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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]

In recent decades, the demand for optimization techniques has grown due to rising complexity in real-world problems. Hence, this work introduces the Hyperbolic Sine Optimizer (HSO), an innovative metaheuristic specifically designed for scientific optimization. Unlike conventional approaches, HSO takes a unique approach by engaging individual members of the population, ensuring a comprehensive exploration of solution spaces. Employing distinctive exploration and exploitation phases, coupled with hyperbolic sinh function convergence, the optimizer enhances speed, simplify parameter adjustment, alleviates slow convergence, and demonstrates efficiency in high-dimensional optimization. This approach is designed to tackle optimization challenges and enhance adaptability in unpredictable real-world scenarios. The evaluation of HSO's performance unfolds through four distinct testing phases. Initially, a set of 65 widely recognized benchmark functions is employed. These functions cover both unimodal and multi-modal varieties across dimensions of 30, 100, 500, and 1000, including fixed-dimensional functions, to comprehensively assess the exploration, exploitation, local optima avoidance, and convergence capabilities of the proposed algorithm. The results of the HSO algorithm are then compared to those of 15 state-of-the-art metaheuristic algorithms and 8 recently published algorithms. Secondly, HSO's performance is assessed in comparison with the benchmark suite from the Institute of Electrical and Electronics Engineers (IEEE) Congress on Evolutionary Computation (CEC). This suite includes 15 benchmark functions for CEC-2015 and an additional 30 benchmark functions for CEC-2017. During the third phase, HSO tackles seven real-world classical engineering design problems by addressing both the constrained and unconstrained optimization challenges of IEEE CEC-2020. Finally, HSO undertakes training for a multilayer perceptron, utilizing four distinct datasets. To qualitatively assess HSO's performance, two statistical analyses—the Friedman and T tests—are employed. The findings of HSO showcase its adaptability and effectiveness as a high-performing optimizer in engineering optimization challenges. Note that the source code of the HSO algorithm are publicly accessible via https://github.com/Shivankur07/Hyperbolic-Sine-Optimizer.git. [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]

This paper introduces the Botox Optimization Algorithm (BOA), a novel metaheuristic inspired by the Botox operation mechanism. The algorithm is designed to address optimization problems, utilizing a human-based approach. Taking cues from Botox procedures, where defects are targeted and treated to enhance beauty, the BOA is formulated and mathematically modeled. Evaluation on the CEC 2017 test suite showcases the BOA's ability to balance exploration and exploitation, delivering competitive solutions. Comparative analysis against twelve well-known metaheuristic algorithms demonstrates the BOA's superior performance across various benchmark functions, with statistically significant advantages. Moreover, application to constrained optimization problems from the CEC 2011 test suite highlights the BOA's effectiveness in real-world optimization tasks. [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 an effective approach for solving economic load dispatch problems contemplating the scheduling a set of thermal generating units to produce a specific power at low consumption costs. These problems can be thought of as nonlinear, non-convex, and highly constrained optimization problems with a large number of local minima. To cope with the above issues in solving such problems, a new meta-heuristic named capuchin search algorithm was adopted. To boost the search performance of this algorithm as well as to mitigate its early convergence and regression to the local optimum, it was hybridized with another algorithm and improved using several positive amendments. First, a memory element was added to this algorithm to ameliorate its position and velocity update mechanisms in order to exploit the most encouraging candidate solutions. Second, two adaptive parametric functions were used to manage the exploration and exploitation features of this algorithm and balance them appropriately. Finally, the hybridization was made using the gradient-based optimizer to strengthen the intensification ability of this algorithm and balance its searching ability to fulfill sensible search performance. The proficiency of the proposed algorithm was divulged by assessing it on computationally difficult economic load dispatch problems under 6 different tests with a generator of 3, 13, 40, 80, and 140 units, each with different constraints and load conditions. The proposed algorithm provided the best performance among many other competitors. Its superiority and practicality were revealed by obtaining optimal solutions for large-scale test cases such as 40-unit and 140-unit test systems. [ABSTRACT FROM AUTHOR]

