analysis to extract features from these components. Next, they optimize both population and global solutions using the GTO algorithm. Finally, they use convolutional neural networks (CNNs) to extract features from load and meteorological data to improve input–output correlations and accomplish short-term load forecasting using a bidirectional short-term memory neural network (BiLSTM). The results clearly demonstrate the model’s superior accuracy compared to other methods, providing valuable insights to optimize power economic dispatch, particularly in low-carbon modes.

El-Dabah et al. (2023) proposed a novel hybrid optimization algorithm, GTO-GBO, which combines the GTO algorithm with the Gradient-Based optimizer (GBO), to optimize the power system stabilizer (PSS) in a multi-machine power system, even under challenging scenarios such as a three-phase short-circuit fault. The algorithm’s effectiveness was first evaluated on benchmark functions, encompassing both unimodal and multimodal properties, where it demonstrated its superiority over other competing algorithms. The study highlights the GTO-GBO algorithm’s ability to strike a balance between global and local search phases, making it a promising tool for addressing real-world engineering challenges. Notably, the algorithm’s application to optimize PSS damping controllers showcased its efficiency and robustness in enhancing power system stability.

Kareem et al. (2022) proposed a novel feature selection (FS) method, GTO-BSA, to enhance the performance of the GTO algorithm for cybersecurity applications in the Internet of Things (IoT). Amidst the growing use of IoT applications and the associated security challenges, intelligent solutions such as intrusion detection systems (IDS) are essential. FS plays a crucial role in improving the efficiency of machine learning algorithms by selecting relevant features and reducing their number. The authors combined GTO with the bird swarms algorithm (BSA) to improve performance and convergence. GTO-BSA outperformed the original GTO, BSA, and other state-of-the-art techniques on various IoT-IDS datasets, demonstrating enhanced convergence rates and higher-quality solutions.

Ahmed et al. (2023) proposed a novel combined feedback and feedforward control system for frequency regulation in multi-area interconnected hybrid microgrids with renewable energy sources (RESs). This control system employs a fractional-order proportional-integral-derivative-accelerated (FOPIDA) controller in the feedforward direction and a fractional-order integral-derivative with a low-pass filter compensator (FOIDN) controller in the feedback direction, forming a FOPIDA-FOIDN controller. The study optimally tunes the parameters of this controller using a hybrid of two metaheuristic optimization algorithms, the GTO algorithm and equilibrium optimizer (EO), named HGTOEO. The proposed control system’s performance is evaluated under various operating conditions and compared to other existing controllers in the literature, such as PID, FOPID, and tilt integral derivative (TID) controllers. The MATLAB simulation results demonstrate the effectiveness and reliability of the HGTOEO-optimized FOPIDA-FOIDN controller, even under load perturbations and variable RES production.

Chandra and Borugadda (2023) introduced an innovative MIMO-NOMA-based approach to enhance energy efficiency and quality of service in 5 G wireless communication. Their solution integrates terahertz (THz) band communication and beamforming-based signal transmission to efficiently accommodate a larger number of users with high multiplexing gain and cope with the challenges posed by an increased number of antenna arrays and users. The process begins with user clustering achieved through a fuzzy k-means clustering algorithm, followed by beamforming among these user clusters. A hybrid minimum mean square error with zero-forcing pre-coder is employed to eliminate inter-cluster interference. Joint power and resource allocation is further optimized using a hybrid artificial gorilla troop with the leader optimization technique to maximize the sum rate of the RF channel. Comprehensive evaluations confirmed the method’s effectiveness in enhancing energy efficiency, spectral efficiency, sum rate, throughput, bit error rate, and mean square error, establishing its potential for significant improvements in 5 G wireless communication

Bamikole and Narasigadu (2023) investigated two recently developed stochastic global optimization algorithms, the Pelican Optimization Algorithm (POA) and GTO algorithm, for addressing phase stability and equilibrium calculations in the process industries, which involve complex systems of nonlinear equations. To enhance performance, they developed two hybrid algorithms, PGOA1 and PGOA2, by combining POA and GTO. The authors evaluated the capabilities of these algorithms in solving computationally challenging and multidimensional phase stability and equilibrium problems. Both POA and GTO performed well, with GTO slightly outperforming POA. However, the hybridized algorithms, PGOA1 and PGOA2, excelled, with PGOA2 proving to be the most robust and reliable, surpassing the other algorithms in performance.

5.7 Multi-objective GTO

Houssein et al. (2023) introduced MOGTO, an advanced version of the GTO designed to tackle multi-objective optimization challenges. MOGTO incorporates an external archive to store Pareto-optimal solutions found by GTO, allowing it to replicate the collective behavior of gorilla groups within the complex search space of multi-objective problems. The performance of MOGTO is comprehensively evaluated, statistically and qualitatively, across various multi-objective problems using the CEC2020 test suite. MOGTO efficiently discovers the minimum number of sink nodes with the lowest localization error in large wireless sensor networks, effectively capping the network and extending its operational life. Comparative assessments against ten established optimization models, including MOGWO, NSGA-II, and MOEA/D, reveal that MOGTO consistently outperforms these models in key evaluation metrics such as hypervolume (HV), inverted generational distance in decision space (IGDX), and Pareto set proximity (PSP) indicators. These findings, substantiated by simulation results, highlight MOGTO’s superior performance in multi-objective optimization contexts.

Elkholy et al. (2023) introduced a novel AI-embedded Smart Energy Management System (SEMS) built on FPGA technology to facilitate intelligent and efficient energy management in isolated microgrid environments. The SEMS adopts a two-tiered control approach, with an FPGA acting as a high-speed central controller at the primary level and the secondary level dedicated to orchestrating operational strategies for optimizing backup energy sources in the microgrid. The study formulates a multi-objective optimization problem to simultaneously reduce operational costs, minimize the loss of power supply probability (LPSP), and curb excess power consumption by a dummy load. To address this challenge, the study deploys two multi-objective optimization algorithms: the GTO algorithm and the Reptile Search Algorithm (RSA). Notably, the results demonstrate the superior performance of the RSA algorithm, delivering substantial cost savings of approximately 6.467% and achieving the lowest LPSP value, thus ensuring a continuous and reliable power supply within the microgrid under investigation.

Hosny et al. (2023) introduced a novel approach to optimize multiple objectives within a complex multi-server-multiuser edge-cloud computing system, considering multi-task dependencies. This approach leverages the Enhanced Multi-objective Gorilla Algorithm (EMGA), which divides gorilla vectors into task lists, processing location lists, and processing level lists. EMGA incorporates specialized initialization and mapping techniques to transform vector values and utilizes a mutation operation to enhance algorithm performance. Extensive simulations conducted on ten test instances have consistently demonstrated EMGA’s superior performance across various performance metrics compared to other algorithms. EMGA holds significant promise for IoT and mobile application developers, as it enhances application efficiency, reduces energy consumption, and minimizes costs associated with on-edge Mobile Edge Computing (MEC) and remote cloud servers.

Cai et al. (2023) introduced a two-step energy optimization technique for parallel pump and chiller systems using the Multi-Objective Gorilla Troops Optimizer (MOGTO). The primary goal of this approach is to balance energy consumption and flow rates, resulting in significant energy savings. Importantly, it eliminates conventional load-on/load-off delays, improving efficiency even when the number of chillers or pumps is reduced. By providing a comprehensive solution for the equilibrium of chillers and chilled water pumps, MOGTO represents a pioneering development in enhancing the energy efficiency of building operations and effectively managing multi-objective optimization challenges in HVAC systems.

Hosny et al. (2023) addressed the complex challenge of computational offloading in multi-access edge computing (MEC) environments, especially for IoT devices and mobile equipment. This challenge involves optimizing multiple conflicting objectives, such as execution time, energy consumption, and computation cost, while considering the offloading of dependent tasks within applications. Existing methods often have shortcomings, either due to computational complexity or a lack of consideration for task dependencies. To overcome these limitations, the authors introduced the Improved Gorilla Troops Algorithm (IGTA) with three primary goals: minimizing application execution latency, reducing device energy consumption, and optimizing MEC resource costs. IGTA incorporates enhancements such as customized crossover operations and a Max-To-Min load-balancing strategy, resulting in significant improvements over the standard Gorilla Troops Algorithm. Compared to GTO, IGTA achieved impressive reductions in latency (33%), energy consumption (93%), and cost usage (34.5%), positioning it as a superior solution to other optimization techniques for this complex computational offloading problem.

Bensoltane and Belli (2023) proposed a novel multi-objective optimization algorithm, CD-MOGTO, which extends the Gorilla Troops Optimizer (GTO) with the crowding distance technique. CD-MOGTO improves leader selection and refines the external archive by incorporating additional non-dominated solutions, thereby enhancing the diversity of the non-dominated solution set. Evaluated on various constrained multi-objective problems, CD-MOGTO demonstrates its effectiveness. Subsequently, it is applied to optimize the design of a brushless direct current motor, effectively addressing six inequality constraints while simultaneously maximizing efficiency and minimizing total mass. The results illustrate CD-MOGTO’s significant potential in solving constrained multi-objective problems and optimizing brushless direct current motors, outperforming other well-established algorithms.

6 Applications of GTO algorithm

The GTO algorithm and its variants have been widely adopted to solve optimization problems in various industries. GTO applications span a broad range of domains, as detailed in the following subsections and summarized in Table 3. Specifically, GTO is used in engineering, image segmentation, scheduling optimization machine learning, deep learning, and energy (Fig. 12).

Fig. 12

GTO application distributions

6.1 Engineering

El-Dabah et al. (2022) investigated the application of the GTO algorithm for fine-tuning power system stabilizer (PSS) units. They minimized the Integral Time Square Error (ITSE) fitness function to achieve optimal PSS tuning. Four distinct controllers were tested on a single-machine scheme model for an infinite bus. The tilt-integral-derivative (TID) controller outperformed the PID controller, lead-lag controller, and fractional-order PID controller (FOPID). The GTO algorithm exhibited faster convergence and avoided local optima better than other optimization techniques. It also exhibited high precision in PSS tuning, highlighting its potential as an effective tool for power system stabilization.

