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Hybridizing metaheuristic algorithms involves synergistically combining different optimization techniques to effectively address complex and challenging optimization problems. This approach aims to leverage the strengths of multiple algorithms, enhancing solution quality, convergence speed, and robustness, thereby offering a more versatile and efficient means of solving intricate real-world optimization tasks. In this paper, we introduce a hybrid algorithm that amalgamates three distinct metaheuristics: the Beluga Whale Optimization (BWO), the Honey Badger Algorithm (HBA), and the Jellyfish Search (JS) optimizer. The proposed hybrid algorithm will be referred to as BHJO. Through this fusion, the BHJO algorithm aims to leverage the strengths of each optimizer. Before this hybridization, we thoroughly examined the exploration and exploitation capabilities of the BWO, HBA, and JS metaheuristics, as well as their ability to strike a balance between exploration and exploitation. This meticulous analysis allowed us to identify the pros and cons of each algorithm, enabling us to combine them in a novel hybrid approach that capitalizes on their respective strengths for enhanced optimization performance. In addition, the BHJO algorithm incorporates Opposition-Based Learning (OBL) to harness the advantages offered by this technique, leveraging its diverse exploration, accelerated convergence, and improved solution quality to enhance the overall performance and effectiveness of the hybrid algorithm. Moreover, the performance of the BHJO algorithm was evaluated across a range of both unconstrained and constrained optimization problems, providing a comprehensive assessment of its efficacy and applicability in diverse problem domains. Similarly, the BHJO algorithm was subjected to a comparative analysis with several renowned algorithms, where mean and standard deviation values were utilized as evaluation metrics. This rigorous comparison aimed to assess the performance of the BHJO algorithm about its counterparts, shedding light on its effectiveness and reliability in solving optimization problems. Finally, the obtained numerical statistics underwent rigorous analysis using the Friedman post hoc Dunn's test. The resulting numerical values revealed the BHJO algorithm's competitiveness in tackling intricate optimization problems, affirming its capability to deliver favorable outcomes in challenging scenarios. [ABSTRACT FROM AUTHOR]

This paper presents a novel bio-inspired metaheuristic algorithm termed the Fossa Optimization Algorithm (FOA), which emulates the natural hunting behavior of the fossa in its habitat. FOA draws its core inspiration from the two-stage hunting technique of the fossa, involving an initial attack on a spotted lemur followed by a pursuit through the trees. The theoretical framework of FOA is elaborated, and its implementation is mathematically modeled in two distinct phases: (i) exploration, which simulates the fossa's positional adjustments during the initial attack on the lemur, and (ii) exploitation, which models the positional changes of the fossa during the chase. The efficacy of FOA is tested against twenty-two constrained optimization problems from the CEC 2011 test suite, as well as four engineering design challenges. The optimization results demonstrate FOA's strong capabilities in both exploration and exploitation, maintaining a balance that facilitates convergence to optimal solutions. FOA's performance is benchmarked against twelve established algorithms, showing that it consistently outperforms its competitors by delivering superior results and ranking as the top optimizer in most of the evaluated functions. These findings indicate that FOA is highly effective in addressing optimization tasks in real-world scenarios. [ABSTRACT FROM AUTHOR]

Supply chain efficiency is a major challenge in today's business environment, where efficient resource allocation and coordination of activities are essential for competitive advantage. Traditional efficiency strategies often struggle for resources for the complex and dynamic network. In response, bio-inspired metaheuristic algorithms have emerged as powerful tools to solve these optimization problems. Referring to the random search nature of metaheuristic algorithms and emphasizing that no metaheuristic algorithm is the best optimizer for all optimization applications, the No Free Lunch (NFL) theorem encourages researchers to design newer algorithms to be able to provide more effective solutions to optimization problems. Motivated by the NFL theorem, the innovation and novelty of this paper is in designing a new meta-heuristic algorithm called Bobcat Optimization Algorithm (BOA) that imitates the natural behavior of bobcats in the wild. The basic inspiration of BOA is derived from the hunting strategy of bobcats during the attack towards the prey and the chase process between them. The theory of BOA is stated and then mathematically modeled in two phases (i) exploration based on the simulation of the bobcat's position change while moving towards the prey and (ii) exploitation based on simulating the bobcat's position change during the chase process to catch the prey. The performance of BOA is evaluated in optimization to handle the CEC 2017 test suite for problem dimensions equal to 10, 30, 50, and 100, as well as to address CEC 2020. The optimization results show that BOA has a high ability in exploration, exploitation, and balance them during the search process in order to achieve a suitable solution for optimization problems. The results obtained from BOA are compared with the performance of twelve well-known metaheuristic algorithms. The findings show that BOA has been successful in handling the CEC 2017 test suite in 89.65, 79.31, 93.10, and 89.65% of the functions for the problem dimension equal to 10, 30, 50, and 100, respectively. Also, the findings show that in order to handle the CEC 2020 test suite, BOA has been successful in 100% of the functions of this test suite. The statistical analysis confirms that BOA has a significant statistical superiority in the competition with the compared algorithms. Also, in order to analyze the efficiency of BOA in dealing with real world applications, twenty-two constrained optimization problems from CEC 2011 test suite and four engineering design problems have been selected. The findings show that BOA has been successful in 90.90% of CEC2011 test suite optimization problems and in 100% of engineering design problems. In addition, the efficiency of BOA to handle SCM applications has been challenged to solve ten case studies in the field of sustainable lot size optimization. The findings show that BOA has successfully provided superior performance in 100% of the case studies compared to competitor algorithms. [ABSTRACT FROM AUTHOR]