This research study proposes a Q-learning-based metaheuristic algorithm framework for thermal design optimization of a shell-and-tube evaporator operating with different refrigerant mixtures, which is a highly complex real-world design problem and has not been investigated yet, in previous literature approaches before. The proposed method, called QL-HEUR, uses Q-learning as a high-level heuristic to iteratively guide the competitive recently emerged low-level metaheuristic algorithms. QL-HEUR is applied to 32 unconstrained optimization benchmark functions, and results are evaluated in statistical analysis. Moreover, three multidimensional constrained optimization problems will be solved. Respective solutions unravel that QL-HEUR is very effective in finding optimum solutions to constrained and unconstrained optimization problems. QL-HEUR is employed on the design optimization of a shell-and-tube heat exchanger running with different mixture pairs as a challenging real-world benchmark case. For the design case in which R134a–R1234yf (0.8:02) mixture is considered, 8.71% of the total cost is saved compared to the preliminary design of a heat exchanger operated with pure R1234yf refrigerant. For the second design case, the application of QL-HEUR results in a decrease of 8.93% for refrigerant composition R32–R134a (0.6:0.4) in comparison with the configuration running with pure R134a. It is also seen that the heat exchanger configuration running with pure R32 refrigerant yields the lowest total cost compared to the cases accomplished by varying mixture ratios of R290 and R32. It can be concluded that the optimum configuration of the heat exchanger operated with a refrigerant mixture can be conveniently employed for minimum total cost and global warming potential. [ABSTRACT FROM AUTHOR]

In this paper, a new bio-inspired metaheuristic algorithm called the Lyrebird Optimization Algorithm (LOA) that imitates the natural behavior of lyrebirds in the wild is introduced. The fundamental inspiration of LOA is the strategy of lyrebirds when faced with danger. In this situation, lyrebirds scan their surroundings carefully, then either run away or hide somewhere, immobile. LOA theory is described and then mathematically modeled in two phases: (i) exploration based on simulation of the lyrebird escape strategy and (ii) exploitation based on simulation of the hiding strategy. The performance of LOA was evaluated in optimization of the CEC 2017 test suite for problem dimensions equal to 10, 30, 50, and 100. The optimization results show that the proposed LOA approach has high ability in terms of exploration, exploitation, and balancing them during the search process in the problem-solving space. In order to evaluate the capability of LOA in dealing with optimization tasks, the results obtained from the proposed approach were compared with the performance of twelve well-known metaheuristic algorithms. The simulation results show that LOA has superior performance compared to competitor algorithms by providing better results in the optimization of most of the benchmark functions, achieving the rank of first best optimizer. A statistical analysis of the performance of the metaheuristic algorithms shows that LOA has significant statistical superiority in comparison with the compared algorithms. In addition, the efficiency of LOA in handling real-world applications was investigated through dealing with twenty-two constrained optimization problems from the CEC 2011 test suite and four engineering design problems. The simulation results show that LOA has effective performance in handling optimization tasks in real-world applications while providing better results compared to competitor algorithms. [ABSTRACT FROM AUTHOR]

