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Hybrid metaheuristics is one of the most exciting improvements in optimization and metaheuristic algorithms. A current research topic combines two algorithms to provide a more advanced solution to optimization problems. The present study applies a new approach called HWOA‐TTA which means a hybrid of the whale optimizer algorithm (WOA) and tiki‐taka algorithm (TTA). The hybrid WOA‐TTA combines the exploitation phase of WOA with the exploration phase of TTA. Two stages in the hybridized model are suggested. First, the WOA exploitation phase incorporates the TTA mechanism. Second, a new approach is included in the research phase to enhance the result with each iteration to a set of unconstrained benchmark test functions and engineering design applications. To verify the performance of the improved algorithm, thirteen benchmark functions have been used to compare HWOA‐TTA with the classical intelligent population algorithms (PSO, TTA, and WOA). The hybrid algorithm is applied to two well‐known engineering mathematical models. The experiments show that the HWOA‐TTA outperforms other algorithms. [ABSTRACT FROM AUTHOR]

The lemur optimizer (LO) is a new metaheuristic algorithm that is inspired by the two primary locomotive patterns of the lemurs. However, LO suffers from improper balance between exploration and exploitation phases and sub-optimal solution stagnation due to poor exploration capability. To address these limitations, an improved lemur optimizer (ILO) with dynamic scaling factors and Gaussian mutation is introduced in this paper. The dynamic scaling factors balance the exploration and exploitation transition by dynamically adjusting their values throughout the optimization process. The proposed algorithm incorporates Gaussian mutation to induce diversity in the population and hence improve the exploration capability. The efficiency of the proposed approach is tested on 33 functions including classical benchmark and CEC-2019 test functions, and a comprehensive comparison is made with six other well-known metaheuristic algorithms. The simulation and statistical results indicate superior performance of ILO in achieving optimal solutions compared to the competing algorithms. The algorithm is further employed to address two constrained classical engineering design problems, demonstrating its robustness. [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 study introduces the CP-EODE algorithm, a novel hybrid of the Equilibrium Optimizer (EO), and the Differential Evolution (DE) algorithm. It addresses EO's tendency toward premature convergence by enhancing its exploration capabilities. The motivation for this research stems from the need for more efficient and economically viable designs in engineering, particularly in the optimization of shell-and-tube heat exchangers (STHEs) and photovoltaic module parameters. The CP-EODE algorithm leverages DE's exploration strengths to enhance EO's performance adopting a cooperative parallel approach that divides the population into EO and DE sub-populations for a more effective search space exploration. The validation of CP-EODE's effectiveness commenced with its application to 29 benchmark functions, where a Friedman test yielded an F r value of 22.19, significantly surpassing the critical value of 7.81, and a Wilcoxon signed rank test confirmed statistical improvements with a z-score beyond − 1.96. Four quality metrics were discussed to provide a detailed assessment of CP-EODE's performance highlighting its robust exploration and exploitation capabilities. In practical applications, CP-EODE demonstrated significant advancements in STHE design achieving up to 19.706% reduction in heat exchanger surface area compared to traditional and other algorithmic designs, showcasing its potential to enhance engineering design efficiency and cost-effectiveness. A critical examination of the algorithm's convergence rate revealed its swift optimization capability, with rapid attainment of optimal solutions in various test cases, further establishing CP-EODE's advantage in handling complex optimization challenges. Through rigorous statistical analysis and performance metrics, CP-EODE emerges as a superior solution for complex optimization challenges, underscoring the value of hybrid algorithmic strategies in engineering optimizations. [ABSTRACT FROM AUTHOR]

This paper proposes a new meta-heuristic optimization algorithm called Cleaner Fish Optimization algorithm (CFO) inspired by cleaner fish. The CFO simulates the movement behavior of cleaner fish when performing "cleaning services" and the behavior of female may change its sex to become a male, and defines two modes of position update. In addition, a two-generation cycle operation strategy is proposed to realize the optimization process. To verify the effectiveness of the CFO algorithm, 23 well-known CEC benchmark functions, CEC-2017 benchmark functions and 4 engineering design problems are adopted. Simulation results show that the proposed algorithm has a faster convergence rate and better optimal solution when it compared with several other meta-heuristic algorithms. [ABSTRACT FROM AUTHOR]