This research presents a novel nature-inspired metaheuristic algorithm called Frilled Lizard Optimization (FLO), which emulates the unique hunting behavior of frilled lizards in their natural habitat. FLO draws its inspiration from the sit-and-wait hunting strategy of these lizards. The algorithm's core principles are meticulously detailed and mathematically structured into two distinct phases: (i) an exploration phase, which mimics the lizard's sudden attack on its prey, and (ii) an exploitation phase, which simulates the lizard's retreat to the treetops after feeding. To assess FLO's efficacy in addressing optimization problems, its performance is rigorously tested on fifty-two standard benchmark functions. These functions include unimodal, high-dimensional multimodal, and fixed-dimensional multimodal functions, as well as the challenging CEC 2017 test suite. FLO's performance is benchmarked against twelve established metaheuristic algorithms, providing a comprehensive comparative analysis. The simulation results demonstrate that FLO excels in both exploration and exploitation, effectively balancing these two critical aspects throughout the search process. This balanced approach enables FLO to outperform several competing algorithms in numerous test cases. Additionally, FLO is applied to twenty-two constrained optimization problems from the CEC 2011 test suite and four complex engineering design problems, further validating its robustness and versatility in solving real-world optimization challenges. Overall, the study highlights FLO's superior performance and its potential as a powerful tool for tackling a wide range of optimization problems. [ABSTRACT FROM AUTHOR]

Supply Chain (SC) Optimization is a key activity in today's industry with the goal of increasing operational efficiency, reducing costs, and improving customer satisfaction. Traditional optimization methods often struggle to effectively use resources while handling complex and dynamic Supply chain networks. This paper introduces a novel biomimetic metaheuristic algorithm called the Wombat Optimization Algorithm (WOA) for supply chain optimization. This algorithm replicates the natural behaviors observed in wombats living in the wild, particularly focusing on their foraging tactics and evasive maneuvers towards predators. The theory of WOA is described and then mathematically modeled in two phases: (i) exploration based on the simulation of wombat movements during foraging and trying to find food and (ii) exploitation based on simulating wombat movements when diving towards nearby tunnels to defend against its predators. The effectiveness of WOA in addressing optimization challenges is assessed by handling the CEC 2017 test suite across various problem dimensions, including 10, 30, 50, and 100. The findings of the optimization indicate that WOA demonstrates a strong ability to effectively manage exploration and exploitation, and maintains a balance between them throughout the search phase to deliver optimal solutions for optimization problems. A total of twelve well-known metaheuristic algorithms are called upon to test their performance against WOA in the optimization process. The outcomes of the simulations reveal that WOA outperforms the other algorithms, achieving superior results across most benchmark functions and securing the top ranking as the most efficient optimizer. Using a Wilcoxon rank sum test statistical analysis, it has been proven that WOA outperforms other algorithms significantly. WOA is put to the test with twenty-two constrained optimization problems from the CEC 2011 test suite and four engineering design problems to showcase its ability to solve real-world optimization problems. The results of the simulations demonstrate that WOA excels in real-world applications by delivering superior solutions and outperforming its competitors. [ABSTRACT FROM AUTHOR]

As a nature-inspired metaheuristic method, the firefly algorithm (FA) arises more attentions in academic and engineering fields. However, too much attraction in FA's global attraction model leads to low computational efficiency, and the stochastic model with fixed randomization parameter is hard to balance the exploitation and exploration of the algorithm. Thus, FA still needs improvement to deal with complex engineering problems. An integrated firefly algorithm (IFA) that combines two novel attractive models with a new stochastic model is proposed to improve the standard FA. Firstly, the attractive model and stochastic model of standard FA are investigated through theoretical analysis and numerical experiments. And the factors that affect the computational efficiency and accuracy of FA are revealed. Based on the analysis results, two new fitness-based update formulas for attractiveness parameter are constructed to avoid the invalidation. The proposed virtual attractive model and global best attractive model can reduce the computation complexity and enhance the exploitation ability. Moreover, an adaptive strategy is presented for the stochastic model to achieve a better balance between exploitation and exploration. The nonlinearly decreased model for the update of parameter α can adjust the population diversity through the iteration and ensure the convergence. Additionally, an adaptive penalty function method is developed to handle the constraints effectively. Then, the initial parameters are tested, and the best initial parameters corresponding to the optimal performance of IFA are obtained. The proposed algorithm is evaluated by CEC2015 hybrid composition and a set of classical functions. The numerical experimental results show that the proposed techniques can enhance the solution accuracy and accelerate the convergence speed. Finally, IFA and other metaheuristic algorithms are applied to solve five engineering design optimization problems with mixed variables and multiple constraint conditions. The results indicate that IFA with adaptive penalty function needs fewer fitness evaluations and costs less computational time to obtain the optimal solutions. Furthermore, it exhibits better accuracy and robustness than other algorithms. [ABSTRACT FROM AUTHOR]

A new bio-inspired metaheuristic algorithm named the Pufferfish Optimization Algorithm (POA), that imitates the natural behavior of pufferfish in nature, is introduced in this paper. The fundamental inspiration of POA is adapted from the defense mechanism of pufferfish against predators. In this defense mechanism, by filling its elastic stomach with water, the pufferfish becomes a spherical ball with pointed spines, and as a result, the hungry predator escapes from this threat. The POA theory is stated and then mathematically modeled in two phases: (i) exploration based on the simulation of a predator's attack on a pufferfish and (ii) exploitation based on the simulation of a predator's escape from spiny spherical pufferfish. The performance of POA is evaluated in handling the CEC 2017 test suite for problem dimensions equal to 10, 30, 50, and 100. The optimization results show that POA has achieved an effective solution with the appropriate ability in exploration, exploitation, and the balance between them during the search process. The quality of POA in the optimization process is compared with the performance of twelve well-known metaheuristic algorithms. The simulation results show that POA provides superior performance by achieving better results in most of the benchmark functions in order to solve the CEC 2017 test suite compared to competitor algorithms. Also, the effectiveness of POA to handle optimization tasks in real-world applications is evaluated on twenty-two constrained optimization problems from the CEC 2011 test suite and four engineering design problems. Simulation results show that POA provides effective performance in handling real-world applications by achieving better solutions compared to competitor algorithms. [ABSTRACT FROM AUTHOR]