In this paper, a new human-based metaheuristic algorithm called Technical and Vocational Education and Training-Based Optimizer (TVETBO) is introduced to solve optimization problems. The fundamental inspiration for TVETBO is taken from the process of teaching work-related skills to applicants in technical and vocational education and training schools. The theory of TVETBO is expressed and mathematically modeled in three phases: (i) theory education, (ii) practical education, and (iii) individual skills development. The performance of TVETBO when solving optimization problems is evaluated on the CEC 2017 test suite for problem dimensions equal to 10, 30, 50, and 100. The optimization results show that TVETBO, with its high abilities to explore, exploit, and create a balance between exploration and exploitation during the search process, is able to provide effective solutions for the benchmark functions. The results obtained from TVETBO are compared with the performances of twelve well-known metaheuristic algorithms. A comparison of the simulation results and statistical analysis shows that the proposed TVETBO approach provides better results in most of the benchmark functions and provides a superior performance in competition with competitor algorithms. Furthermore, in order to measure the effectiveness of the proposed approach in dealing with real-world applications, TVETBO is implemented on twenty-two constrained optimization problems from the CEC 2011 test suite. The simulation results show that TVETBO provides an effective and superior performance when solving constrained optimization problems of real-world applications compared to competitor algorithms. [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 present work compares the performance of scientific law-inspired optimization algorithms for real-life constrained optimization applications. Ten such scientific law-inspired algorithms developed during the past decade are considered in this article. A constrained engineering application of the Stirling heat engine system is investigated with these algorithms. Four operating variables and two output constraints of the Stirling heat engine are considered for optimization. Comparative results are presented with statistical data to judge the performance of the algorithms and subsequently to identify the statistical significance and rank of each algorithm. The effects of various constraint handling methods on the performance of the algorithms are evaluated and presented. The behaviour of the constraint handling methods is analysed and presented. The effect of output constraints on the performance of the algorithms is also evaluated and presented. Finally, the convergence behaviour of the competitive algorithms is obtained and demonstrated. [ABSTRACT FROM AUTHOR]

How to steadily find satisfactory solutions for high-dimensional multimodal and composition optimization problems is still a challenging issue. To fight against this pain-point problem, we propose sardine optimization algorithm (SOA) with agile locality and globality strategies for real optimization problems. Inspired by the survival philosophy of sardines, SOA simulates the transformation, migration, reproduction, elimination, and spread of sardines. As a varied-population-size optimization algorithm, the features of SOA are summarized as two key points. (i) Agile locality and globality strategies use adjacent and corresponding period ratios to control the local and global search behaviors. To our best knowledge, these strategies are a new technical road to balance exploration and exploitation efforts. (ii) Besides, SOA uses unique search operators based on the center movement of sardine schools. Specifically, when the center of one sardine school moves in these search operators, all sardines in this school also move in the same direction. This mobility style is different from most meta-heuristic algorithms, as far as we know. We used all unconstrained optimization problems in the CEC2013 test suite and six real-world constrained optimization problems as our benchmarks. SOA outperforms eight algorithms (like the two winning algorithms of CEC2013 and CEC2014), especially for high-dimension multimodal and composition optimization problems. For instance, Wilcoxon results between SOA and the two winning algorithms of CEC2013 and CEC2014 for 90-dimensional unconstrained optimization problems of the CEC2013 test suite are 16:10 and 18:8. The coding of SOA can be downloaded from "https://github.com/1654402787/SOA" (unzip password: soasoasoa1357). [ABSTRACT FROM AUTHOR]

The optimal methods for the synthesis of mechanisms in rehabilitation usually require solving constrained optimization problems. Metaheuristic algorithms are frequently used to solve these problems with the inclusion of Constraint-Handling Techniques (CHTs). Nevertheless, the most used CHTs in the synthesis of mechanisms, such as penalty function and feasibility rules, generally prioritize the search for feasible regions over the minimization of the objective function, and it notably influences the exploration and exploitation of the algorithm such that it could induce in the premature convergence to the local minimum and thus the solution quality could deteriorate. In this work, a Neuronal Constraint-Handling (NCH) technique is proposed and its performance is studied in the solution of mechanism synthesis for rehabilitation. The NCH technique uses a neural network to search for the fittest solutions into the feasible and the infeasible region to pass them to the next generation of the evolutionary process of the Differential Evolution (DE) algorithm and consequently improve the obtained solution quality. Two synthesis problems with four–bar and cam–linkage mechanisms are the study cases for developing lower-limb rehabilitation routines. The NCH is compared with four state-of-the-art constraint-handling techniques (penalty function, feasibility rules, stochastic ranking, ϵ -constrained method) included into four representative metaheuristic algorithms. The irace package is used for both the algorithm settings and neuronal network training to fairly and meaningfully compare through statistics to confirm the overall performance. The statistical results confirm that, despite changes in the rehabilitation trajectories, the proposal presents the best overall performance among selected algorithms in the studied synthesis problems for rehabilitation, followed by penalty function and feasibility rule. [ABSTRACT FROM AUTHOR]