The forensic-based investigation (FBI) is a metaheuristic algorithm inspired by the criminal investigation process. The collaborative efforts of the investigation and pursuit teams demonstrate the FBI's involvement during the exploitation and exploration phases. When choosing the promising population, the FBI algorithm's population selection technique focuses on the same region. This research aims to propose a dynamic population selection method for the original FBI and thereby enhance its convergence performance. To achieve this objective, the FBI may employ dynamic oppositional learning (DOL), a dynamic version of the oppositional learning methodology, to dynamically navigate to local minima in various locations. Therefore, the proposed advanced method is named DOLFBI. The performance of DOLFBI on the CEC2019 and CEC2022 benchmark functions is evaluated by comparing it with several other popular metaheuristics in the literature. As a result, DOLFBI yielded the lowest fitness value in 18 of 22 benchmark problems. Furthermore, DOLFBI has shown promising results in solving real-world engineering problems. It can be argued that DOLFBI exhibits the best convergence performance in cantilever beam design, speed reducer, and tension/compression problems. DOLFBI is often utilized in truss engineering difficulties to determine the minimal weight. Its success is comparable to other competitive MAs in the literature. The Wilcoxon signed-rank and Friedman rank tests further confirmed the study's stability. Convergence and trajectory analyses validate the superior convergence concept of the proposed method. When the proposed study is compared to essential and enhanced MAs, the results show that DOLFBI has a competitive framework for addressing complex optimization problems due to its robust convergence ability compared to other optimization techniques. As a result, DOLFBI is expected to achieve significant success in various optimization challenges, feature selection, and other complex engineering or real-world problems. [ABSTRACT FROM AUTHOR]

Swarm intelligence (SI) algorithms represent a class of Artificial Intelligence (AI) optimization metaheuristics used for solving complex optimization problems. However, a key challenge in solving complex problems is maintaining the balance between exploration and exploitation to find the optimal global solution and avoid local minima. This paper proposes an innovative Swarm Intelligence (SI) algorithm called the Four Vector Intelligent Metaheuristic (FVIM) to address the aforementioned problem. FVIM's search strategy is guided by four top-performing leaders within a swarm, ensuring a balanced exploration-exploitation trade-off in the search space, avoiding local minima, and mitigating low convergence issues. The efficacy of FVIM is evaluated through extensive experiments conducted over two datasets, incorporating both qualitative and quantitative statistical measurements. One dataset contains twenty-three well-known single-objective optimization functions, such as fixed-dimensional and multi-modal functions, while the other dataset comprises the CEC2017 functions. Additionally, the Wilcoxon test was computed to validate the result's significance. The results illustrate FVIM's effectiveness in addressing diverse optimization challenges. Moreover, FVIM has been successfully applied to tackle engineering design problems, such as weld beam and truss engineering design. [ABSTRACT FROM AUTHOR]

This study presents the Hybrid COASaDE Optimizer, a novel combination of the Crayfish Optimization Algorithm (COA) and Self-adaptive Differential Evolution (SaDE), designed to address complex optimization challenges and solve engineering design problems. The hybrid approach leverages COA's efficient exploration mechanisms, inspired by crayfish behaviour, with the symmetry of SaDE's adaptive exploitation capabilities, characterized by its dynamic parameter adjustment. The balance between these two phases represents a symmetrical relationship wherein both components contribute equally and complementary to the algorithm's overall performance. This symmetry in design enables the Hybrid COASaDE to maintain consistent and robust performance across a diverse range of optimization problems. Experimental evaluations were conducted using CEC2022 and CEC2017 benchmark functions, demonstrating COASaDE's superior performance compared to state-of-the-art optimization algorithms. The results and statistical analyses confirm the robustness and efficiency of the Hybrid COASaDE in finding optimal solutions. Furthermore, the applicability of the Hybrid COASaDE was validated through several engineering design problems, where COASaDE outperformed other optimizers in achieving the optimal solution. [ABSTRACT FROM AUTHOR]