The biogeography-based optimization (BBO) algorithm is known for its simplicity and low computational overhead, but it often struggles with falling into local optima and slow convergence speed. Against this background, this work presents a multi-strategy enhanced BBO variant, named MSBBO. Firstly, the example chasing strategy is proposed to eliminate the destruction of the inferior solutions to superior solutions. Secondly, the heuristic crossover strategy is designed to enhance the search ability of the population. Finally, the prey search–attack strategy is used to balance the exploration and exploitation. To verify the performance of MSBBO, we compare it with standard BBO, seven BBO variants (PRBBO, BBOSB, HGBBO, FABBO, BLEHO, MPBBO and BBOIMAM) and seven meta-heuristic algorithms (GWO, WOA, SSA, ChOA, MPA, GJO and BWO) on multiple dimensions of 24 benchmark functions. It concludes that MSBBO significantly outperforms all competitors both on convergence accuracy, speed and stability, and MSBBO basically converges to the same results on 10,000 dimensions as on 1000 dimensions. Further, MSBBO is applied to six real-world engineering design problems. The experimental results show that our work is still more competitive than other latest optimization techniques (COA, EDO, OMA, SHO and SCSO) on constrained optimization problems. [ABSTRACT FROM AUTHOR]

In this paper, a new bio-inspired metaheuristic algorithm named the Kookaburra Optimization Algorithm (KOA) is introduced, which imitates the natural behavior of kookaburras in nature. The fundamental inspiration of KOA is the strategy of kookaburras when hunting and killing prey. The KOA theory is stated, and its mathematical modeling is presented in the following two phases: (i) exploration based on the simulation of prey hunting and (ii) exploitation based on the simulation of kookaburras' behavior in ensuring that their prey is killed. The performance of KOA has been evaluated on 29 standard benchmark functions from the CEC 2017 test suite for the different problem dimensions of 10, 30, 50, and 100. The optimization results show that the proposed KOA approach, by establishing a balance between exploration and exploitation, has good efficiency in managing the effective search process and providing suitable solutions for optimization problems. The results obtained using KOA have been compared with the performance of 12 well-known metaheuristic algorithms. The analysis of the simulation results shows that KOA, by providing better results in most of the benchmark functions, has provided superior performance in competition with the compared algorithms. In addition, the implementation of KOA on 22 constrained optimization problems from the CEC 2011 test suite, as well as 4 engineering design problems, shows that the proposed approach has acceptable and superior performance compared to competitor algorithms in handling real-world applications. [ABSTRACT FROM AUTHOR]

This work presents a new nature-inspired meta-heuristic algorithm named spider wasp optimization (SWO) algorithm, which is based on replicating the hunting, nesting, and mating behaviors of the female spider wasps in nature. This proposed algorithm has various unique updating strategies, making it applicable to a wide range of optimization problems with different exploration and exploitation requirements. The proposed SWO is compared with nine newly published and well-established metaheuristics over four different benchmarks: (1) Standard benchmark, including 23 unimodal and multimodal test functions; (2) test suite of CEC2017, (3) test suite of CEC2020, and (4) test suite of CEC2014 to validate its reliability. Moreover, two classical engineering design problems, namely, welded bean and pressure vessel designs, and parameter estimation of the single-diode, double-diode, and triple-diode photovoltaic models are used to further evaluate the performance of SWO in optimizing real-world optimization problems. Experimental findings demonstrate that SWO is more competitive compared with the state-of-art meta-heuristic methods for four validated benchmarks and superior to all observed real-world optimization problems. Specifically, SWO achieves an overall effective percentage of 78.2% on the standard benchmark, 92.31% on CEC2014, 77.78% on CEC2017, 60% on CEC2020, and 100% on real-world problems. The source code of SWO is publicly available at https://www.mathworks.com/matlabcentral/fileexchange/126010-spider-wasp-optimizer-swo. [ABSTRACT FROM AUTHOR]

The Mayfly Optimization Algorithm (MOA), as a new biomimetic metaheuristic algorithm with superior algorithm framework and optimization methods, plays a remarkable role in solving optimization problems. However, there are still shortcomings of convergence speed and local optimization in this algorithm. This paper proposes a metaheuristic algorithm for continuous and constrained global optimization problems, which combines the MOA, the Aquila Optimizer (AO), and the opposition-based learning (OBL) strategy, called AOBLMOA, to overcome the shortcomings of the MOA. The proposed algorithm first fuses the high soar with vertical stoop method and the low flight with slow descent attack method in the AO into the position movement process of the male mayfly population in the MOA. Then, it incorporates the contour flight with short glide attack and the walk and grab prey methods in the AO into the positional movement of female mayfly populations in the MOA. Finally, it replaces the gene mutation behavior of offspring mayfly populations in the MOA with the OBL strategy. To verify the optimization ability of the new algorithm, we conduct three sets of experiments. In the first experiment, we apply AOBLMOA to 19 benchmark functions to test whether it is the optimal strategy among multiple combined strategies. In the second experiment, we test AOBLMOA by using 30 CEC2017 numerical optimization problems and compare it with state-of-the-art metaheuristic algorithms. In the third experiment, 10 CEC2020 real-world constrained optimization problems are used to demonstrate the applicability of AOBLMOA to engineering design problems. The experimental results show that the proposed AOBLMOA is effective and superior and is feasible in numerical optimization problems and engineering design problems. [ABSTRACT FROM AUTHOR]

