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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]

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]

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]

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]