This work proposes a novel technique to conduct back‐analysis of lateral displacement of deep cement mixing (DCM) columns in deep excavation construction. For the first time, we propose a process to investigate both soil and underground structure end‐to‐end automatically. The novel technique is a complex combination of three crucial factors: (1) a nature‐inspired optimization algorithm (O), (2) a three‐dimensional PLAXIS Geotechnical Engineering software (P) and (3) a modern Python language programming (P), hereinafter called the a nature‐inspired optimization algorithm (O), a three‐dimensional PLAXIS Geotechnical Engineering software (P) and a modern Python language programming (P) (OPP) technique. The novel meta‐heuristic algorithm simulated the co‐evolved partnership behavior of shrimps and goby fishes, termed Shrimp and Goby Association (SGA), which plays an important role in complex analyses. A series of exams to determine the SGA's performance is conducted on 38 benchmark test functions (IEEE Congress on Evolutionary Computation 2017 and 2019) and three real‐world engineering design problems to showcase its applicability. The metaheuristic and PLAXIS 3D analysis work well together, which makes the back‐analysis technique powerfully to determinate stiffness parameters instead of the traditional approaches. Based on the optimized parameters, the lateral deflection of DCM and soil are well predicted for excavation. This study proposes a technique to estimate efficiently the stiffness parameter for very soft soil. As a consequence of the optimization process, an equation to determine the stiffness parameter of DCM columns from laboratory test is also proposed. Based on the obtained results, this research provides a comprehensive methodology for predicting risk, enhancing safety, saving time and money, and effectively designing and constructing underground structures. [ABSTRACT FROM AUTHOR]

This paper introduces the election optimization algorithm (EOA), a meta-heuristic approach for engineering optimization problems. Inspired by the democratic electoral system, focusing on the presidential election, EOA emulates the complete election process to optimize solutions. By simulating the presidential election, EOA introduces a novel position-tracking strategy that expands the scope of effectively solvable problems, surpassing conventional human-based algorithms, specifically, the political optimizer. EOA incorporates explicit behaviors observed during elections, including the party nomination and presidential election. During the party nomination, the search space is broadened to avoid local optima by integrating diverse strategies and suggestions from within the party. In the presidential election, adequate population diversity is maintained in later stages through further campaigning between elite candidates elected within the party. To establish a benchmark for comparison, EOA is rigorously assessed against several renowned and widely recognized algorithms in the field of optimization. EOA demonstrates superior performance in terms of average values and standard deviations across the twenty-three standard test functions and CEC2019. Through rigorous statistical analysis using the Wilcoxon rank-sum test at a significance level of 0.05, experimental results indicate that EOA consistently delivers high-quality solutions compared to the other benchmark algorithms. Moreover, the practical applicability of EOA is assessed by solving six complex engineering design problems, demonstrating its effectiveness in real-world scenarios. [ABSTRACT FROM AUTHOR]

The present work proposes a comprehensive metaheuristic methodology for the development of a medical robot for the upper limb rehabilitation, which includes the topological optimization of the device, kinematic models (5 DOF), human–robot interface, control and experimental tests. This methodology applies two cutting-edge triads: (1) the three points of view in engineering design (client, designer and community) and (2) the triad formed by three pillars of Industry 4.0 (autonomous machines and systems, additive manufacturing and simulation of virtual environments). By applying the proposed procedure, a robotic mechanism was obtained with a reduction of more than 40% of its initial weight and a human–robot interface with three modes of operation and a biomechanically viable kinematic model for humans. The digital twin instance and its evaluation through therapeutic routines with and without disturbances was assessed; the average RMSEs obtained were 0.08 rad and 0.11 rad, respectively. The proposed methodology is applicable to any medical robot, providing a versatile and effective solution for optimizing the design and development of healthcare devices. It adopts an innovative and scalable approach to enhance their processes. [ABSTRACT FROM AUTHOR]