Gürses et al. (2022) introduced a novel approach to optimizing the cost of plate-fin heat exchangers (PFHE) using the GTO algorithm. PFHE is a crucial component in thermal systems, and the optimization problem involves minimizing initial and running costs while adhering to stringent boundary conditions. A comparative analysis of the GTO algorithm against nine benchmark metaheuristic algorithms was conducted, and the GTO algorithm was found to be the most robust and effective algorithm, achieving a 100% success rate. These exceptional results highlight GTO’s potential for broad applications in engineering design optimization, demonstrating its effectiveness in addressing complex and multidisciplinary constraint problems.

Abd Elaziz et al. (2023) introduced a novel parameter identification method for proton exchange membrane fuel cells (PEMFCs), which are essential components in many applications. Accurate modeling of PEMFC designs with multiple variable quantities and nonlinear factors is crucial for their reliable performance. The proposed method uses the GTO algorithm to optimize a fitness function that minimizes the sum of squared errors (SSEs) between the current and estimated voltage cases. A series of test cases were used to validate the effectiveness of this approach. Comparative analyses using SSEs and standard deviation measures over numerous independent runs demonstrated that the proposed method outperformed other well-known comparative techniques, particularly in steady-state and dynamic situations. This research demonstrates the promising results and superior performance of the proposed parameter identification method for PEMFCs.

Natarajan et al. (2022) conducted research on wire-cut Electrical Discharge Machining (EDM), focusing on the challenge of machining aluminum alloy. They used a Box-Behnken design to experiment with various machining parameters, including pulse-on time, pulse-off time, wire feed, and current settings. They closely observed surface roughness after machining and used it to create an Adaptive Neuro Fuzzy Inference System (ANFIS) model to generate synthetic data. They then employed the GTO algorithm, with its set of search operators, to optimize machining parameters. The GTO algorithm achieved a remarkably low surface roughness value of 0.500953 $\mu$m. Statistical tests and ranking comparisons confirmed the GTO algorithm’s superior performance in machining this specific material.

Ho et al. (2023) introduced a novel GTO-ANN approach for structural damage diagnosis. Their study aimed to identify damaged segments in a simply supported girder bridge. GTO was employed to optimize the number and size of hidden layers in the ANN architecture. The finite element structure of the bridge was modeled, and stiffness reductions at various locations were simulated to mimic single and multi-damage scenarios. Input data was obtained from changes in frequency and mode shapes, and the objective function aimed to minimize the error between predicted and target damage locations and severity. The results demonstrated that while the computational cost of the GTO-ANN approach was higher, it offered superior accuracy and precision compared to using ANN alone. Measures such as mean absolute error (MAE) and root-mean-square error (RMSE) proved to be better indicators of prediction accuracy in this context.

Pasandideh and Yaghoubi (2022) compared the performance of the GTO optimizer algorithm to the GWO and PSO algorithms for optimizing dam reservoir operations. The primary objective was to minimize downstream demand deficit during the operational period, while also considering various operational and environmental constraints. The authors applied these optimization algorithms to the Jamishan reservoir dam in Kermanshah province. The results of the study showed that the GTO algorithm is effective in optimizing dam reservoir operations. Performance indicators, including RMSE, MAE, NSE, RSR, reliability, resiliency, vulnerability, and the minimized objective function, favored the GTO algorithm over the GWO and PSO algorithms.

Kumar et al. (2022) introduced the application of the GTO method to a tilt integral derivative (TID) controller for load frequency control (LFC) in a restructured thermal-hydraulic system. The system’s dynamic properties were assessed using step load perturbations, and its performance was evaluated using the integral square error. The results indicate that the GTO method outperforms the grey-wolf optimizer (GWO), enhancing the TID controller’s performance for load frequency control. Additionally, the study compared the TID and proportional integral derivative (PID) controllers with various optimization strategies, providing insights into different approaches to managing power transactions in a restructured thermal-hydraulic system.

Draz et al. (2023) introduced an innovative method for automating the configuration of overcurrent relays using the GTO algorithm. Their study focuses on achieving optimal coordination of protective devices within a network to minimize the extent of faults, emphasizing the use of appropriate sequencing and coordination time margins (CTMs). The GTO was applied and tested on a practical distribution network with distributed generation located in Egypt’s Western Desert. The GTO method effectively tackles the relay coordination challenge, delivering competitive outcomes with minimal CTMs, thus showcasing its efficiency in automating overcurrent relay configurations to enhance the protection of power systems.

Moradi et al. (2023) introduced an innovative and efficient approach to flood routing by enhancing the Muskingum method, focusing on both cost and time-effectiveness. This pioneering approach integrates the nonlinear Muskingum model with a novel lateral flow equation, creating a hybrid Muskingum model with 12 decision variables. To optimize these critical variables, they employ the GTO algorithm. The authors conducted six case studies to thoroughly assess the model’s performance, demonstrating substantial improvement over previous research. Notably, when applied to the previously unexamined Dinavar River flood, the approach showcased its adaptability and the GTO’s effectiveness in minimizing the target function. This innovative method provides a promising means to enhance flood routing in a cost and time-efficient manner.

Alkan and Kaniappan Chinnathai (2021) conducted an extensive performance evaluation of eight state-of-the-art population-based metaheuristic optimization algorithms, namely the African Vultures Optimization Algorithm (AVOA), Crystal Structure Algorithm (CryStAl), Human-Behavior Based Optimization (HBBO), Gradient-Based Optimizer (GBO), Gorilla Troops Optimizer (GTO), Runge–Kutta Optimizer (RUN), Social Network Search (SNS), and Sparrow Search Algorithm (SSA), to assess their effectiveness in addressing real-world engineering design challenges. The algorithms were applied to five distinct mechanical component design problems. The results showed that the SNS algorithm consistently delivered robust and high-quality solutions within a reasonable computation time across all design problems. GTO and GBO also demonstrated competitive performance, while AVOA showcased efficiency in terms of computation time.

Oussama et al. (2023) proposed an optimization method for coordinating directional overcurrent relays (DOCRs) in interconnected power systems, aiming to achieve selectivity, sensitivity, and fast fault-clearing times. Coordinating DOCRs involves calculating time dial settings (TDS) and plug settings (PS), posing a complex nonlinear optimization problem to minimize the overall operating time of the necessary relays for efficient fault management. To address this coordination challenge, the study employed the GTO algorithm, conducting tests on IEEE 3-bus and 8-bus systems. The results demonstrated the effectiveness of GTO in reducing relay operation time and achieving optimal DOCR coordination.

Sabo et al. (2023) conducted a comparative analysis of five metaheuristic optimization algorithms, classifying them into two categories: nature-inspired and non-nature-inspired. The nature-inspired algorithms, including artificial eco-system optimization (AEO), African vulture optimization algorithm (AVOA), and gorilla troop optimization (GTO), were compared with the non-nature-inspired gradient-based optimization (GBO) and Runge Kutta optimization (RUN) in the context of optimizing multi-machine power system stabilizers (PSSs). These stabilizers play a vital role in improving the damping of electromechanical modes in power systems. The study formulated the PSS design as an optimization problem and used eigenvalue-based objective functions. The results of this comparative analysis on the Western System Coordinating Council (WSCC) multi-machine power test system indicated that non-nature-inspired algorithms (GBO and RUN) outperformed the nature-inspired ones, showing faster reduction of low-frequency oscillations, improved damping, convergence rates, and overall statistical performance.

Padhy et al. (2023) proposed an integrated methodology for order reduction of high-order single input single output (SISO) systems, transforming them into corresponding low-order models (LOMs) while maintaining system stability. This model order reduction (MOR) technique combines the GTO algorithm and the Routh approximation (RA) method. GTO determines the numerator coefficients of the LOM, while RA determines the denominator coefficients. The results demonstrate that the LOM preserves the essential characteristics of the high-order system during the order reduction process.

Hashemi et al. (2023) introduced an optimization approach for the design of power and distribution transformers to minimize power losses, enhance transformer efficiency, and reduce operational costs. Given the non-convex nature of transformer design problems, the study employed four heuristic optimization algorithms: the Firefly Optimization Algorithm (FA), the Arithmetic Optimization Algorithm (AOA), the Grey Wolf Optimization Algorithm (GWO), and the GTO algorithm. These algorithms optimized transformer design variables with significant performance impact. Comparative analysis against a 1000 kVA eco-friendly distribution transformer using empirical methods revealed that the proposed method, combined with the mentioned algorithms, led to a substantial reduction in power losses of up to 3.5% and a decrease in transformer weight of up to 8.3%. This improved efficiency, resulting in cost savings, longer transformer lifespan, and reduced emissions. These findings demonstrate the versatility of the model for designing various oil-immersed distribution transformers.

Sankar and Chatterjee (2023) proposed a proactive approach to plan distribution networks in response to the increasing adoption of plug-in electric vehicles (PEVs), which impose substantial loads on the grid. The study focused on optimizing the placement and sizing of renewable distributed generators (DGs), such as wind turbines and solar photovoltaic units, within the distribution system. This planning considered uncertainties in wind and solar power generation, realistic time-varying mixed loads, and various PEV charging profiles. The GTO algorithm was used to identify the most suitable locations and capacities for these renewable DGs. The optimization aimed to minimize real power loss, and bus voltage deviation, and enhance voltage stability. The methodology was tested on a 33-bus benchmark distribution network, with results demonstrating the effectiveness of the GTO algorithm in achieving these objectives.

Kumar et al. (2021) assessed the performance of a newly developed soft computing algorithm called the Artificial Gorilla Troops Optimizer (GTO) by employing it to determine the optimal parameters for modeling a widely used polycrystalline solar photovoltaic (PV) module. This modeling included both single and double diode types to accurately capture system performance. The GTO algorithm derived the parameters of the equivalent model by constructing the objective function using multiple data points from the PV module datasheet. Comprehensive results based on practical data from an S75 PV module data sheet demonstrated the effectiveness of the GTO algorithm in optimizing PV system parameters.