This paper presents a novel metaheuristic algorithm called Rock Hyraxes Swarm Optimization (RHSO) inspired by the behavior of rock hyraxes swarms in nature. The RHSO algorithm mimics the collective behavior of Rock Hyraxes to find their eating and their special way of looking at this food. Rock hyraxes live in colonies or groups where a dominant male watch over the colony carefully to ensure their safety leads the group. Forty-eight (22 unimodal and 26 multimodal) test functions commonly used in the optimization area are used as a testing benchmark for the RHSO algorithm. A comparative efficiency analysis also checks RHSO with Particle Swarm Optimization (PSO), Artificial-Bee-Colony (ABC), Gravitational Search Algorithm (GSA), and GreyWolf Optimization (GWO). The obtained results showed the superiority of the RHSO algorithm over the selected algorithms; also, the obtained results demonstrated the ability of the RHSO in convergence towards the global optimal through optimization as it performs well in both exploitation and exploration tests. Further, RHSO is very effective in solving real issues with constraints and new search space. It is worth mentioning that the RHSO algorithm has a few variables, and it can achieve better performance than the selected algorithms in many test functions. [ABSTRACT FROM AUTHOR]

Success of metaheuristic algorithms depends on the efficient balance between of exploration and exploitation phases. Any optimization algorithm requires a combination of diverse exploration and proper exploitation to avoid local optima. This paper proposes a new improved version of the Woodpecker Mating Algorithm (WMA), based on opposition-based learning, known as the OWMA aiming to develop exploration and exploitation capacities and establish a simultaneous balance between these two phases. This improvement consists of three major mechanisms, the first of which is the new Distance Opposition-based Learning (DOBL) mechanism for improving exploration, diversity, and convergence. The second mechanism is the allocation of local memory of personal experiences of search agents for developing the exploitation capacity. The third mechanism is the use of a self-regulatory and dynamic method for setting the Hα parameter to improve the Running Away function (RA) performance. The ability of the proposed algorithm to solve 23 benchmark mathematical functions was evaluated and compared to that of a series of the latest and most popular metaheuristic methods reviewed in the research literature. The proposed algorithm is also used as a Multi-Layer Perceptron (MLP) neural network trainer to solve the classification problem on four biomedical datasets and three function approximation datasets. In addition, the OWMA algorithm was evaluated in five optimization problems constrained by the real world. The simulation results proved the superior and promising performance of the proposed algorithm in the majority of evaluations. The results prove the superiority and promising performance of the proposed algorithm in solving very complicated optimization problems. [ABSTRACT FROM AUTHOR]