This study presents an advanced metaheuristic approach termed the Enhanced Gorilla Troops Optimizer (EGTO), which builds upon the Marine Predators Algorithm (MPA) to enhance the search capabilities of the Gorilla Troops Optimizer (GTO). Like numerous other metaheuristic algorithms, the GTO encounters difficulties in preserving convergence accuracy and stability, notably when tackling intricate and adaptable optimization problems, especially when compared to more advanced optimization techniques. Addressing these challenges and aiming for improved performance, this paper proposes the EGTO, integrating high and low-velocity ratios inspired by the MPA. The EGTO technique effectively balances exploration and exploitation phases, achieving impressive results by utilizing fewer parameters and operations. Evaluation on a diverse array of benchmark functions, comprising 23 established functions and ten complex ones from the CEC2019 benchmark, highlights its performance. Comparative analysis against established optimization techniques reveals EGTO's superiority, consistently outperforming its counterparts such as tuna swarm optimization, grey wolf optimizer, gradient based optimizer, artificial rabbits optimization algorithm, pelican optimization algorithm, Runge Kutta optimization algorithm (RUN), and original GTO algorithms across various test functions. Furthermore, EGTO's efficacy extends to addressing seven challenging engineering design problems, encompassing three-bar truss design, compression spring design, pressure vessel design, cantilever beam design, welded beam design, speed reducer design, and gear train design. The results showcase EGTO's robust convergence rate, its adeptness in locating local/global optima, and its supremacy over alternative methodologies explored. [ABSTRACT FROM AUTHOR]

One of the most important tasks in handling real-world global optimization problems is to achieve a balance between exploration and exploitation in any nature-inspired optimization method. As a result, the search agents of an algorithm constantly strive to investigate the unexplored regions of a search space. Aquila Optimizer (AO) is a recent addition to the field of metaheuristics that finds the solution to an optimization problem using the hunting behavior of Aquila. However, in some cases, AO skips the true solutions and is trapped at sub-optimal solutions. These problems lead to premature convergence (stagnation), which is harmful in determining the global optima. Therefore, to solve the above-mentioned problem, the present study aims to establish comparatively better synergy between exploration and exploitation and to escape from local stagnation in AO. In this direction, firstly, the exploration ability of AO is improved by integrating Dynamic Random Walk (DRW), and, secondly, the balance between exploration and exploitation is maintained through Dynamic Oppositional Learning (DOL). Due to its dynamic search space and low complexity, the DOL-inspired DRW technique is more computationally efficient and has higher exploration potential for convergence to the best optimum. This allows the algorithm to be improved even further and prevents premature convergence. The proposed algorithm is named DAO. A well-known set of CEC2017 and CEC2019 benchmark functions as well as three engineering problems are used for the performance evaluation. The superior ability of the proposed DAO is demonstrated by the examination of the numerical data produced and its comparison with existing metaheuristic algorithms. [ABSTRACT FROM AUTHOR]

As a swarm-based metaheuristic algorithm, the crow search algorithm (CSA) has attracted a lot of attention owing to its simplicity and flexibility. However, CSA tends to have low efficiency. To improve the optimization efficiency, this article proposes a modified version of CSA based on group strategy with an adaptive mechanism (GCSA). On this basis, crows are divided into multiple competing groups, and are assigned different roles and statuses. Then, the group strategy including different search modes is implemented to increase the solution diversity and search efficiency. Moreover, benefiting from the adaptive mechanism, the search range of crows changes in different stages to balance exploration and exploitation capabilities. To evaluate the performance of the proposed algorithm, 35 benchmark test functions (including 10 CEC2020 functions) and three engineering design problems are solved by GCSA and 11 other algorithms. The results prove that GCSA generally provides more competitive results than other metaheuristic algorithms. [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]