Khatir et al. (2022) introduced an enhanced Frequency Response Function (FRF) indicator for damage detection in complex structures using vibration-based methods. They applied the improved indicator to various structures, including 2D and 3D trusses. Numerical models built with the Finite Element Method demonstrated the indicator’s ability to detect and localize single and multiple damages. Additionally, after eliminating healthy elements, the indicator was integrated into an objective function for damage quantification, employing optimization techniques such as Gradient-Based Optimizer (GBO), African Vulture Optimization algorithm (AVOA), Dingo Optimization Algorithm (DOA), and the GTO algorithm. The results revealed the accuracy of all optimization techniques in predicting the extent of damage, with GTO demonstrating superior convergence efficiency. Finally, the study assessed the indicator’s performance in the presence of noise, emphasizing its robustness.

Pachpore et al. (2022) presented a mathematical model to analyze sliding friction in root canal therapy, a crucial component of effective dental treatment. The process involves using gutta-percha to create a fluid-tight seal in the root canal, which is then compressed vertically with a plugger, generating sliding friction between the gutta-percha and the canal walls. The researchers employed the GTO algorithm to optimize the model and identify theoretical bounds, revealing a significant improvement in the estimation of sliding frictional forces in this dental context.

Ahmed et al. (2022) introduced the $\hbox {TI}^\lambda$ - $\hbox {PD}^\mu$N controller, a novel Load Frequency Control (LFC) structure that combines a tilt fraction-order integral ($\hbox {TI}^\lambda$) controller with a proportional fraction-order derivative controller with a filter ($\hbox {PD}^\mu$N). The authors optimally designed this controller using the GTO algorithm, demonstrating the GTO algorithm’s superiority to other optimization methods such as differential evolution and firefly algorithms. The proposed controller’s performance, particularly in a two-area hybrid power system, was validated against other controllers from the literature, such as the $\hbox {PI}^\lambda$ $\hbox {D}^\mu$ and ITD controllers. Additionally, the study showed that the proposed coordination scheme involving the $\hbox {TI}^\lambda$ - $\hbox {PD}^\mu$N controller, interline power flow controller, and a redox flow battery significantly improved system frequency stability under various conditions, including load perturbations, renewable power fluctuations, and communication time delays.

Yakout et al. (2022) presented a study to optimize the parameters of a solid oxide fuel cell (SOFC) model to improve its accuracy. They employed four newly developed metaheuristic optimization algorithms: the Chimp Optimization Algorithm (ChOA), the African Vultures Optimization Algorithm (AVOA), the Honey Badger Algorithm (HBA), a,d the GTO algorithm. These algorithms were used to identify the optimal parameters of the SOFC’s steady-state model using experimental data. Additionally, a Proportional-Integral-Derivative (PID) controller was incorporated into the dynamic model to improve the transient response of a 100 kW stack. Extensive statistical comparisons revealed that GTO and HBA outperformed other methods, producing accurate SOFC parameter values and accurate voltage-current and power-current characteristics.

Azuara et al. (2023) presented an immersive virtual reality (VR) project at the National Institute of Electricity and Clean Energies to simulate the underwater conditions of the Gulf of Mexico, with a focus on the operations of remotely operated vehicles (ROVs) used to transport hydrocarbons through subsea pipelines. These pipelines are susceptible to leaks due to the challenging underwater environment, including fluid properties and high pressures, resulting in environmental hazards and financial losses. To address this issue, the authors introduced the GTO algorithm to optimize the collaborative efforts of ROVs in repairing marine pipeline leaks within a virtual environment that accurately replicates the conditions of the Gulf of Mexico, accounting for factors such as marine currents and individual ROV characteristics, including arm configurations and maneuvering capabilities.

Aarif and Sudabattula (2023) proposed a strategic solution to minimize line losses in electrical distribution networks by optimally placing capacitors. This approach not only reduces line losses but also maintains bus voltage at the required level, improving network stability and reliability. The placement of distributed generation (DG) units is determined based on the line voltage stability index (VSI), and the sizing of DG units is accomplished using probabilistic and stochastic metaheuristic algorithms such as Particle Swarm Optimization with Perturbed Velocities Algorithm (PSODE) and GTO algorithm. Testing on 28-bus and 85-bus IEEE distribution systems validated the effectiveness of this approach, showcasing the optimal placement of DG units and the resulting improvements in voltage profiles and reduced power losses.

Achite et al. (2022) introduced the M5-GTO model, a hybrid machine-learning solution for efficiently estimating coagulant dosage (CD) in water treatment. The model offers a cost-effective and time-saving alternative to the traditional jar test by utilizing nine key input parameters, including raw water production, turbidity, conductivity, TDS, salinity, pH, water temperature, SM, and O2. Comparative analyses against various other modeling techniques have demonstrated the M5-GTO model’s superior accuracy, achieving highly precise CD modeling. The model exhibited considerably lower mean absolute error (MAE), root mean square error (RMSE), relative RMSE, and normalized RMSE, and boasted a robust correlation coefficient, outperforming alternative algorithms by up to 73%. The partial dependence plots from the model emphasize the significant influence of raw water production and water temperature on CD. This makes the M5-GTO model a promising tool for modeling various parameters in water treatment plants.

Rahman, Yun, As’arry, and Zuhari (n.d.) presented the GTO algorithm-based PID controller design for vehicle suspension systems to surpass the limitations of conventional PID control approaches. The study thoroughly investigated different control objective functions and demonstrated the GTO-PID controller’s effectiveness in substantially enhancing the vibration absorption capabilities of semi-active suspension systems, achieving a significant 28.92% reduction in body acceleration response amplitude. This outcome represents a major advancement in control strategies for vehicle suspension systems, improving road-handling performance and passenger ride comfort.

Mohamed et al. (2023) addressed the challenging task of controlling robotic manipulators, characterized by multi-input, multi-output dynamics, nonlinearity, high coupling, parameter uncertainties, and external disturbances. They introduced six hybrid control structures combining the robustness of integer- and fractional-order Proportional, Integral, and Derivative (PID) controllers with the function mapping capabilities of neural networks. The tuning of these controllers for a 2-Link Rigid Robot Manipulator (2-LRRM) was achieved using the GTO algorithm to minimize the Integral of Time Square Error (ITSE). Through extensive robustness testing, encompassing variations in initial positions, external disturbances, and parameters, the Neural Network Fractional Order Proportional Integral Derivative Controller (NNFOPID) emerged as the top-performing solution among the proposed approaches.

Reddy and Saha (2022) investigated the use of swarm intelligence techniques to enhance the control of doubly fed induction generators (DFIGs) under unbalanced grid voltages. DFIGs are directly connected to the grid, making them susceptible to performance degradation under such conditions. Traditional mitigation approaches include dual vector and proportional-resonant control strategies. This study evaluated the effectiveness of incorporating swarm intelligence to optimize controller gains, comparing its application in both dual vector and proportional-resonant controllers. Three swarm intelligence techniques-particle swarm optimization, the bat algorithm, and the GTO algorithm-were employed. The system was subjected to single-phase voltage dips of 5% and 10%. The results demonstrated that these modern swarm intelligence techniques successfully optimize controller gains, indicating their potential applicability in a range of scenarios as the field of swarm intelligence continues to evolve.

Zhang et al. (2022) introduced a novel task assignment method for unmanned aerial vehicle (UAV) swarms based on the GTO algorithm. This approach addresses the challenge of efficiently assigning multiple targets and tasks on the ground to minimize costs. The method formulates a Cooperative Multiple Task Assignment Problem (CMTAP) model to minimize the sum of distance and loss costs associated with task assignments. It begins with an initial task assignment scheme using real number encoding and then uses GTO to find the solution with the minimum objective function value. Experimental results demonstrate the effectiveness of this method. GTO shows faster convergence, higher stability, and lower task assignment costs than other optimization techniques, including PSO, GWO, and Depth First Search (DFS).

Alrayes et al. (2022) introduced a novel Artificial Intelligence-based Secure Communication and Classification for Drone-Enabled Emergency Monitoring Systems (AISCC-DE2MS) approach. This method is designed to improve both the security and classification aspects of using Unmanned Aerial Vehicles (UAVs) with camera sensors for emergency disaster monitoring. In a two-stage process, AISCC-DE2MS first employs the GTO algorithm and ECC-Based ElGamal Encryption to ensure secure communication. Next, for emergency situation classification, it leverages DenseNet for feature extraction, Penguin Search Optimization (PESO) for hyperparameter tuning, and Long Short-Term Memory (LSTM) for classification. Comprehensive simulations conducted using the AIDER dataset unequivocally validate the superior performance of the AISCC-DE2MS model across diverse metrics, highlighting its pivotal role in drone-enabled emergency monitoring systems.

6.2 Image segmentation

Alsubaei et al. (2023) introduced BSBE-PPODLC, a novel two-stage approach to content security in remote sensing image (RSI) classification. The first stage encrypts RSIs using block-scrambling-based encryption (BSBE) method, while the second stage extracts features using DenseNet, classifies images with an extreme gradient boosting (XGBoost) classifier, and optimizes hyperparameters using the GTO algorithm. Evaluations on RSI datasets show that BSBE-PPODLC outperforms existing models, proving to be a valuable tool for protecting the privacy and security of RSIs in a variety of applications.

Nayak and Mondal (2022) introduced a breast magnetic resonance imaging (MRI) registration technique leveraging the GTO algorithm. Accurate registration of breast MRI images is crucial for breast cancer diagnosis and classification. A comparative analysis between the GTO-based and PSO-based registration methods revealed that the GTO-based approach outperforms the PSO-based method, highlighting its potential for enhancing breast cancer diagnosis and classification.

Sreedevi and Manike (2023) introduced an innovative deep learning-based approach for tomato leaf disease (TLD) classification, tackling the challenges of time-consuming manual prediction and high implementation costs. This method addresses low-resolution image issues through contrast enhancement in image preprocessing and deep convolutional neural networks (DCNNs). Disease segmentation is performed using Mask Region-Based Convolutional Neural Networks (Mask R-CNN), with classifier scores optimized through Controlling Parameter-based Artificial Gorilla Troops Optimization (CP-AGTO). The proposed model achieves an impressive 92% accuracy and 93% sensitivity, outperforming recent methodologies in TLD classification.