The Competitive Swarm Optimizer (CSO) has emerged as a prominent technique for solving intricate optimization problems by updating only half of the population in each iteration. Despite its effectiveness, the CSO algorithm often exhibits a slow convergence rate and a tendency to become trapped in local optimal solutions, as is common among metaheuristic algorithms. To address these challenges, this paper proposes a hybrid approach combining the CSO with the Salp Swarm algorithm (SSA), CL-SSA, to increase the convergence rate and enhance search space exploration. The proposed approach involves a two-step process. In the first step, a pairwise competition mechanism is introduced to segregate the solutions into winners and losers. The winning population is updated through strong exploitation using the SSA algorithm. In the second step, non-winning solutions learn from the winners, achieving a balance between exploration and exploitation. The performance of the CL-SSA is evaluated on various benchmark functions, including the CEC2017 benchmark with dimensions 50 and 100, the CEC2008lsgo benchmark with dimensions 200, 500 and 1000, as well as a set of seven well-known constrained design challenges in various engineering domains defined in the CEC2020 conference. The CL-SSA is compared to other metaheuristics and advanced algorithms, and its results are analyzed through statistical tests such as the Friedman and Wilcoxon rank-sum tests. The statistical analysis demonstrates that the CL-SSA algorithm exhibits improved exploitation, exploration, and convergence patterns compared to other algorithms, including SSA and CSO, as well as popular algorithms. Furthermore, the proposed hybrid approach performs better in solving most test functions. [ABSTRACT FROM AUTHOR]

• A new metaheuristic algorithm named arctic puffin optimization (APO) was proposed. • The APO algorithm simulates the aerial flight and underwater foraging behavior of arctic puffins. • APO was assessed using 51 test problems and 6 engineering design problems. • APO is compared with nine published over different benchmarks problems. • APO is superior to comparative algorithms in testing functions, especially in hybrid functions. In this paper, we innovatively propose the Arctic Puffin Optimization (APO), a metaheuristic optimization algorithm inspired by the survival and predation behaviors of the Arctic puffin. The APO consists of an aerial flight (exploration) and an underwater foraging (exploitation) phase. In the exploration phase, the Levy flight and velocity factor mechanisms are introduced to enhance the algorithm's ability to jump out of local optima and improve the convergence speed. In the exploitation phase, strategies such as the synergy and adaptive change factors are used to ensure that the algorithm can effectively utilize the current best solution and guide the search direction. In addition, the dynamic transition between the exploration and development phases is realized through the behavioral conversion factor, which effectively balances global search and local development. In order to verify the advancement and applicability of the APO algorithm, it is compared with nine advanced optimization algorithms. In the three test sets of CEC2017, CEC2019, and CEC2022, the APO algorithm outperforms the other compared algorithms in 72%, 70%, and 75% of the cases, respectively. Meanwhile, the Wilcoxon signed-rank test results and Friedman rank-mean statistically prove the superiority of the APO algorithm. Furthermore, on thirteen real-world engineering problems, APO outperforms the other compared algorithms in 85% of the test cases, demonstrating its potential in solving complex real-world optimization problems. In summary, APO proves its practical value and advantages in solving various complex optimization problems by its excellent performance. [ABSTRACT FROM AUTHOR]

Several constrained optimization problems have been adequately solved over the years thanks to the advances in the area of metaheuristics. Nevertheless, the question as to which search logic performs better on constrained optimization often arises. In this paper, we present Dual Search Optimization (DSO), a co-evolutionary algorithm that includes an adaptive penalty function to handle constrained problems. Compared to other self-adaptive metaheuristics, one of the main advantages of DSO is that it is able auto-construct its own perturbation logics, i.e., the ways solutions are modified to create new ones during the optimization process. This is accomplished by co-evolving the solutions (encoded as vectors of integer/real values) and perturbation strategies (encoded as Genetic Programming trees), in order to adapt the search to the problem. In addition to that, the adaptive penalty function allows the algorithm to handle constraints very effectively, yet with a minor additional algorithmic overhead. We compare DSO with several algorithms from the state-of-the-art on two sets of problems, namely: (1) seven well-known constrained engineering design problems and (2) the CEC 2017 benchmark for constrained optimization. Our results show that DSO can achieve state-of-the-art performances, being capable to automatically adjust its behavior to the problem at hand. [ABSTRACT FROM AUTHOR]

To enhance the optimization ability of the satin bowerbird optimization (SBO) algorithm, in this paper, a novel quantum-inspired SBO with Bloch spherical search is proposed. In this algorithm, satin bowerbirds are encoded using qubits described on the Bloch sphere, each satin bowerbird occupies three locations in the search space and each location represents an optimization solution. Using the search method of general SBO to adjust the two parameters of the qubit, qubit rotation is performed on the Bloch sphere, which simultaneously updates the three locations occupied by a qubit and quickly approaches the global optimal solution. Finally, the experimental results of five examples of structural engineering design show that the proposed algorithm is superior to other state-of-the-art metaheuristic algorithms in terms of the performance measures. [ABSTRACT FROM AUTHOR]

Optimization problems have numerous real-life applications in science and engineering. The engineering design problems are usually subject to various constraints. Although many state-of-the-art metaheuristic optimization algorithms have been developed during the last decades, these algorithms require additional constraint-handling mechanisms to cope with constrained optimization problems. Therefore, selecting a suitable constraint-handling mechanism requires extensive trial-and-error experiments, which is time-consuming and demanding. In this study, a comparative analysis of the eight constraint handling mechanisms is carried out, guiding decision-makers in their optimization practices. The constraint-handling techniques are used along with the Whale Optimization Algorithm (WOA), and 19 real-life mechanical design problems, which are also part of the CEC2020 benchmark suite, are tested in the experimental analysis. The nonparametric statistical analysis incorporating Nemenyi and Holm post-hoc procedures shows that the inverse tangent constraint-handling and eclectic penalty methods exhibit high performance in real-life mechanical design problems. [ABSTRACT FROM AUTHOR]