Harris Hawks Optimization (HHO) is a novel meta-heuristic optimization algorithm. The algorithm is inspired by the behavior of Harris Hawks collaborating with each other to pursue prey in nature. The algorithm has the advantages of simple structure, fewer parameters, easy implementation, and excellent performance on high-dimensional problems. However, the algorithm also suffers from the inability to strike a good balance between exploration and exploitation, low convergence accuracy, and slow convergence speed in the early stage. In response to these defects, this paper will introduce three strategies to the HHO: a non-negative stochastic shrinkage exponential energy function, a Cauchy-Gaussian-based dynamic variance reduction selection strategy, and a greedy-difference-based selection strategy. The improved algorithm TSHHO is analyzed on the well-established 28 benchmark test functions, and four industrial engineering design problems. The experimental results show that the TSHHO algorithm proposed in this paper can achieve a better balance in the exploration and development stages,the strategies significantly improve the search efficiency, convergence accuracy, and robustness of the algorithm. [ABSTRACT FROM AUTHOR]

Structural engineering is a field with several optimization approaches. Concordantly, the goal in optimum design is the generation of the lightest, cheapest, or most sustainable engineering design for any type of structure or structural member. In this study, some optimization approaches were presented for structures including 25 and 72-bar space trusses. To find the smallest weights were ensured for both structures. Optimization approaches related to metaheuristics and modifications of them were developed by inspired by features of nature, abilities of lives and mechanisms of chemical/physical processes. The employed three techniques that are flower pollination algorithm, Jaya algorithm and the hybrid algorithm developed via them were compared to each other through some parameters by calculating different statistical expressions containing the best, average and standard deviation of the objective function. Also, the performance of whole metaheuristic versions is evaluated with some literature researches to find the most effective one to minimize the structural weights. These results have observed that the all versions of proposed metaheuristic algorithms are generally successful, and effective to minimize the objective function comparison to algorithms used in previous studies. Moreover, the best values of objective functions can be decreased at the 0.02–0.06 rates as minimum and maximum compared to the previous studies and algorithms, respectively. [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]

This review aims to exploit a study on different benchmark test functions used to evaluate the performance of Meta-Heuristic (MH) optimization techniques. The performance of the MH optimization techniques is evaluated with the different sets of mathematical benchmark test functions and various real-world engineering design problems. These benchmark test functions can help to identify the strengths and weaknesses of newly proposed MH optimization techniques. This review paper presents 215 mathematical test functions, including mathematical equations, characteristics, search space and global minima of the objective function and 57 real-world engineering design problems, including mathematical equations, constraints, and boundary conditions of the objective functions carried out from the literature. The MATLAB code references for mathematical benchmark test functions and real-world design problems, including the Congress of Evolutionary Computation (CEC) and Genetic and Evolutionary Computation Conference (GECCO) test suite, are presented in this paper. Also, the winners of CEC are highlighted with their reference papers. This paper also comprehensively reviews the literature related to benchmark test functions and real-world engineering design challenges using a bibliometric approach. This bibliometric analysis aims to analyze the number of publications, prolific authors, academic institutions, and country contributions to assess the field's growth and development. This paper will inspire researchers to innovate effective approaches for handling inequality and equality constraints. [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]

This paper presents the Multiscale Medalist Learning Algorithm (MMLA) as a novel heuristic approach for complex engineering optimization problems. By extending the Medalist Learning Algorithm, MMLA offers enhanced solution efficiency. The algorithm divides the learning process into successive periods with reduced search spaces, enabling focused search efforts in promising areas. Within each period, predefined learning stages are implemented. Top performers, known as medalists, engage in self-improvement operations through neighborhood searches, while common learners either learn from medalists or adapt based on the current state using neighborhood fluctuation. The MMLA balances exploration and exploitation capabilities through a natural growth curve that determines the learning efficiency. The MMLA's effectiveness and robustness are illustrated through the solution of a two-dimensional benchmark optimization problem and the successful resolution of ten well-known engineering design optimization problems. Comparative analysis demonstrates that the MMLA consistently outperforms other algorithms, providing competitive solutions with strict feasibility and minimal variation. [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]