Damarla and Sumathi (2022) introduced a robust IoT- and AI-powered deep convolutional neural network (DCNN) solution for the challenging task of diagnosing and classifying skin cancer from dermoscopy images. Manual detection of skin lesions is difficult and time-consuming, making automated methods an essential alternative. The DCNN is thoughtfully designed to extract distinctive features from skin lesions, and a three-task approach involving deep feature extraction, feature selection through the GTO algorithm, and a two-level classification process is proposed. On the HAM10000 dataset, their method achieves an impressive accuracy rate of 93.58%, surpassing state-of-the-art techniques and demonstrating its scalability and effectiveness in processing skin lesion images.

6.3 Scheduling optimization

Singh et al. (2022) introduced an innovative approach to optimize the bidding strategy of a wind farm integrated system to maximize social welfare. Their method determines the optimal wind farm location using locational marginal price (LMP) analysis. Monte Carlo simulation (MCS) in conjunction with the GTO algorithm computes market equilibrium metrics, including market-clearing volume (MCV) and clearing price (MCP). Bid prices and quantities for consumers and suppliers are then determined through the MCS process. Notably, this is the first application of the GTO algorithm to the market-clearing power simulation (MCPS) problem, specifically in the context of integrating wind farms into the Poolco power market. The results highlight increased social welfare with wind farm integration, benefiting market buyers with lower MCPs. Additionally, the GTO algorithm outperforms other optimization algorithms, including HBA, SMO, ABC, and PSO.

Sah et al. (2022) introduced an innovative approach to enhancing automatic generation control (AGC) in reheat thermal interconnected power systems (IPS). AGC plays a vital role in maintaining power balance in IPS, addressing parameter uncertainty, vague loading behavior, and nonlinearities. The study used a fractional-order PID (FOPID) controller optimized by the GTO algorithm to determine the controller parameters. Practical IPS nonlinearities, such as generation rate constraints (GRC) and generation deadband (GDB), were considered. The study conducted a comparative analysis involving four state-of-the-art metaheuristic approaches and assessed the proposed controller’s performance under parametric uncertainties, demonstrating its superior performance.

Rengaraj alias Muralidharan and Latha (2023) introduced a novel fault-tolerant aware scheduling scheme, the Gorilla Troops Optimizer-Based Fault Tolerant Aware Scheduling Scheme (GTO-FTASS), for cloud computing environments. Cloud computing allocates resources on demand, but task execution failures and resource fluctuations are common challenges. GTO-FTASS leverages the social intelligence of gorilla troops to schedule tasks while considering fault tolerance. It includes a fitness function that incorporates the expected time of completion (ETC) and the probability of task failure. Additionally, a fault detector identifies failed tasks or VMs and schedules remedial actions. Experimental validation demonstrates that GTO-FTASS outperforms recent scheduling approaches in terms of fault tolerance and overall performance in the cloud computing environment.

Van Yen et al. (2021) proposed the GTO algorithm to tackle the short-term fixed-head hydrothermal scheduling problem (ST-HTS). The research considers constraints associated with reservoir management and the cost of electricity generation in thermal power plants. GTO has performed superior to other state-of-the-art metaheuristic algorithms and commonly used methods in addressing this specific engineering problem. It provides an effective solution for ST-HTS and outperforms other methods like Improved Particle Swarm Optimization (IPSO) and Tunicate Swarm Algorithm (TSA) across various evaluation criteria.

6.4 Machine learning

Gong et al. (2022) introduced an innovative approach to enhance rolling bearing fault diagnosis accuracy while reducing or eliminating parameter tuning. Their bubble entropy-based method combines Variational Mode Decomposition with Refined Composite Multiscale Bubble Entropy (VMD-RCMBE) to extract fault-related features. MCFS effectively performs feature selection and dimensionality reduction. The GTO Optimized Kernel Extreme Learning Machine (GTO-KELM) is then used for model training and pattern recognition. Rigorous validation on two distinct bearing fault datasets confirmed this approach’s effectiveness, with remarkable classification accuracy exceeding 99.8%, all without parameter tuning. This technique presents a highly promising solution for rolling bearing fault diagnosis, offering both improved accuracy and operational efficiency.

Isham et al. (2023) introduced a novel bearing diagnosis approach using the GTO-based Extreme Learning Machine (GTO-ELM) method. This approach aims to improve machinery condition assessment accuracy and efficiency. While the Extreme Learning Machine (ELM) offers rapid learning and generalization advantages, its performance can be hindered by suboptimal parameter selection. The GTO algorithm is employed to optimize ELM parameters, enhancing its effectiveness in bearing fault diagnosis. GTO-ELM demonstrated significantly improved convergence speed and diagnostic performance over conventional ELM methods on two datasets representing various operating conditions, including normal and various fault types. Notably, it even outperformed the Whale Optimization Algorithm (WOA)-ELM by approximately 10-12%.

Ahmed et al. (2022) introduced an enhanced method to improve the performance of intrusion detection systems (IDS) for cybersecurity in the Internet of Things (IoT) and smart home environments. They introduced an alternative feature selection (FS) model based on the GTO algorithm. Feature selection is essential for enhancing anomaly detection in IDSs. The study evaluated the method’s effectiveness by conducting experiments with three datasets: NSL-KDD, CICIDS2017, and Bot-IoT. Initially, a feature extraction (FE) model was applied to reduce the dimensionality of these datasets. Subsequently, the FS model processed the extracted features for detection. Comparative results demonstrated the proposed method’s superior performance over other IDS techniques, as indicated by various performance metrics.

Zhao et al. (2023) introduced a novel approach for predicting the 28-day compressive strength of high-performance concrete using machine learning techniques. They evaluated standalone radial basis function (RBF) modeling and two ensemble optimization algorithms, GTO and Moth-Flame Optimization (MFO). The authors conducted a thorough assessment of model performance using various evaluation metrics, including R2, RMSE, MAE, SI, and NRMSE, within the cross-validation framework. They also applied sensitivity analysis to gauge the individual input parameters’ impact on outcome prediction. The results unequivocally revealed improved predictive accuracy across all methods. Particularly noteworthy is the RBF-MFO model, which exhibited the highest precision with an R2 value of 0.996, surpassing the RBF-GTO model, which achieved an R2 value of 0.987. These findings highlight the effectiveness of the combined RBF-MFO model in accurately forecasting compressive strength.

Rahman, Chek, and Ramli (n.d.) proposed an innovative method for the condition monitoring of two electric motors using an intelligent vibration-based anomaly detection algorithm. They used metaheuristic-optimized feedforward neural networks (FNNs) to develop a robust model. They preprocessed an experimental dataset containing motor vibration data and trained a two-layer neural network using the GTO metaheuristic algorithm. The model achieved high prediction accuracy, even in the presence of artificial faults, demonstrating the model’s effectiveness.

Gong et al. used (2023) a new diagnostic algorithm named Improved Hierarchical Refined Composite Multiscale Multichannel Bubble Entropy (IHRCMMCBE) for fault diagnosis of rotating machinery. IHRCMMCBE leverages cutting-edge techniques to characterize faults more comprehensively. Multi-Cluster Feature Selection (MCFS) optimizes feature extraction, selecting the most informative features efficiently and effectively. For fault recognition, the EigenClass classifier optimized by the GTO algorithm is employed, which optimizes hyperparameters and enhances fault identification. IHRCMMCBE is versatile and data-independent, effectively characterizing various machinery types, fault categories, degrees, and composite faults. It is also computationally efficient and achieves a classification accuracy of 97.85% for bearing fault identification and 97.57% for gearbox fault identification.

Mohamed and Mustafa (2022) proposed the GTO algorithm for training multilayer perceptrons (MLPs). This study evaluates the performance of GTO on five well-known classification datasets, assessing its precision and convergence consistency as key performance metrics. GTO’s results are compared to those of established optimization algorithms, namely Grey Wolf Optimization (GWO), Whale Optimization Algorithm (WOA), and Sine Cosine Algorithm (SCA). Notably, this is the first study to apply GTO as an MLP trainer, and it highlights GTO’s ability to determine optimal weights and biases for classification problems.

Pachauri et al. (2024) introduced a novel approach to predict the higher heating value (HHV) of biomass from its ultimate analysis, the Gorilla Troop Optimization (GTO)-based Blended Ensemble Machine (GBEM). GBEM combines support vector regression, Gaussian process regression, and decision trees as base learners, with an adaptive linear neural network as the meta-learner. GTO optimizes the hyperparameters of GBEM, improving its performance and resulting in a lower average absolute relative deviation (AARD%) of 2.959%, outperforming other machine learning models.

Aneetchan and Geetha (2023) introduced a novel approach, the Gorilla Troops Optimization with Deep Learning-based Crop Recommendation and Yield Prediction Model (GTODL-CRYPM), to address the complex task of crop recommendation and yield prediction in Indian agriculture. The model leverages deep learning techniques, including long short-term memory (LSTM) and deep belief networks (DBN), optimized by the GTO algorithm. GTODL-CRYPM enables farmers to determine suitable crops for specific regions and periods, along with yield predictions. Extensive experiments on benchmark datasets demonstrate the model’s effectiveness and superior performance compared to existing approaches. This technology can significantly benefit the Indian agricultural sector by streamlining crop selection and enhancing yield predictions.

Saufi et al. (2022) addressed the challenge of hyperparameter selection in convolutional neural networks (CNNs) for bearing fault diagnosis. CNNs are widely used in various applications, but hyperparameter selection is a complex process involving over ten parameters that are typically tuned through trial and error. The paper introduces a novel approach that employs four swarm intelligence algorithms: Whale Optimization Algorithm (WOA), Dragonfly’s Algorithm (DA), Ant Lion Optimizer (ALO) and GTO algorithm to optimize the CNN model. The study utilizes datasets from three distinct bearing speeds and demonstrates that integrating the optimization algorithms into the CNN model achieves less than 5% error on both training and testing datasets for all three bearing datasets. This approach simplifies the hyperparameter selection process and enhances the performance of CNN models in bearing fault diagnosis.