[Display omitted] • A hybrid algorithm for reliable and efficient parameter estimation of the PV model. • Significant advancements are achieved in methodology and objective function design. • Performance of the algorithm is analyzed with partial shading and noise effects. • Proposed approach achieves enhancements in the overall performance and accuracy. • It outperforms other algorithms in terms of accuracy, consistency, and convergence. A reliable methodology is essential for accurately estimating the parameters of PV models, enabling reliable performance evaluations, effective control studies, accurate analysis of partial shading effects, and optimal optimization of Photovoltaic (PV) systems. It ensures that the obtained parameters reflect the true characteristics of the PV system, leading to more accurate and reliable results in various applications. The existing literature extensively explores the utilization of powerful Metaheuristic Algorithms (MAs) to address the complex constrained optimization problem in PV systems and achieve optimal solutions. However, it is important to note that a significant portion of these MAs primarily concentrates on the development of methodologies, often overlooking the design of the objective function tailored for PV systems. This oversight has created a theoretical gap in this research domain, underscoring the necessity for additional exploration and investigation to address this limitation. To address the existing theoretical gap, this study focused on developing an objective function that accurately estimates the initial root parameters of Photovoltaic (PV) models. This objective function was designed by incorporating the first-order Berndt-Hall-Hall-Hausman (BHHH) numerical method, along with the non-linear damping parameter of the Levenberg-Marquardt technique (LM). By implementing this approach, the study aimed to significantly improve the precision and reliability of estimating the initial root parameters in PV models, effectively filling the theoretical void in this specific research area. Then in terms of methodology, the Enhanced Henry Gas Solubility Optimization (EHGSO) algorithm is combined with the Sine-Cosine mutualism phase of Symbiotic Organisms Search (SOS) for efficiently estimating the unknown parameters of PV models. The keystone of EHGSO in terms of methodology enhances exploration at the beginning of optimization and intensifies exploitation in later iterations. The proposed EHGSO methodology based on the adaptive damping BHHH technique (EHGSO AdBHHH) is tested on Single Diode (SD), and Double Diode (DD) PV models using actual experimental data. EHGSO AdBHHH exhibits outstanding accordance with attained experimental data compared with other algorithms, and its superiority is validated using several statistical criteria. [ABSTRACT FROM AUTHOR]

An application of bat algorithm (BA) as a metaheuristic optimization approach in materials and design to an engineering problem has been presented in this paper. The purpose of the case study was to develop a new float as a part of measurement system according to the setup configuration and test environment. With this regard, several materials such as Acrylic, PVC, Nylon, Teflon (PTFE), and low-density polyethylene as feasible options for the float body in terms of mechanical, thermal, and chemical properties were selected. Then, optimal concurrent design of the float system with selected materials based on structural and performance constraints was addressed. For this purpose, the design was formulated into a constrained optimization problem and BA was used to find the optimal solutions in order to minimize the float length. The convergence of the design variables and constraints to optimal values was also investigated. Generalized reduced gradient method was used as well for validation and comparison of the BA results. It was found that the new optimal float had a pretty good performance in the test measurement. The results showed that BA can be a quite efficient approach to solve constrained optimization problems in materials and design. It is also suggested that the new float problem can be considered as a benchmark problem in materials and design to validate the robustness of the optimization algorithms. [ABSTRACT FROM AUTHOR]

The optimization of continuous space poses a great challenge among the scientific community. When the objective function is nonlinear, the choices of direct search spaces are preferred over the other methods. The use of the hybrid algorithm for these types of optimization is becoming increasingly popular. This study introduced a self-adaptation procedure in a single objective hybrid algorithm and its application for unconstrained and constrained optimization test functions. This single objective hybrid algorithm is based on two popular metaheuristic algorithms, namely the cuckoo search and covariance matrix adaptation evolution strategy. Self-adaptation is a popular way of parameter selection and has a significant place in the computing field. The adaptation is introduced in two significant parameters of this algorithm. Five metaheuristic algorithms, namely cuckoo search, covariance matrix adaptation evolution strategy, particle swarm intelligence, firefly algorithm, and the newly introduced self-adapted single objective hybrid algorithm, were analyzed using unconstrained (unimodal and multimodal) and constrained benchmark test functions. An encouraging performance of this proposed algorithm for unconstrained and constrained test functions was observed. [ABSTRACT FROM AUTHOR]