Purpose: In line with computational technological advances, obtaining optimal solutions for engineering problems has become attractive research topics in various disciplines and real engineering systems having multiple objectives. Therefore, it is aimed to ensure that the multiple objectives are simultaneously optimized by considering them among the trade-offs. Furthermore, the practical means of solving those problems are principally concentrated on handling various complicated constraints. The purpose of this paper is to suggest an algorithm based on symbiotic organisms search (SOS), which mimics the symbiotic reciprocal influence scheme adopted by organisms to live on and breed within the ecosystem, for constrained multi-objective engineering design problems. Design/methodology/approach: Though the general performance of SOS algorithm was previously well demonstrated for ordinary single objective optimization problems, its efficacy on multi-objective real engineering problems will be decisive about the performance. The SOS algorithm is, hence, implemented to obtain the optimal solutions of challengingly constrained multi-objective engineering design problems using the Pareto optimality concept. Findings: Four well-known mixed constrained multi-objective engineering design problems and a real-world complex constrained multilayer dielectric filter design problem are tackled to demonstrate the precision and stability of the multi-objective SOS (MOSOS) algorithm. Also, the comparison of the obtained results with some other well-known metaheuristics illustrates the validity and robustness of the proposed algorithm. Originality/value: The algorithmic performance of the MOSOS on the challengingly constrained multi-objective multidisciplinary engineering design problems with constraint-handling approach is successfully demonstrated with respect to the obtained outperforming final optimal designs. [ABSTRACT FROM AUTHOR]

This study tenders a new nature-inspired metaheuristic algorithm (MA) based on the behavior of the Genghis Khan shark (GKS), called GKS optimizer (GKSO), which is used for numerical optimization and engineering design. The inspiration for GKSO comes from the predation and survival behavior of GKS, and the entire optimization process is achieved by simulating four different activities of GKS, including hunting (exploration), movement (exploitation), foraging (switch from exploration to exploitation), and self-protection mechanism. These operators are mimicked using various mathematical models to efficiently perform optimization tasks of agents in different regions of the search space. In an effort to validate this method's viability and superiority, an in-depth analysis of the proposed GKSO is carried out from both qualitative and quantitative perspectives. Qualitative analysis verifies that GKSO has good exploration and exploitation (ENE) capability. Simultaneously, GKSO is quantitatively analyzed with eight existing fish optimization algorithms and the other nine well-known MAs on CEC2019 and CEC2022, respectively. Among them, a series of experimental scenarios are conducted to validate the applicability and robustness of GKSO by exploring its performance for CEC2022 at different dimensions and maximum fitness evaluation quantity. Statistical results indicate that GKSO has a strong advantage in the competition between two different types of algorithms. Furthermore, five different kinds of real-world constrained optimization problems (OPs) in CEC2020 benchmark constrained optimization functions, including 50 engineering case suites, are selected to evaluate GKSO's performance and the other seven optimizers, further validating GKSO's extensive usefulness and validity in solving practical complex problems. [ABSTRACT FROM AUTHOR]

This paper proposes a multi-objective version of recently developed Spotted Hyena Optimizer (SHO) called Multi-objective Spotted Hyena Optimizer (MOSHO). It is used to optimize the multiple objectives problems. In the proposed algorithm, a fixed-sized archive is employed for storing the non-dominated Pareto optimal solutions. The roulette wheel mechanism is used to select the effective solutions from archive to simulate the social and hunting behaviors of spotted hyenas. The proposed algorithm is tested on 24 benchmark test functions and compared with six recently developed metaheuristic algorithms. The proposed algorithm is then applied on six constrained engineering design problems to demonstrate its applicability on real-life problems. The experimental results reveal that the proposed algorithm performs better than the others and produces the Pareto optimal solutions with high convergence. [ABSTRACT FROM AUTHOR]

Metaheuristic algorithms are proven to be more effective on finding global optimum in numerous problems including the constrained optimization area. The algorithms have the capacity to prevail over many deficiencies in conventional algorithms. Besides of good quality of performance, some metaheuristic algorithms have limitations that may deteriorate by certain degree of difficulties especially in real-world application. Most of the real-world problems consist of constrained problem that is significantly important in modern engineering design and must be considered in order to perform any optimization task. Therefore, it is essential to compare the performance of the algorithm in diverse level of difficulties in constrained region. This paper introduces Tree Physiology Optimization (TPO) algorithm for solving constrained optimization problem and compares the performance with other existing metaheuristic algorithms. The constrained problems that are included in the comparison are three engineering design and nonlinear mathematic problems. The difficulties of each proposed problem are the function complexity, number of constraints, and dimension of variables. The performance measure of each algorithm is the statistical results of finding the global optimum and the convergence towards global optimum. [ABSTRACT FROM AUTHOR]

This paper presents a novel metaheuristic algorithm named as Spotted Hyena Optimizer (SHO) inspired by the behavior of spotted hyenas. The main concept behind this algorithm is the social relationship between spotted hyenas and their collaborative behavior. The three basic steps of SHO are searching for prey, encircling, and attacking prey and all three are mathematically modeled and implemented. The proposed algorithm is compared with eight recently developed metaheuristic algorithms on 29 well-known benchmark test functions. The convergence and computational complexity is also analyzed. The proposed algorithm is applied to five real-life constraint and one unconstrained engineering design problems to demonstrate their applicability. The experimental results reveal that the proposed algorithm performs better than the other competitive metaheuristic algorithms. [ABSTRACT FROM AUTHOR]