6.5 Deep learning

Almutairi et al. (2023) proposed a medical data classification model for breast cancer (BC) detection using big data techniques and the Wisconsin BC datasets. The model incorporates the GTO algorithm for feature selection and leverages Deep Q Learning (DQL) within a Deep Reinforcement Learning (DRL) and Deep Neural Network (DNN) framework. The study encompasses essential data collection, preprocessing, feature selection, and classification stages, involving three distinct datasets (WBCD, WDBC, WPBC) from various sources. The preprocessing phase addresses missing values and normalizes the data, followed by GTO-driven feature selection. The DQL model classifies data into benign and malignant BC cases, achieving impressive accuracy rates of 98.90% for WBCD, 99.02% for WDBC, and 98.88% for WPBC. Notably, this model consistently outperforms other models across various performance metrics.

In response to the growing importance of early Alzheimer’s disease (AD) detection, Baghdadi et al. (2022) leveraged computer vision and deep learning technology. Their study introduced an empirical framework for precise AD classification using multi-class MRI datasets. Key elements of this framework included deploying a Convolutional Neural Network (CNN), Transfer Learning (TL), and the GTO algorithm to fine-tune parameters and hyperparameters. GTO’s nature-inspired optimization capabilities were used to optimize the hyperparameters of the TL process. The study used the ADNI dataset, which contains MRI images associated with Alzheimer’s disease. The results highlighted the remarkable accuracy of the MobileNet and Xception models, reaching 96.65% and 96.25%, respectively. This research underscores the potential of deep learning and GTO in enhancing AD classification through medical image analysis.

Hamdy et al. (2023) introduced an advanced deep-learning model for predicting interactions between long non-coding RNA (lncRNA) and microRNA (miRNA) in plants. Regulating biological processes is crucial for these interactions. The model combines Independently Recurrent Neural Networks (IndRNNs) and Convolutional Neural Networks (CNNs) to automatically analyze genetic sequences. The GTO Algorithm and an intelligent preying algorithm were used to tune the model’s hyperparameters. The model outperformed current deep learning and shallow machine learning models, achieving an accuracy rate of 97.7% on large-scale data, particularly for extended sequences. This innovative approach holds great promise for decoding functional activities in plant genomics.

Albraikan et al. (2023) have introduced an innovative approach to address Red Palm Weevil (RPW) detection, a pest that poses a significant threat to palm trees. Traditional visual analysis methods for RPW detection are inaccurate and time-consuming. To improve RPW detection accuracy and efficiency, this study presents the Red Palm Weevil Detection using the GTO algorithm with Deep Learning (RPWD-GTODL) method. The RPWD-GTODL approach utilizes Gabor filtering for image preprocessing and a Mask RCNN object detector with MobileNetv2 as its backbone network for RPW detection and localization. Experimental results using RPW datasets reveal a remarkable accuracy of 99.27%, demonstrating the effectiveness of RPWD-GTODL in RPW detection and localization. RPWD-GTODL offers a promising solution for accurately identifying and localizing RPW, which is essential for effective pest control and management in palm tree cultivation.

Govindaraju et al. (2023) presented a study focused on enhancing security in the Internet of Things (IoT) by leveraging software-defined networking (SDN) for effective detection of Distributed Denial-of-Service (DDoS) attacks. These attacks pose a significant threat, disrupting network operations and accessibility. To address this concern, the research leverages optimized deep learning models to achieve real-time DDoS attack detection within the SDN framework. The study collects data encompassing both regular and DDoS network traffic via SDN, and by employing feature selection techniques, it streamlines the model’s complexity while reducing training time. By integrating Long Short-Term Memory (LSTM) models in conjunction with the GTO algorithm for feature selection, the proposed intrusion detection system (IDS) attains an impressive detection accuracy rate of 97.59%. These findings demonstrate the potential of deep learning and feature selection methodologies to bolster DDoS protection within SDN environments.

Gokilavani et al. (2023) introduced a groundbreaking development in thyroid cancer diagnosis with their innovative model, the GTO algorithm with Deep Learning Based Thyroid Cancer Classification on Histopathological Images (GTODL-TCHI). This model is meticulously designed to analyze histopathological images (HIs) for the precise identification and classification of thyroid diseases. The GTODL-TCHI model encompasses several essential components to achieve its objectives. It commences with image denoising through the application of non-local mean filtering (NLMF), followed by image segmentation via a fully convolutional network (FCN). Feature vector generation is executed using the GTO algorithm, working in tandem with DenseNet121. The final step involves feature classification, achieved through a stacked sparse autoencoder (SSAE) model. In rigorous evaluations using histopathological image datasets, the GTODL-TCHI model consistently demonstrated substantial performance enhancements when compared to recent state-of-the-art deep learning models. This signifies a noteworthy advancement in the realm of thyroid cancer diagnosis, offering substantial promise in improving the accuracy and effectiveness of such diagnostic processes.

Mahalakshmi (2023) used an innovative transfer learning (TL)-based method for kidney stone classification. This approach leverages deep convolutional neural network (DCNN) models, specifically DenseNet169, MobileNetv2, and GoogleNet, to classify kidney stones. Furthermore, the hyperparameters of the DCNN model are optimized using the GTO algorithm. The TL model outperforms other DCNN models across various evaluation metrics, demonstrating its effectiveness in kidney stone classification.

Badawy et al. (2023) developed a groundbreaking framework for automating the accurate classification of oral cancer using microscopic histopathology slide images. This novel approach leverages the power of convolutional neural networks (CNNs), transfer learning (TL), and two state-of-the-art metaheuristic optimization algorithms, the Aquila Optimizer (AO) and Gorilla Troops Optimizer (GTO), to mitigate bias and unpredictability issues in the preprocessing and optimization phases. The study employed well-established pre-trained TL models and a dataset containing "normal" and "oral squamous cell carcinoma" (OSCC) images. The results demonstrate that AO consistently outperforms GTO across all models, with DenseNet201 achieving an astounding average accuracy rate of 99.25% with AO. This framework represents a significant leap forward in automated oral cancer detection, highlighting the potential of optimized deep learning models in healthcare diagnostics.

Ramesh et al. (2023) introduced an innovative AI-based m-health system for accurate cardiovascular disease (CVD) prediction. The system utilizes deep learning techniques, comprising data collection, normalization, AI-based classification, and decision-making modules. Health data, such as blood pressure, heart rate, and glucose level, are collected from smart devices through service providers. Noise reduction and data normalization are performed to enhance prediction accuracy. The study incorporates the GTO algorithm to select relevant features and employs bidirectional long-term memory (Bi-LSTM) for CVD-type classification. The model’s performance is rigorously evaluated and compared using various metrics, demonstrating its effectiveness in CVD prediction, with significant promise for improving healthcare support and outcomes, especially in resource-deficient areas.

Salvadi et al. (2023) proposed a novel quantum computing-enhanced deep learning approach for human activity recognition (HAR), a critical task in various applications, especially human-intelligent video surveillance. Their ORQC-CNN (Optimized Random Quantum Circuits with Convolutional Neural Networks) model integrates quantum-classified layers into a classical CNN architecture and uses the GTO algorithm for variational quantum parameter updates. Extensive evaluations under various conditions demonstrate that ORQC-CNN significantly outperforms previous HAR models, promising advancements in the field.

6.6 Energy

Fathy and Yousri (2023) proposed a novel maximum power point tracking (MPPT) approach using GTO to improve the efficiency of thermoelectric generator (TEG) devices with non-uniform temperature distributions. Their study evaluated $9 \times 9$ and $15 \times 15$ TEG arrays under various temperature scenarios. Comparative assessments against established MPPT techniques, including incremental resistance (INR), cuckoo search (CS), seagull optimization algorithm (SOA), particle swarm optimizer (PSO), and cuckoo search (CS), revealed the superior performance of the MPPT-based GTO. The MPPT-based GTO consistently achieved a remarkable 99.9% efficiency and generated higher power outputs across different TEG array configurations. These findings highlight the MPPT-based GTO’s efficacy in optimizing TEG system performance and suggest its potential applicability in real-world scenarios.

Ramadan et al. (2022) introduced the GTO algorithm to optimize the sizes and locations of Renewable Distributed Generations (RDGs) in distribution systems. Their multi-objective study considered load and RDG power output uncertainties using probability density functions. Monte Carlo simulation generated 30 manageable scenarios. Applying GTO to an IEEE 69-bus system and a real 30-bus Egyptian distribution network yielded significant advantages, with cost reductions of 25.97% to 28.3%, emissions reductions of 51.1% to 52.34%, voltage deviation reductions of 66.95% to 67.25%, and system stability improvements of 5.6% to 7.7%, compared to the base cases. The GTO algorithm’s superiority in addressing RDG allocation problems under both deterministic and probabilistic conditions was evident, as it outperformed other techniques.

To address system frequency fluctuations caused by the uncertain nature of renewable energy resources (RESs) in microgrids (MGs), Ramesh et al. (2023) developed an autonomous diesel wind energy-based microgrid (DWMG) that integrates a wind turbine generator (WTG) and a diesel generator (DEG). This system includes a wind-powered dynamic model, a speed regulator, and a proportional-integral-derivative (PID) frequency controller to manage WTG power fluctuations. Additionally, they use integral type sliding mode control (I-SMC) to improve frequency regulation, especially in the face of load and source uncertainties. The controller parameters are optimized using the GTO algorithm. The results demonstrate the approach’s effectiveness, with reduced frequency deviations, shorter settling times, and decreased integral errors compared to existing methods.

Murugan et al. (2022) introduced an innovative approach that leverages the GTO algorithm to optimize artificial neural networks (ANNs) for energy management in DC-AC hybrid distribution networks. Their energy management system (EMS) considers various factors, including distributed generation, load demand, and battery charge levels. The ANN is initially trained using profile data and subsequently fine-tuned using GTO to ensure optimal performance. Simulations on small-scale hybrid DC/AC microgrids demonstrated the proposed system’s superiority over existing methods, achieving an impressive efficiency rate of 99.55%. This approach emerges as a highly effective solution for energy management in distribution networks.