The objective of moveout parameter inversion is to derive sets of parameter models that can be used for moveout correction and stacking at each common midpoint location to increase the signal‐to‐noise ratio of the data and to provide insights into the kinematic characteristics of the data amongst other things. In this paper, we introduce a data‐driven user‐constrained optimization scheme that utilizes manual picks at a point on each reflector within a common midpoint gather to constrain the search space in which an optimization procedure can search for the optimal parameter sets at each reflection. The picks are used to create boundary curves which can be derived approximately via an optimization technique or analytically via the derivation of an analytical bounds function. In this paper, we derive analytical forms of bounds functions for four different moveout cases. These are normal moveout, non‐hyperbolic moveout, azimuthally dependent normal moveout and azimuthally dependent non‐hyperbolic moveout. The optimization procedure utilized here to search for the optimal moveout parameters is the particle swarm optimization technique. However, any metaheuristic optimization procedure could be modified to account for the constraints introduced in this paper. The technique is tested on two‐layer synthetic models based on three of the four moveout cases discussed in this paper. It is also applied to an elastic forward modelled synthetic model called the HESS model, and finally to real 2D land data from Alaska. The resultant stacks show a marked improvement in the signal‐to‐noise ratio compared to the raw stacks. The results for the normal moveout, non‐hyperbolic moveout and azimuthally dependent normal moveout tests suggest that the method is viable for said models. Results demonstrate that our method offers potential as an alternative to conventional parameter picking and inversion schemes, particularly for some cases where the number of parameters in the moveout approximation is 2 or greater. [ABSTRACT FROM AUTHOR]

This paper explores the behavior of the Flower Pollination Algorithm (FPA) and Particle Swarm Optimization (PSO) metaheuristic algorithm in resolving Resource Constrained Project Scheduling Problems (RCPSP) that can model certain practical issues in distributed applications. A RCPSP type problem has at the input a set of activities between which there are precedence relationships and for whose execution it is necessary to allocate resources that are limited. The solution determines the order of execution of the activities with respect to the precedence relations between them and the allocation of the available resources so that the total duration is minimal. The experimental results showed that a near optimal solution can be obtained faster than with other traditional algorithms, mainly for optimization problems in the continuous space. Two versions of FPA and PSO were used, namely combinatorial and priority based optimization. Because during evolution the individuals’ position changes do not guarantee the precedence order preservation, a new tasks reordering procedure is proposed in this paper. [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]

In the optimization of constrained type problems, the main difficulty is the elimination of the constraint violations in the evolutionary search process. Evolutionary algorithms are designed by default according to the requirements of unconstrained and continuous global optimization problems. Since there are no constraint functions in these type of problems, the constraint violations are not considered in the design of the guiding mechanism of evolutionary algorithms. In this study, two new methods were introduced to redesign the evolutionary algorithms in accordance with the requirements of constrained optimization problems. These were (i) constraint space-based, called Fitness-Distance-Constraint (FDC), selection method and (ii) dynamic guiding mechanism. Firstly, thanks to the FDC guide selection method, the constraint violation values of the individuals in the population were converted into score values and the individuals who increase the diversity in the search process were selected as guide. On the other hand, in dynamic guiding mechanism, the FDC method was applied in case of constraint violation, otherwise the default guide selection method was used The proposed methods were used to redesign the guiding mechanism of adaptive guided differential evolution (AGDE), a current evolutionary algorithm, and the FDC-AGDE algorithm was designed. The performance of the FDC-AGDE was tested on eleven different constrained real-world optimization problems. The results of the FDC-AGDE and AGDE were evaluated using the Friedman and Wilcoxon test methods. According to Wilcoxon pairwise results, the FDC-AGDE showed better performance than the AGDE in nine of the eleven problems and equal performance in two of the eleven problems. Moreover, the proposed algorithm was compared with the competitive and up-to-date MHS algorithms in terms of the results of Friedman test, Wilcoxon test, feasibility rate, and success rate. According to Friedman test results, the first three algorithms were the FDC-AGDE, LSHADE-SPACMA, and AGDE algorithms with the score of 2.69, 4.05, and 4.34, respectively. According to the mean values of the success rates obtained from the eleven problems, the FDC-AGDE, LSHADE-SPACMA, and AGDE algorithms ranked in the first three with the success rates of 67%, 48% and 28%, respectively. Consequently, the FDC-AGDE algorithm showed a superior performance comparing with the competing MHS algorithms. According to the results, it is expected that the proposed methods will be widely used in the constrained optimization problems in the future. [Display omitted] • Fitness-Distance-Constraint (FDC) method has been proposed. • FDC based dynamic guide selection mechanism has been introduced for MHS algorithms. • FDC-AGDE algorithm has been proposed for optimization of constrained problems. • The AGDE algorithm with FDC was 39% more successful than the version without FDC. [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]