This paper introduces the Golf Sport Inspired Search (GSIS) algorithm as an evolutionary search method for numerical optimization. Each solution is generated with the aid of the step-length and search direction. The step-length is determined with the aid of the Tait's model of the trajectory of the golf ball, which is a physical model. The search direction is from the current position in the search space toward the position of a different individual or its reflected position. Such a direction determines the movement direction in the optimization process. A crossover operator is introduced to increase exploration at the starting and exploitation at the ending stages of the search. Performance of the GSIS is compared with many algorithms on 23 + 14 unconstrained classic functions, 29 functions of CEC 2017 benchmark suite and six constrained engineering design problems. Experiments indicate that with the aid of its cleverly designed operators, GSIS is able to produce promising results. Besides a cooperative game theoretic approach is introduced, which is able to measure the effectiveness of different operators in reducing the search cost. Such an approach can be used to measure the effectiveness of different operators that an evolutionary or swarm-intelligence algorithm owns. [ABSTRACT FROM AUTHOR]

The whale optimization algorithm has received much attention since its introduction due to its outstanding performance. However, like other algorithms, the whale optimization algorithm still suffers from some classical problems. To address the issues of slow convergence, low optimization precision, and susceptibility to local convergence in the whale optimization algorithm (WOA). Defining the optimization behavior of whale individuals as quantum mechanical behavior, a whale optimization algorithm based on atom-like structure differential evolution (WOAAD) is proposed. Enhancing the spiral update mechanism by introducing a sine strategy guided by the electron orbital center. Improving the random-walk foraging mechanism by applying mutation operations to both the electron orbital center and random individuals. Performing crossover operations between the newly generated individuals from the improved mechanisms and random dimensions, followed by a selection process to retain superior individuals. This accelerates algorithm convergence, enhances optimization precision, and prevents the algorithm from falling into local convergence. Finally, implementing a scouting bee strategy, where whale individuals progressively increase the number of optimization failures within a limited parameter L. When a threshold is reached, random initialization is carried out to enhance population diversity. Conducting simulation experiments to compare the improved algorithm with the whale optimization algorithm, other optimization algorithms, and other enhanced whale optimization algorithms. The experimental results indicate that the improved algorithm significantly accelerates convergence, enhances optimization precision, and prevents the algorithm from falling into local convergence. Applying the improved algorithm to five engineering design problems, the experimental results demonstrate that the improved algorithm exhibits good applicability. [ABSTRACT FROM AUTHOR]

Gaining-sharing knowledge based algorithm (GSK) is a recently emerged meta-heuristic algorithm based on human behavior and has been successfully applied to solve various optimization problems. However, GSK tends to get trapped in local optimum due to the rapid loss of population diversity during the optimization process, resulting in an imbalance between exploration and exploitation. To overcome this deficiency, this paper proposes an enhancing population diversity based GSK (EPD-GSK) framework. The proposed EPD-GSK framework incorporates three components: (1) The utilization of Sobol sequence with low divergence to initialize the population, enhancing the diversity of initial solutions. (2) The integration of the Cauchy mutation strategy in the junior phase to perturb individuals and expand the search space. (3) The application of the reverse learning update mechanism in the senior phase, increasing the likelihood of escaping local optimum. These techniques promote population diversity throughout the exploration and exploitation stages. The proposed EPD-GSK framework was evaluated on CEC2017, CEC2020, and the latest CEC2022 test suites as well as on four constrained real-world engineering design problems. The experimental results demonstrate that EPD-GSK can effectively improve the performance of various existing GSK algorithms. Furthermore, EPD-GSK also exhibits better performance compared with other state-of-the-art algorithms. • Enhancing population diversity based GSK (EPD-GSK) framework is proposed. • EPD-GSK integrates Sobol sequence, Cauchy mutation and reverse learning update. • EPD-GSK significantly improves the performance of various existing GSK algorithms. • EPD-GSK also outperforms other well-known meta-heuristic algorithms. [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]