Ramzi and Souhil (2022) introduced a novel metaheuristic approach, the GTO algorithm, for solving optimal power flow (OPF) problems with stochastic wind power. The primary aim of this research is to minimize the total generation cost (TGC) by optimizing the scheduling of thermal and wind units while adhering to various constraints. To address wind power uncertainty, the Weibull probability density function is incorporated into the optimization problem. The wind power cost function comprises direct costs, penalty costs for underestimating available wind power, and reserve costs for overestimating available wind power. The study evaluated the GTO algorithm’s performance using the IEEE-30 bus system with integrated wind farms and found it to be highly competitive compared to the Artificial Hummingbird Algorithm (AHA). This demonstrates GTO’s promise as an approach for OPF problems with stochastic wind power.

Ginidi et al. (2021) introduced a novel application of the GTO method for extracting parameters from solar photovoltaic (PV) models. This endeavor addresses the intricate nonlinear characteristics of PV systems, particularly their current–voltage and power-voltage relationships. Numerical analyses on different PV modules demonstrate the GTO’s effectiveness, focusing on Single-Diode (SD) and Double-Diode (DD) models. The study showcases the GTO algorithm’s superiority by comparing it to other recent optimization techniques and highlighting its ability to closely emulate experimental PV performance under varying irradiance and temperature conditions.

Fayaz-dastgerdi et al. (2023) introduced the use of the GTO algorithm to optimize load flow analysis for renewable microgrids in island mode. Traditional load flow methods often struggle to address the complexities of islanded microgrids, making GTO a valuable tool. The authors also proposed a hybrid objective function that minimized the mean voltage phase error, voltage amplitude, and the absolute value of active and reactive power mismatches. Simulation results showed that this objective function improved several performance indicators, and GTO outperformed other optimization techniques in the context of load flow optimization for microgrid systems with renewable energy sources.

Mohamed and Hamed (2023) introduced an innovative approach to enhance the performance of photovoltaic systems in challenging conditions, including critical disturbances and shading. Conventional Maximum Power Point Tracking (MPPT) methods often struggle to track the Maximum Power Point (MPP) precisely in dynamic weather conditions, resulting in undesired oscillations. To address this issue, the authors proposed the GTO technique in combination with a Fractional Order Proportional-Integral-Derivative (FOPID) controller. Through MATLAB/Simulink simulations, the proposed FGTO controller is compared to a conventional PID controller based on GTO and other MPPT techniques like Perturb and Observe (P &O) and Incremental Conductance (IC). The results demonstrate the effectiveness of the GTO-based fractional MPPT system, showcasing rapid convergence, stability, and high efficiency, achieving up to 99.42% performance across various climatic conditions.

Maged et al. (2022) have introduced the GTO algorithm for optimizing the control of autonomous microgrids. This study focuses on designing and optimizing proportional-integral (PI) controller parameters for microgrid control, particularly for voltage and frequency regulation. The microgrid operates as an islanded system, disconnected from the main power grid and relying on multiple decentralized energy resources and local loads. The control system aims to regulate voltage and frequency effectively across various points of common coupling, even when faced with load variations and other operational challenges. Comparative analysis with a PI controller designed using PSO demonstrates the superior performance of the GTO-based controller. This indicates that the GTO algorithm is highly effective in optimizing the control of autonomous microgrids, leading to enhanced microgrid operations, especially in scenarios with varying loads and other operational challenges.

Ali et al. (2021) introduced a novel approach to enhance the frequency response of a hybrid microgrid system using a cascaded Proportional Integral-Fractional Order Proportional-Integral-Derivative (PI-FOPID) controller. The GTO algorithm was used to meticulously tune the controller’s optimal gains. The cascaded PI-FOPID controller was rigorously compared to a single-structure Fractional Order PID (FOPID) controller, which was also optimized using GTO and other conventional optimization techniques. Simulations conducted in MATLAB/Simulink demonstrated the efficacy of the proposed controller. It delivered significant improvements in terms of the system’s maximum overshoot/undershoot and settling time, surpassing other methods by 99.8% and 75.9%, respectively. These findings highlight the considerable potential of this novel control strategy for enhancing the frequency response of hybrid microgrid systems.

Abdelfatah et al. (2022) proposed a novel optimization strategy using the GTO algorithm to optimize the configuration of a microgrid system in New West Qena City, Egypt. The microgrid system comprises photovoltaic panels, a diesel generator, and a battery storage system, and the optimization process takes into account local meteorological data. The primary objectives of this study are to minimize the cost of energy (COE), reduce the net present cost (NPC) of the hybrid system, and evaluate the loss of power supply probability (LPSP). The study evaluates the effectiveness of the GTO algorithm in obtaining the most favorable solution through rigorous statistical analysis. Comparative assessments against other optimizers like ALO and GWO reveal that the GTO approach outperforms the others, establishing itself as the most efficient choice for designing the microgrid system.

Abishek and Dulal Chandra (2023) proposed an enhanced frequency control model for a centralized-control technical virtual power plant (TVPP) that integrates distributed energy resources (DERs). Centralized TVPPs are designed to provide frequency control support, but they often face challenges due to communication delays and dead band restrictions on the droop control signal. This study addresses these issues by incorporating frequency dead-band and communication delays into both the primary (droop control) and secondary (ACE control) loops for the DERs within the VPP. Additionally, the authors propose a novel approach using 2DOF-PID controllers tuned with the GTO algorithm. Comparative assessments demonstrate that the GTO algorithm outperforms classical optimization algorithms, and the 2DOF-PID controller exhibits superior dynamic performance compared to GTO-optimized PID and PI controllers. Sensitivity analysis results underscore the robustness of the proposed GTO-optimized 2DOF-PID controller to system uncertainties, making it a promising solution for VPP frequency control within centralized TVPPs incorporating DERs.

Ginidi et al. (2022) proposed the GTO algorithm as a powerful solution for the complex Optimal Power Flow Issue (OPFI) in electric power networks (EPNs). OPFI involves multifaceted optimizations, encompassing goals like cost reduction, emissions minimization, power loss mitigation, and voltage stability enhancement in EPNs. Inspired by gorilla social dynamics, GTO incorporates principles of migration, competition, and coordination among virtual gorilla agents. The authors comprehensively evaluated GTO’s performance using a real-world Egyptian West Delta-EPN, the IEEE 57-bus EPN, and the IEEE 118-bus system, both with and without Thyristor-Controlled Series Capacitor (TCSC) devices. They also extended GTO to the substantial IEEE 118-bus system, where it surpassed the capabilities of particle swarm optimization. The results vividly demonstrate significant reductions in fuel costs, emissions, voltage instability, and power losses across different EPNs, firmly establishing GTO as a highly efficacious optimization technique compared to other leading-edge methodologies.

Mouassa et al. (2023) introduced the GTO algorithm to tackle the challenging optimal power flow (OPF) problem, especially in the presence of uncertainties related to renewable energy sources (RES). The OPF problem involves complex nonlinear optimization, which is particularly challenging with intermittent energy sources. To address this, the researchers employ nature-inspired optimization algorithms. Their objective function incorporates system costs, encompassing reserve costs for overestimation of photovoltaic (PV) solar and wind energy, and penalty costs for underestimation. Case studies on the IEEE 30-bus system and Adrar’s isolated power grid demonstrate the consistency and robustness of their algorithm. The results show that the GTO algorithm outperforms various algorithms across different function landscapes, emerging as the most effective approach for discovering high-quality optimal solutions.

Li et al. (2023) introduced an innovative deep belief network (DBN)-based method for energy consumption forecasting, addressing a critical and intricate real-time issue in energy management. Their approach enhances the DBN structure through their custom-GTO algorithm to improve the accuracy of power demand prediction. The DBN/GTO approach is evaluated through a case study that encompasses various demand types, including short-, long-, and medium-term forecasts. Comparative evaluations against established techniques demonstrate the efficiency of this method in achieving precise and dependable energy consumption forecasting, thereby facilitating collaboration between consumers and power providers.

Alhejji et al. (2023) proposed a new approach to address load frequency control in micro-grids (MGs) during islanded operation to address high-frequency oscillations caused by variable loads, renewable energy sources, and plug-in electric vehicles (PEVs). Their proposed strategy involves a cascade controller that combines proportional-derivative (PD) and proportional-integral (PI) controllers, optimized using the GTO algorithm. The study evaluates the controller’s performance under various scenarios, considering load fluctuations, wind speed, and solar irradiance changes. The findings demonstrate that the PD-PI controller outperforms traditional PID and PI controllers in mitigating frequency oscillations in MGs effectively, especially in the presence of PEVs.

Yakout et al. (2023) proposed an enhanced reinforcement learning (RL) agent that leverages the deep deterministic policy gradient (DDPG) algorithm to optimize frequency control in hybrid power systems. The RL agent takes weighted signals associated with system frequency and deviation as inputs and seeks to maximize a reward function that ensures the system operates within an acceptable frequency range. To further improve the controller’s performance, the authors employed the GTO algorithm to optimize the observation weights. The proposed control technique is evaluated in a two-area system comprising various energy sources and storage units, including batteries and superconducting magnetic energy storage. Comparative analysis against traditional PI and PID controllers demonstrates the superior performance of the GTO-based RL controller in enhancing frequency control in hybrid power systems.

Hatata et al. (2023) proposed a central controller-based coordination approach for voltage control devices in smart distribution networks (SDNs), considering D-STATCOMs, OLTC transformers, and distributed generation-based renewable energy resources (RERs). The proposed approach aims to maintain voltage profiles within permissible limits, minimize power losses under various conditions, and reduce energy wastage from RERs. These problems are formulated as a multi-objective optimization problem. To find optimal solutions, the authors utilized the GTO algorithm, considering load demand uncertainties and the stochastic nature of power generation from RERs, such as PV panels and wind turbines. The proposed method operates on an IoT-based communication protocol, enhancing data exchange among network-connected agents. Tests on practical distribution networks demonstrate that the GTO-based approach outperforms other evolutionary methods, offering more accurate results in voltage coordination.

Asiri et al. (2022) proposed an innovative approach to mitigate energy constraints in wireless sensor networks (WSNs) by combining the improved duck and traveler optimization (IDTO) algorithm with the GTO algorithm. This approach focuses on cluster-based multi-hop routing (MHR) to enhance the efficiency and longevity of WSNs. The IDTO algorithm is used to select cluster heads (CHs) and form clusters, while the GTO technique optimizes the selection of routes to the destination. Both the clustering and routing processes incorporate fitness functions with multiple input parameters. Thorough experimental validation demonstrates the superior performance of the proposed IDTOMHR model compared to other contemporary methods, establishing it as a promising solution for improving energy efficiency in WSNs.