The present study aims to optimize the engineering design and manufacturing problems with a novel hybrid optimizer named: AOA-NM (Arithmetic optimization-Nelder mead). To overcome the local optima trap shortcoming and improve the solution quality of a recently introduced arithmetic optimization algorithm (AOA), the Nelder–Mead local search methodology has been incorporated into the basic AOA framework. The objective of the proposed hybridization approach was to facilitate the refinement of the exploration–exploitation behaviour of the AOA search. In the numerical validation stage, numerous multidimensional benchmarks from the CEC2020 were used as challenging testing functions to investigate the suggested AOA-NM optimizer. To investigate the viability of the proposed hybridized algorithm in real-world applications, it is investigated for ten constrained engineering design problems, and the performance was contrasted with other distinguished metaheuristics extracted from the literature. Additionally, a hands-on manufacturing problem of milling process parameter optimization and vehicle structure shape optimization is posed and solved at the forefront to evaluate both AOA and AOA-NM efficacy. The proficiency of the AOA-NM algorithm, in terms of both solution quality and stability, is confirmed by performed comparative analysis and found to be robust in handling challenging practical issues. • A novel hybrid arithmetic optimization algorithm is developed and applied to challenging engineering optimization problems. • Theoretical and numerical comparisons are extensively investigated. • The results show the merits of the proposed hybrid method used in solving the real-world case studies. [ABSTRACT FROM AUTHOR]

• The population is divided into three sub-populations. • A novel population evolution strategy is introduced to improve the basic WOA. • The proposed algorithm (MEWOA) has high solution accuracy and converges fast. • CEC 2019 test suite and 30 benchmark functions are used to test MEWOA. • MEWOA is applied to four engineering design problems. The whale optimization algorithm (WOA) tends to suffer from slow convergence speed and quickly falling into the local optimum. In this work, a WOA variant is proposed based on multi-population evolution (MEWOA) to address these problems. Firstly, individuals are classified into three equal-sized sub-populations: exploratory sub-population, exploitative sub-population, and modest sub-population, according to their fitness. Secondly, the moving strategies of each sub-population are assigned using different mechanisms. The exploratory and exploitative sub-populations perform global and local search, respectively, while the modest sub-population randomly explores or exploits the search space. Finally, we introduce a novel population evolution strategy to help MEWOA improve its global optimization ability and avoid local optimum. MEWOA is compared with five state-of-the-art WOA variants and seven basic metaheuristic algorithms over 30 benchmark functions with dimensions of 100, 500, 1000, and 2000 respectively. It is observed that MEWOA achieves faster convergence speed, shows shorter runtime, and provides higher solution accuracy than other algorithms on the majority of benchmark functions. In addition, we tested MEWOA's ability to solve challenging real-world and constrained optimization problems on the CEC 2019 test suite and four engineering design problems. The experimental results demonstrate the competitiveness and merits of the proposed MEWOA algorithm. [ABSTRACT FROM AUTHOR]

This work presents a novel nature-inspired metaheuristic called Nutcracker Optimization Algorithm (NOA) inspired by Clark's nutcrackers. The nutcrackers exhibit two distinct behaviors that occur at separate periods. The first behavior, which occurs during the summer and fall seasons, represents the nutcracker's search for seeds and subsequent storage in an appropriate cache. During the winter and spring seasons, another behavior based on the spatial memory strategy is regarded to search for the hidden caches marked at different angles using various objects or markers as reference points. If the nutcrackers cannot find the stored seeds, they will randomly explore the search space to find their food. NOA is herein proposed to mimic these various behaviors to present a new, robust metaheuristic algorithm with different local and global search operators, allowing it to solve various optimization problems with better outcomes. NOA is evaluated on twenty-three standard test functions, test suites of CEC-2014, CEC-2017, and CEC-2020 and five real-world engineering design problems. NOA is compared with three classes of existing optimization algorithms: (1) SMA, GBO, EO, RUN, AVOA, RFO, and GTO as recently-published algorithms, (2) SSA, WOA, and GWO as highly-cited algorithms, and (3) AL-SHADE, L-SHADE, LSHADE-cnEpSin, and LSHADE-SPACMA as highly-performing optimizers and winners of CEC competition. NOA was ranked first among all methods and demonstrated superior results when compared to LSHADE-cnEpSin and LSHADE-SPACMA as the best-performing optimizers and the winners of CEC-2017, and AL-SHADE and L-SHADE as the winners of CEC-2014. • Nutcracker optimization algorithm (NOA) is a nature-inspired algorithm. • NOA is mimicking the search, cache, and recovery behaviors of nutcrackers. • NOA is tested against test functions and five engineering design problems. • NOA is compared to other well-known optimization algorithms. • Results and statistical analysis demonstrated superiority of the proposed NOA. [ABSTRACT FROM AUTHOR]

• Weighted-leader Search (WLS) utilizes multiple top solutions to evolve population. • WLS develops a simple framework containing four search mechanisms to balance exploration and exploitation. • In CEC tests and large-scale tests, WLS exhibits an outstanding ability among the multiple state-of-the-art methods in terms of accuracy and efficiency. • WLS is successfully applied in addressing the real-world optimization application of coordinated 4D path planning of UAV swarm. Aiming at the robustness and real-time requirements of engineering applications, this paper develops a novel metaheuristic algorithm with a simple mathematical framework for numerical optimization, namely the weighted-leader search (WLS). With the WLS, a weighted mean point of the top solutions is developed to evolve the population. Additionally, several simple local search mechanisms are introduced to prevent the algorithm from premature convergence. Moreover, the WLS possesses fewer constant coefficients to reduce the parameter sensitivity. The performance of the WLS is evaluated with the CEC 2017 test suite with 10D, 30D, 50D and 100D problems, the CEC 2008 test suite with 100D, 500D and 1000D problems, large-scale benchmarks with 100D, 500D and 1000D (or beyond) problems and constrained engineering design problems. The statistical results of the experiments indicate that the WLS exhibits an outstanding ability among the state-of-the art algorithms in different competitions, which verifies the accuracy and efficiency of our algorithm in solving complex problems, as well as its robustness in large-scale evaluation. Moreover, the WLS is employed to address the cooperative path planning problem of an unmanned aircraft vehicle (UAV) swarm with 100 members. Through problem model construction, the path planning issue is transformed into a constrained optimization problem and solved by the WLS. The experimental results show that the proposed WLS is able to solve the path planning problem in real time within the constraints and significantly outperforms the other competitors, demonstrating the accuracy and time savings of the algorithm in solving real-world optimization problems. [ABSTRACT FROM AUTHOR]