• An ameliorated Golden jackal optimization (AGJO) is proposed using three optimization strategies. • Three numerical experiments and six engineering problems are verified. • The GJO's exploration and exploitation abilities are completely enhanced by AGJO. • The optimization performance of AGJO is verified compared to other algorithms. • Engineering problems show AGJO's strong ability to solve real problems. Golden jackal optimization (GJO), a lately published meta-heuristic optimization algorithm, is inspired by the foraging behavior of pairs of golden jackals and shows an acceptable optimization performance. However, GJO exists a shortage in balancing exploration and exploitation, as it completely focuses on exploitation in the later iterations. A new variant of GJO, named Ameliorated Golden jackal optimization (AGJO), is proposed in this study. Three strategies are employed in AGJO to alleviate the imbalance between the exploration and exploitation of GJO: the enhanced movement strategy, the global search strategy, and the multi-angle position update strategy for prey. An environmental disturbance factor is added to the third strategy to strengthen GJO's ability to evade the local optimal solution. The performance of AGJO is tested and compared with GJO and seven well-known meta-heuristic algorithms for 23 classical benchmark functions, CEC 2017 and the first ten functions of CEC 2006 with constaints. These results show that AGJO performs better over 90% of these functions compared to GJO. Also, AGJO is also highly competitive in terms of optimization capability and convergence speed compared with other algorithms. Finally, AGJO is applied to optimize engineering problems, including five classical engineering design problems with constraints and a displacement prediction problem of composite pipes. Results show that AGJO is a potential algorithm for solving these real problems rather than GJO and other algorithms. [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]

• Proposing a multi-objective boxing match algorithm as human-based algorithm. • Simulating the boxer's behavior to attract a good support from his coach and fans. • Validating the proposed algorithm to solve multi-objective optimization problems. • Developing an efficient search method to produce a variety of acceptable solutions. • Considering solutions to increase the probability of reaching a Pareto-optimal set. In the last two decades, due to having fast computation after inventing computers and also considering real-world optimization problems, research on developing new algorithms for problem having more than one objective have been one of the appealing and attractive topics both for academia and industrial practitioners. By this motivation, we introduce a Multi-Objective Boxing Match Algorithm (MOBMA) in this paper. The proposed algorithm studies the multi-objective version of the Boxing Match Algorithm (BMA) by incorporating a unique search strategy and new solutions-producing mechanism, enhancing the algorithm's capability for exploration and exploitation phases. Besides, its performance is analyzed with famous and capable multi-objective metaheuristics. We consider ten multi-objective benchmarks and three classical engineering problems. Statistical analyses are also conducted on the benchmark test functions from three engineering design problems. This study shows the superior performance of the proposed algorithm, considering both quantitative and qualitative analyses. [ABSTRACT FROM AUTHOR]

This paper proposes a new Multi-Objective Mantis Search Algorithm (MOMSA) to handle complex optimization problems, including real-world engineering optimization problems. The Mantis Search Algorithm (MSA) is a recently reported nature-inspired metaheuristic algorithm, and it has been inspired by the unique hunting behavior and sexual cannibalism of praying mantises. The proposed MOMSA algorithm employs the same underlying MSA mechanisms for convergence combined with an elitist non-dominated sorting approach to estimate Pareto-optimal solutions. In addition, MOMSA employs the crowding distance mechanism to enhance the coverage of optimal solutions across all objectives. To validate its performance, we conduct 29 case studies, encompassing twenty multi-objective benchmark problems (ZDT, DTLZ, and CEC 2009) and nine engineering design problems. Furthermore, MOMSA is applied to the IEEE-30 bus system, addressing both single- and multi-objective optimal power flow problems across eight distinct cases. Results are compared with some state-of-the-art approaches using various performance metrics such as GD, MS, IGD, and HV. The findings demonstrate MOMSA's ability to effectively balance convergence, diversity, and uniformity, providing valuable insights for decision-makers addressing complex problems. The source code of MOMSA is publicly accessible at https://www.mathworks.com/matlabcentral/fileexchange/159623-momsa-multi-objective-mantis-search-algorithm. • MOMSA: A Novel Multi-Objective Optimization Algorithm. • Enhancing Engineering Design through MOMSA. • Pareto-Optimal Front Maintenance by MOMSA. • MOMSA in Complex Power System Optimization. • Comparative Analysis with Leading Methods. [ABSTRACT FROM AUTHOR]