Shaheen et al. (2022) proposed an innovative approach to tackling the Optimal Power Flow Problem (OPFP) in Electrical Power Systems (EPSs) using the GTO technique. They comprehensively evaluate their approach on a 30-bus EPS specified by IEEE and an operational Wind-Diesel EPS in Egypt, considering a wide range of scenarios with diverse objective functions, including fuel cost, transmission losses, and environmental impact. By introducing multi-dimensional objectives, the study achieves significant reductions in single objectives, ranging from 7.67% to 61.95% compared to their initial states across six different single-objective scenarios. Rigorously evaluated against various contemporary methods, GTO demonstrates its effectiveness and stability. Comparative analysis with similar approaches in the literature underscores the robustness and validity of the developed GTO solution, positioning it as a promising tool for optimizing EPSs across diverse scenarios.

Chen et al. (2023) proposed two innovative real-time methods for identifying model parameters in photovoltaic (PV) arrays, aiming to improve fault diagnosis and health state evaluation. Their approach first introduces a modeling technique for PV arrays to facilitate real-time parameter identification. They also present a preprocessing method to enhance the quality of measured current–voltage (I-V) curves. The GTO algorithm is then employed to extract parameters from these curves. The historical parameters obtained from the extraction process serve as data sources for real-time parameter identification methods, including time series prediction and irradiance-temperature (G-T) grid searching. The performance of these methods is evaluated using various metrics, with a focus on the root mean square error (RMSE) between calculated and measured I-V curves. The results demonstrate the effectiveness of these approaches, with RMSE values ranging from 0.01A to 0.1A, offering valuable contributions to the accurate identification of parameters in PV arrays.

Gude et al. (2021) proposed using the GTO algorithm to tune the control parameters of power system stabilizers (PSS) in a two-area, four-machine test system. The primary goal is to improve the damping ratio of system poles and reduce power oscillations by optimizing the PSS controller parameters. The study aims to identify the most suitable controller parameter values using the GTO algorithm, thereby enhancing the power system’s stability across different operational scenarios. This application demonstrates GTO’s effectiveness in optimizing PSS parameters to improve power system stability.

Hashish et al. (2023) proposed a novel metaheuristic optimization algorithm, the GTO algorithm, to address the optimal power flow (OPF) problem in hybrid power systems incorporating photovoltaic (PV) and wind energy (WE) sources. This paper presents two key applications of GTO: solving the classical OPF to minimize total fuel cost and addressing the probabilistic optimum power flow (POPF) to account for the uncertainty associated with renewable energy sources (RESs). The algorithm’s effectiveness was verified through tests on IEEE 30-bus and 118-bus standard systems under various scenarios. The results demonstrated that integrating PV and WE sources can significantly reduce overall system cost, establishing GTO’s efficacy for optimizing hybrid power systems.

Patil et al. (2022) addressed the challenges of system security and stability in a wind-integrated deregulated power network. They focused on power market imbalance costs, which result from discrepancies between expected wind speed (EWS) and real wind speed (RWS). These discrepancies lead to penalties or rewards enforced by the independent system operator (ISO). To mitigate this issue and enhance system profit, the study incorporated solar photovoltaic (PV) and battery energy storage systems alongside the wind farm. Additionally, the research assessed system risk using Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR) metrics on modified IEEE 14 and modified IEEE 30 bus test systems. The integration of solar PV and battery storage systems, managed by three different optimization methods, including the GTO algorithm, was shown to effectively reduce system risk and minimize power market imbalance costs.

Das et al. (2022) addressed the challenges of increasing electricity demand and barriers to constructing new thermal power plants and transmission lines by proposing a solution that integrates renewable energy sources and flexible AC transmission systems (FACTS) within the power network. This integration allows renewable sources to contribute power to the grid and FACTS devices to enhance the thermal limit of existing transmission lines, promoting stable and secure electrical network operation. The research focused on optimizing the operation of wind farms and FACTS devices to reduce system risks and improve economic efficiency in both regulated and deregulated environments. The system’s risk was assessed using Value at Risk (VaR) and Conditional Value at Risk (CVaR) metrics on modified IEEE 14-bus and modified IEEE 30-bus systems. Comparative analyses with different optimization techniques, including the GTO algorithm, revealed the positive impact of renewable integration on system risk and operating costs.

Eid et al. (2022) proposed an optimization approach for distribution systems that integrate renewable energy sources (RES) such as photovoltaic (PV) and wind turbine (WT) units with electric vehicle charging stations (EVCS) and battery energy storage systems (BESS). The optimization, which uses the GTO algorithm, aims to minimize power loss and total voltage deviation in a 108-bus distribution system. The GTO algorithm optimizes the positions and sizes of PV and WT units in one stage, followed by optimizing BESS operation in the second stage, considering different EVCS charging profiles. The results demonstrate significant reductions in energy loss and utility power consumption, highlighting the effectiveness of GTO in optimizing distribution networks with RES and BESS units.

Li et al. (2022) introduced an innovative crude oil price forecasting model, ICEEMDAN-SSCE-TVMD-GTO-KELM, to address the challenges posed by the highly volatile nature of crude oil prices. The model integrates a range of techniques to significantly enhance forecasting accuracy. It begins with secondary decomposition using ICEEMDAN, followed by the application of state space correlation entropy (SSCE) to identify components with elevated complexity. The most intricate component is further decomposed into multiple sub-series. Finally, the enhanced kernel-based extreme learning machine (KELM) is optimized using the GTO algorithm to forecast all individual components. Extensive experimental assessments conducted using West Texas Intermediate (WTI) and Brent oil data highlight the model’s exceptional forecasting precision, outperforming nine alternative forecasting methods. This underscores the model’s potential as an effective tool for accurate crude oil price forecasting.

Li et al. (2023) introduced a multifaceted forecasting model, WVMD-GTO-LSTM-EC, to address the intricate task of accurately predicting photovoltaic power generation. Acknowledging the inherent randomness and low prediction accuracy associated with photovoltaic power, the authors proposed a holistic solution that amalgamates various components: fuzzy C-means (FCM) clustering for identifying pertinent meteorological factors, improved variational mode decomposition (VMD) facilitated by the white shark optimizer (WSO) for decomposing daily data, long short-term memory (LSTM) refined through the GTO algorithm, and an error correction (EC) mechanism. Comprehensive assessments demonstrate the model’s superior forecasting capabilities, with empirical results obtained using Australian solar power generation data showcasing its high accuracy. The model surpasses eight other comparative models with an impressive correlation coefficient (R) of 0.99 and exceptional performance on crucial metrics including MAPE, MAE, RMSE, and R2. This model underscores its effectiveness in addressing the challenges of photovoltaic power prediction.

Essa et al. (2023) introduced a novel cooling technique for photovoltaic thermal (PVT) systems to maintain PV panel temperatures within an acceptable range. This technique incorporates rectangular cascade channels that facilitate perpendicular cooling of the PV panel with two different orientations. As a result, the average PV cell temperature is reduced by 27K, leading to significant enhancements in electrical, thermal, and overall efficiencies of 4.8%, 59.5%, and 73.33%, respectively. The study also presents an artificial neural network (ANN) prediction model using a radial basis function neural network (RBFNN) optimized by the GTO algorithm. This model accurately predicts crucial PVT system performance parameters, demonstrating its effectiveness in PVT system performance modeling.

Maged et al. (2023) 74484conducted a comparative analysis of control strategies for autonomous microgrid systems, examining fuzzy logic control optimized with the African vulture and Particle Swarm Optimization algorithms, and a proportional-integral controller optimized with the Gorilla Troops Optimization algorithm. The performance of these control methods was evaluated through simulations in MATLAB/Simulink and real-time experiments with OPAL prototyping. The findings revealed that the fuzzy logic controller optimized with the African vulture algorithm outperformed other techniques, offering robust and effective control with significantly enhanced accuracy. This outcome highlights its potential for ensuring optimal power distribution to various loads within distributed power grid systems.

Shahinzadeh et al. (2023) explored the complex problem of determining optimal electricity pricing for consumers in the retail market, a matter of critical importance for both retailer profitability and consumer interests. The study focused on a retail intermediary agent in a smart grid environment, considering various uncertainties, such as those associated with market prices, load profiles, and weather conditions. The authors applied a Monte Carlo method to address these uncertainties and employed the GTO method to optimize retailer strategies and maximize profitability under different electricity market scenarios, including fixed pricing, time-based rate pricing, and real-time pricing. The proposed model was evaluated through simulations, providing valuable insights into effective pricing and energy resource management.

Can et al. (2023) proposed a novel PID-(1+l) controller for automatic generation control (AGC) in a two-area nonreheat thermal power system integrated with renewable energy sources (RESs), such as photovoltaic panels and wind turbines. This innovative controller addresses common issues in AGC studies, such as stability, peak deviation, and transient response. The study optimally tunes the controller’s gain parameters using newly developed metaheuristic algorithms, such as the Honey Badger Algorithm (HBA), the African Vulture Optimization Algorithm (AVOA), and the GTO algorithm. Through extensive testing under various conditions, including random load changes, RES generation, and system parameter adjustments, the proposed controller demonstrates significant improvements in overshoot and settling time values, offering a promising solution for AGC in integrated power systems.

Table 3 The applications of GTO algorithm

7 Evaluation and analysis of the GTO algorithm

7.1 CEC2020 benchmark evaluation

The efficiency of the GTO method is assessed by employing 10 mathematical benchmark functions sourced from CEC 2020 function as shown in Table 4. This evaluation involves the application of various statistical criteria and measurements, including the average (mean), standard deviation (STD), and the identification of the best and worst solutions produced by the GTO and other algorithms. Additionally, the Friedman test is utilized to rank these algorithms. The outcomes are then compared with established techniques, specifically Aquila Optimizer (AO) Abualigah et al. (2021), Harris Hawks Optimizer (HHO) Heidari et al. (2019), Sine Cosine Algorithm (SCA) Mirjalili (2016), Salp Swarm Algorithm (SSA) Mirjalili et al. (2017), Whale Optimization Algorithm (WOA) Mirjalili and Lewis (2016), Slime Mould Algorithm (SMA) Li et al. (2020), Arithmetic Optimization Algorithm(AOA) Abualigah et al. (2021), Grey Wolf Optimizer (GWO) Mirjalili et al. (2014), and Multi-Verse Optimizer (MVO) Mirjalili et al. (2016). The configuration of these algorithms can be given in Table 5.