The policy of balance between exploration capability and exploitation capability directly affects the solution performance of the meta -heuristic algorithm in a limited time. In order to better balance the exploration and exploitation capabilities of the algorithm and meet the solution requirements of complex real-world problems, the adaptive balance optimization algorithm (ABOA) is proposed in this paper. The algorithm consists of a global search phase (GSP) and a local search phase (LSP) and is controlled by a fixed parameter. ABOA not only considers the balance of exploration and exploitation capabilities of the algorithm throughout the whole iterative process but also focuses on the balance of exploration and exploitation in both GSP and LSP. The search in both phases is focused around the respective search centers from outside to inside. ABOA balances the exploration and exploitation capabilities of the algorithm throughout the search process by two adaptive policies: changing the search area and changing the search center. Fifty-two unconstrained benchmark test functions were employed to evaluate the performance of ABOA. The results of ABOA were compared with nine excellent optimization algorithms available in the literature. The statistical results and Friedman test showed that ABOA was significantly competitive. Finally, the results of the examined engineering design problems showed that ABOA can solve the constrained optimization problem better compared to other methods. [ABSTRACT FROM AUTHOR]

Tree-Seed Algorithm is a kind of swarm intelligence optimization algorithm. It is used to solve various problems widely, but it still has some shortcomings need to be overcame, such as imbalance between exploration and exploitation, local stagnation, premature convergence, and so on. In this study, an enhanced meta-heuristic optimization algorithm, called Migration Tree-Seed Algorithm (MTSA), is proposed inspiring by Grey Wolf Optimizer (GWO). The hierarchical gravity learning and random-based migration mechanisms are introduced to overcome the intrinsic defects of the basic TSA. Firstly, hierarchy mechanism ensures the tree migration to guide the seed generation avoiding the local stagnation. Secondly, random-based migration mechanism increases the seed diversity to improve the exploration ability. Finally, the coordinated update of the two mechanisms actuate a suitable trade-off between exploration ans exploitation. We use IEEE CEC 2014 benchmark functions to compare MTSA with basic TSA, the TSA variants (STSA, EST-TSA, fb_TSA), GWO, ABC, SCA, BOA, JAYA and RSA. MTSA is subsequently applied to three classical engineering design problems reported in the specialized literature. Both results show that the MTSA is very competitive and effective compared with other well-known meta-heuristics, proving its excellent applicability in real-world challenging problems with unknown search spaces. • A modified MTSA is proposed based on the hierarchy mechanism of the GWO and random-based migration mechanism. • Procedure of updating seeds positions allows obtaining neighbouring solutions in terms of α , β , and δ trees for mostly promoting exploitation. • The proposed enhanced MTSA is evaluated using 30 benchmark functions in IEEE CEC 2014 and applying in three engineering problems. • The experimental results were superior to some well-known or variant algorithms in continuous optimization domain. [ABSTRACT FROM AUTHOR]

Abstract: Several constrained and unconstrained optimization problems have been adequately solved over the years thanks to advances in the metaheuristics area. In the last decades, different metaheuristics have been proposed employing new ideas, and hybrid algorithms that improve the original metaheuristics have been developed. One of the most successfully employed metaheuristics is the Differential Evolution. In this paper it is proposed a Multi-View Differential Evolution algorithm (MVDE) in which several mutation strategies are applied to the current population to generate different views at each iteration. The views are then merged according to the winner-takes-all paradigm, resulting in automatic exploration/exploitation balance. MVDE was tested to solve a set of well-known constrained engineering design problems and the obtained results were compared to those from many state-of-the-art metaheuristics. Results show that MVDE was very competitive in the considered problems, largely outperforming several of the compared algorithms. [Copyright &y& Elsevier]

A new algorithm, Material Generation Algorithm (MGA), was developed and applied for the optimum design of engineering problems. Some advanced and basic aspects of material chemistry, specifically the configuration of chemical compounds and chemical reactions in producing new materials, are determined as inspirational concepts of the MGA. For numerical investigations purposes, 10 constrained optimization problems in different dimensions of 10, 30, 50, and 100, which have been benchmarked by the Competitions on Evolutionary Computation (CEC), are selected as test examples while 15 of the well-known engineering design problems are also determined to evaluate the overall performance of the proposed method. The best results of different classical and new metaheuristic optimization algorithms in dealing with the selected problems were taken from the recent literature for comparison with MGA. Additionally, the statistical values of the MGA algorithm, consisting of the mean, worst, and standard deviation, were calculated and compared to the results of other metaheuristic algorithms. Overall, this work demonstrates that the proposed MGA is able provide very competitive, and even outstanding, results and mostly outperforms other metaheuristics. [ABSTRACT FROM AUTHOR]