The development of efficient optimization algorithms is crucial across various scientific disciplines. As the complexity and diversity of optimization problems continue to grow, researchers seek faster and stronger algorithms capable of optimizing a wide range of functions. This paper introduces Lung performance-based optimization (LPO), a novel and efficient algorithm inspired by the regular and intelligent performance of lungs in the human body. LPO draws inspiration from the intricate mechanisms and adaptability of the respiratory system. The lungs exhibit remarkable efficiency in oxygen exchange, demonstrating a high level of optimization in their function. The forced oscillation technique measures air pressure and airflow rate to evaluate the respiratory system as an electrical impedance. The impedance curves have two distinct components, respiratory resistance (ZR) and respiratory reactance (ZX), which can be analyzed clinically and from an engineering perspective to gain insights into the respiratory system's workings. LPO aims to provide an innovative approach to solving complex optimization problems by emulating and harnessing this natural efficiency. To evaluate the effectiveness of LPO, experiments were conducted using the unconstrained optimization functions CEC2005 and CEC2014, as well as engineering design optimization problems. These problems were compared against numerous contemporary algorithms proposed in the literature. The results demonstrate that LPO excels in handling these optimization problems and exhibits the potential to tackle a wide range of modern optimization challenges. The findings highlight the power and effectiveness of LPO as a new optimization algorithm. With its inspiration rooted in the sophisticated performance of the lungs, LPO offers a unique perspective in the optimization landscape. Its ability to handle diverse optimization problems and its potential for application in various domains make LPO a promising algorithm for future research and practical implementation. Note that the source code of the LPO is publicly available at https://www.optim-app.com/projects/lpo. [ABSTRACT FROM AUTHOR]

Grey prediction evolutionary algorithm (GPE) is an emerging category of meta-heuristic algorithm based on mathematical model. It generates offspring by predicting the macroscopic evolutionary trend of population series. On the contrary, the mining of local evolutionary trend are flawed. To address this imperfection, this paper introduces a quadratic function as a surrogate model to mine the local evolutionary trend of population series for the first time. Thereby an improved grey prediction evolutionary algorithm called grey prediction evolutionary algorithm with a surrogate model based on quadratic interpolation (GPE-QI) is designed. The surrogate model based on quadratic interpolation is regarded as an external auxiliary tool to mine the local evolutionary trend of population series by using currently superior individuals. Through utilizing the mined local trend information, a donor population closer to the optimal solution is formed to improve the prediction direction of the algorithm. The performance of GPE-QI is tested on CEC2019, CEC2020 benchmark functions and six engineering design problems. The experimental results demonstrate the stronger competitiveness of GPE-QI to well-established algorithms in terms of solving accuracy and convergence rate. If this paper is accepted, MATLAB codes associated with this paper will be uploaded to https://github.com/Zhongbo-Hu/Prediction-Evolutionary-Algorithm-HOMEPAGE. • Improvement can be made by enhancing local search of grey prediction evolution. • Mine local evolutionary trend of population series by quadratic interpolation. • Construct a surrogate model by using the local evolutionary trend. • Design an improved grey prediction evolutionary algorithm with a surrogate model. • The proposed algorithm is more competitive than the well-established. [ABSTRACT FROM AUTHOR]