Table 4 CEC2020

Table 5 Metaheuristic algorithms parameters settings

A comprehensive overview of the configuration parameters for each algorithm is presented in Table 4. To ensure equitable comparisons, all parameters for the algorithms are maintained at the values stipulated in their original publications. Furthermore, the experiments encompassed the utilization of a uniform population size of 50 individuals, with the termination condition specified as a maximum of 1000 iterations. These simulations were executed on a computer with a 2.0 GHz processor and 16 GB RAM, utilizing MATLAB R2022b on a Windows 10 platform.

The results of these experiments are systematically documented in Table 6 for each of the 30-dimensional functions from CEC 2020. Upon analyzing these outcomes, it becomes evident that the GTO method excels in various evaluation criteria. Notably, the GTO method secures the top position in six functions out of 10 (specifically F1, F5, F7, F8, F9, and F10), takes the second position in F4 and F6, and ranks third in F3.

Table 6 Statistical results of GTO versus other metaheuristics on CEC 2020 benchmark functions

In this section, we investigate the convergence behavior of the GTO algorithm relative to other competitive algorithms. Figure 13 showcases the convergence curves for the CEC 2005 functions, revealing that the GTO algorithm consistently reaches a stable point for all functions, signifying its capability to converge effectively. Additionally, the algorithm attains the lowest average of the best solutions more swiftly than most other functions. This rapid convergence towards (near) optimal solutions is noteworthy and suggests that the GTO algorithm is a viable choice for optimizing problems necessitating swift computation, such as online optimization problems.

Boxplot analysis serves as a valuable tool for visualizing the characteristics of data distribution, offering enhanced insight into result distribution, particularly for functions laden with numerous local minima. As depicted in Fig. 14, boxplots illustrate the distribution of results for each algorithm and function, representing quartile data distributions. The whiskers’ edges signify the algorithm’s minimum and maximum data points, while the rectangle ends indicate the lower and upper quartiles. A narrow boxplot indicates a high level of data consensus. Figure 14 displays boxplots for ten functions with dimension 30, demonstrating that the boxplots for the GTO algorithm are consistently narrower than those of other algorithms, often resulting in lower values.

To gauge the significance of the performance disparity between the GTO and other competing algorithms, we employ Wilcoxon’s rank-sum test, a non-parametric statistical test used to compare two samples and determine if they exhibit different medians. In this context, it is employed to evaluate the performance distinction between the GTO algorithm and other competing algorithms. Table 7 presents a paired algorithm comparison of the average best-so-far solutions using Wilcoxon’s rank-sum test with a 5% significance level. This table delineates the pair-wise comparison of the best-so-far solution averages for each function, along with the corresponding p-values. A p-value less than or equal to 0.05 implies that the performance difference between the GTO algorithm and the other competing algorithms is statistically significant. This indicates that the GTO algorithm’s superior performance is not random but rather a result of its optimization principles and strategies.

Fig. 13

Convergence curve for GTO against other competitors – CEC2020

Fig. 14

Box Plot of CEC2017 functions from F1 - F10 for all algorithms

Table 7 Comparison between original AGTO and other well-known and recently published algorithms in the literature

7.2 Comprehensive evaluation against similar algorithms in the literature

This subsection assesses AGTO’s efficiency compared to similar algorithms outlined in the literature, as demonstrated in Table 7. The findings reveal distinctions between AGTO and other algorithms in certain attributes, such as the number of parameters and complexity. However, AGTO shares common properties with other algorithms regarding advantages and limitations. Therefore, enhancing the original AGTO is essential to augment its capabilities and address its weaknesses, surpassing other algorithms.

8 Discussion and results

Much like other optimization techniques, GTO has experienced substantial growth and has emerged as a dependable tool for tackling intricate challenges. GTO, an artificial intelligence approach, leverages stochastic computational processes to identify near-optimal solutions for both one-dimensional and multi-dimensional objectives outlined in its objective function. GTO adheres to standard operating procedures, offering a readily implementable and efficient solution that finds utility across a wide array of domains. The outcomes compiled in this comprehensive survey paper furnish compelling substantiation of GTO’s exceptional performance, particularly with regard to its efficacy and precision in achieving optimal outcomes. This assertion is underpinned by a meticulous evaluation and scrutiny of the results obtained through GTO in comparison to recently introduced optimization techniques, reaffirming its competitiveness and effectiveness in addressing real-world issues.

The GTO offers several key advantages, including its simplicity, rapid convergence, smooth convergence curves, precise solution generation, and minimal demand for control parameters. However, it is important to acknowledge that GTO also has some inherent limitations stemming from its structural design, which can be summarized as follows:

• The potential for exploration within the GTO hinges on two primary parameters: $\beta$ and p. Nonetheless, these parameters are typically held at fixed, constant values. Consequently, there is a need for experimentation to render these parameters adaptable and applicable across a diverse range of problem scenarios.

• Since GTO adopted a migration strategy, it can introduce significant computational overhead which can become substantial in large-scale problems or when there are many subpopulations, potentially leading to increased computational costs and time.

• It is worth noting that self-learning mechanisms, which enable nature-inspired algorithms to learn from prior experiences and adjust their search strategies for enhanced performance in locating optimal solutions, are not a part of the traditional GTO framework.

• GTO has been documented in the literature as having certain limitations, including poor population diversity, elevated computational costs, sluggish convergence rates, and susceptibility to local minimum trapping issues. Addressing these challenges can involve the implementation of efficient population creation strategies or techniques for preserving population diversity.

• It is imperative to consistently work on refining the equilibrium between the exploration process and the exploitation process in stochastic population-based optimizers. This approach is essential to guarantee a precise estimation of the global optimum.

• The primary limitation of the GTO is closely associated with the No Free Lunch (NFL) Theorem (Wolpert and Macready 1997; Wang et al. 2023). According to the NFL theorem, no single superior optimizer can outperform all other optimizers for every optimization problem across all scenarios. Consequently, the convergence of GTO is intricately linked to the inherent characteristics of the problems search space. Hence, it is imperative to modify and hybridize the GTO search behavior to align with the specific characteristics of diverse optimization problems search spaces.

Furthermore, the research survey highlights several notable limitations, including:

• The predominant application of classical GTO for addressing a wide array of real-world optimization problems. Limited utilization of GTO and its variants in addressing discrete and multi-objective problems.

• GTO has predominantly found application in power and control engineering, as well as in the optimization of machine learning models.

• The prevalence of hybridization as the primary strategy employed to enhance GTO efficiency.

• Occasional usage of methods like Lévy flight, Chaotic sequences, and other efficiency-enhancing techniques, although their implementation remains relatively limited.

9 Conclusion and future works

This paper provides a comprehensive review of prior research pertaining to GTO, its various variants, and their application in a wide range of domains. Within this investigation, we outline the process of gathering research papers and offer an overview of the GTO. This summary encompasses details regarding the time demands associated with GTO and its sensitivity to various parameters. Additionally, it delves into the development of GTO and the diverse methods that have evolved from it. The research findings consistently demonstrate that GTO, as well as its modifications and hybridizations with other algorithms, yield superior outcomes across various optimization problems in terms of execution, efficiency, and accuracy when compared to alternative evolutionary algorithms like GA, PSO, and SA. The practical implementation of GTO and its variants algorithms in fields including renewable systems, engineering and design, feature selection, image segmentation, data clustering, and industrial engineering enhances the quality of solutions, ultimately leading to improved system/component performance and analysis. The paper also offers a comprehensive survey of the existing literature on this subject, providing an in-depth understanding of this field. Furthermore, we evaluate GTO performance using mathematical benchmark functions from CEC2005. The outcomes of this assessment underscore GTO’s exceptional performance, positioning it as the leading choice among the nine nature-inspired metaheuristics studied.

Expanding on the preceding discussion, several promising avenues for future research in the domain of GTO and optimization strategies can be identified:

• Parameter Exploration: To enhance GTO adaptability across a broad spectrum of problems and problem dimensions, further investigation into its parameters, including population size, is essential. Investigating methods for controlling GTO parameters and their impact on the balance between exploration and exploitation during the search process represents a promising avenue for future research. This could involve deterministic, adaptive, or self-adaptive parameter tuning mechanisms.

• Performance Enhancement: Improving GTO performance can be achieved through the incorporation of co-evolution, communication, and information exchange among solutions. Future research should explore unique and well-established enhancement methodologies, particularly those grounded in randomization, to boost GTO capabilities. For instance, effective local search agents, such as hill climbing, $\varepsilon$-hill climbing, simulated annealing, tabu search, among others, can be integrated into the GTO optimization model to enhance its exploitation capabilities.

• Expanded Applications and Exploring New Problem Domains: Exploring the application of GTO variants to multi-objective and discrete problems represents a promising avenue for future research. Additionally, deploying GTO in fields like machine learning and computer vision holds potential for innovative applications. Researchers are likely to explore the application of GTO in fields like renewable energy, chemical engineering, robotics, and image processing, capitalizing on its demonstrated success in solving a wide array of problems.

• Quantitative Evaluation: While much of the research on GTO has relied on qualitative methods, there is an opportunity to develop a suitable mathematical framework for GTO. This could pave the way for more robust and realistic evaluation methods, moving beyond the limitations of current theoretical approaches.

• The local convergence challenge faced by the Expectation Maximization (EM) algorithm in estimating Hidden Markov Models (HMMs) presents a noteworthy challenge. To overcome this issue, future research might explore the integration of the GTO. Refining and evaluating the GTO-EM hybrid could potentially improve HMM parameter estimation, offering implications for addressing diverse optimization challenges in the realms of machine learning and statistical modeling.