Benefiting from population, randomness and simple structures, metaheuristic methods show excellent performance for solving global optimization problems. However, in some cases, in order to get promising solutions, the existing metaheuristic methods usually need to be modified. This work reports a new technique, called specular reflection learning, for improving the optimization performance of metaheuristic methods. Specular reflection learning is motivated by specular reflection phenomenon in physics. Note that, there is a close relationship between opposition-based learning and specular reflection learning. Opposition-based learning can be seen as a special case of specular reflection learning. In order to investigate the effectiveness of specular reflection learning, specular reflection learning is employed to improve backtracking search algorithm (BSA). The performance of the proposed backtracking search algorithm with specular reflection learning is evaluated by 88 test functions extracted from the well-known CEC 2013, CEC 2014 and CEC 2017 test suites, and two constrained engineering design problems. Experimental results confirm that specular reflection learning is a more effective technique for improving BSA compared with opposition-based learning, which establishes the foundation for the applications of specular reflection learning on other metaheuristics. In addition, the source code of this work can be found from https://www.mathworks.com/matlabcentral/fileexchange/79030-bsa_srl. • The specular reflection learning model is built. • A new variant of BSA, called BSA_SRL, is proposed for global optimization. • BSA_SRL is used for solving CEC 2013, CEC 2014 and CEC 2017 test suites. • BSA_SRL is evaluated by constrained engineering optimization problems. [ABSTRACT FROM AUTHOR]

In this research, an easy-to-use particle swarm optimizer (PSO) for solving constrained engineering design problems involving mixed-integer-discrete-continuous (MIDC) variables that adopt two kinds of diversity-enhancing mechanisms to achieve superior reliability and validity was developed. As an initial diversity-boosting tool, the local neighborhood topology of each particle is set up such that information exchange is restricted to a limited number of consecutively numbered particles. This topological mechanism forces each particle to move in the search space while interacting only with its neighboring subpopulation. The second diversity-enhancing task is to ensure that the exploration behavior of each particle in the search space is governed such that it follows the diversity classifier decision applied to its subpopulation. This diversity classification iteratively adjusts the three-phase velocity-related mechanism of each particle such that it approaches or retreats from its previous best position/the current best position among the subpopulation. In summary, this PSO tool not only introduces the social interaction of the particle within its cyclically neighboring subpopulation but also exploits the three-phase velocity behavior law governed by the distributed diversity measures categorized for each neighboring subpopulation. This scheme has superior reliability, as well as high practicality for engineering optimization problems involving MIDC variables, which are handled by the widely adopted straightforward rounding-off technique used in most swarm-inspired metaheuristic search technologies. [ABSTRACT FROM AUTHOR]

This paper introduces a bio-inspired metaheuristic optimization algorithm named Tunicate Swarm Algorithm (TSA). The proposed algorithm imitates jet propulsion and swarm behaviors of tunicates during the navigation and foraging process. The performance of TSA is evaluated on seventy-four benchmark test problems employing sensitivity, convergence and scalability analysis along with ANOVA test. The efficacy of this algorithm is further compared with several well-regarded metaheuristic approaches based on the generated optimal solutions. In addition, we also executed the proposed algorithm on six constrained and one unconstrained engineering design problems to further verify its robustness. The simulation results demonstrate that TSA generates better optimal solutions in comparison to other competitive algorithms and is capable of solving real case studies having unknown search spaces. Note that the source codes of the proposed TSA algorithm are available at [ABSTRACT FROM AUTHOR]

This paper is devoted to the implementation and application of an improved version of the metaheuristic algorithm called magnetic charged system search. Some modifications and novelties are introduced and tested. Firstly, the authors' attempt is to develop a self-adaptive and user-friendly algorithm which can automatically set all the preliminary parameters (such as the numbers of particles, the maximum iterations number) and the internal coefficients. Indeed, some mathematical laws are proposed to set the parameters and many coefficients can dynamically change during the optimization process based on the verification of internal conditions. Secondly, some strategies are suggested to enhance the performances of the proposed algorithm. A chaotic local search is introduced to improve the global best particle of each iteration by exploiting the features of ergodicity and randomness. Moreover, a novel technique is proposed to handle bad-defined boundaries; in fact, the possibility to self-enlarge the boundaries of the optimization variables is considered, allowing to achieve the global optimum even if it is located on the boundaries or outside. The algorithm is tested through some benchmark functions and engineering design problems, showing good results, followed by an application regarding the problem of time-suboptimal manoeuvres for satellite formation flying, where the inverse dynamics technique, together with the B-splines, is employed. This analysis proves the ability of the proposed algorithm to optimize control problems related to space engineering, obtaining better results with respect to more common and used algorithms in literature. • The Improved Magnetic Charged System Search Algorithm is developed and described. • Internal coefficients can automatically adapt to different problems. • Several benchmark functions are tested to verify the algorithm robustness. • A satellite formation flying test is performed to validate the algorithm. • The results demonstrate the validity of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Firefly-Algorithm (FA) is an eminent nature-inspired swarm-based technique for solving numerous real world global optimization problems. This paper presents an overview of the constraint handling techniques. It also includes a hybrid algorithm, namely the Stochastic Ranking with Improved Firefly Algorithm (SRIFA) for solving constrained real-world engineering optimization problems. The stochastic ranking approach is broadly used to maintain balance between penalty and fitness functions. FA is extensively used due to its faster convergence than other metaheuristic algorithms. The basic FA is modified by incorporating opposite-based learning and random-scale factor to improve the diversity and performance. Furthermore, SRIFA uses feasibility based rules to maintain balance between penalty and objective functions. SRIFA is experimented to optimize 24 CEC 2006 standard functions and five well-known engineering constrained-optimization design problems from the literature to evaluate and analyze the effectiveness of SRIFA. It can be seen that the overall computational results of SRIFA are better than those of the basic FA. Statistical outcomes of the SRIFA are significantly superior compared to the other evolutionary algorithms and engineering design problems in its performance, quality and efficiency. [ABSTRACT FROM AUTHOR]