Nowadays it is becoming more and more attractive to execute workflow applications in the cloud because it enables workflow applications to use computing resources on demand. Meanwhile, it also challenges traditional workflow scheduling algorithms that only concentrate on optimizing the execution time. This paper investigates how to minimize execution cost of a workflow in clouds under a deadline constraint and proposes a metaheuristic algorithm L-ACO as well as a simple heuristic ProLiS. ProLiS distributes the deadline to each task, proportionally to a novel definition of probabilistic upward rank, and follows a two-step list scheduling methodology: rank tasks and sequentially allocates each task a service which meets the sub-deadline and minimizes the cost. L-ACO employs ant colony optimization to carry out deadline-constrained cost optimization: the ant constructs an ordered task list according to the pheromone trail and probabilistic upward rank, and uses the same deadline distribution and service selection methods as ProLiS to build solutions. Moreover, the deadline is relaxed to guide the search of L-ACO towards constrained optimization. Experimental results show that compared with traditional algorithms, the performance of ProLiS is very competitive and L-ACO performs the best in terms of execution costs and success ratios of meeting deadlines. [ABSTRACT FROM AUTHOR]

In this article, A novel nature-inspired optimization algorithm known as Lightning Attachment Procedure Optimization (LAPO) is proposed. The proposed approach mimics the lightning attachment procedure including the downward leader movement, the upward leader propagation, the unpredictable trajectory of lightning downward leader, and the branch fading feature of lightning. Final optimum result would be the lightning striking point. The proposed method is free from any parameter tuning and it is rarely stuck in the local optimum points. To evaluate the proposed algorithm, 29 mathematical benchmark functions are employed and the results are compared to those of 9 high quality well-known optimization methods The results of the proposed method are compared from different points of views, including quality of the results, convergence behavior, robustness, and CPU time consumption. Superiority and high quality performance of the proposed method are demonstrated through comparing the results. Moreover, the proposed method is also tested by five classical engineering design problems including tension/compression spring, welded beam, pressure vessel designs, Gear train design, and Cantilever beam design and a high constraint optimization problem known as Optimal Power Flow (OPF) which is a high constraint electrical engineering problem. The excellence performance of the proposed method in solving the problems with large number of constraints and also discrete optimization problems are also concluded from the results of the six engineering problem. [ABSTRACT FROM AUTHOR]

Optimization of multi-modal functions is challenging even for evolutionary and swarm-based algorithms as it requires an efficient exploration for finding the promising region of the search space, and effective exploitation to precisely find the global optimum. Grey Wolf Optimizer (GWO) is a recently developed metaheuristic algorithm that is inspired by nature with a relatively small number of parameters for tuning. However, GWO and most of its variants may suffer from the lack of population diversity, premature convergence, and the inability to preserve a good balance between exploratory and exploitative behaviors. To address these limitations, this work proposes a new variant of GWO incorporating memory, evolutionary operators, and a stochastic local search technique. It further integrates Linear Population Size Reduction (LPSR) technique. The proposed algorithm is comprehensively tested on 23 numerical benchmark functions, high dimensional benchmark functions, 13 engineering case studies, four data classifications, and three function approximation problems. The benchmark functions are mostly taken from the CEC 2005 and CEC 2010 special sessions, and they include rotated, shifted functions. The engineering case studies are from the CEC 2020 real-world non-convex constrained optimization problems. The performance of the proposed GWO is compared with popular metaheuristics, namely, particle swarm optimization (PSO), gravitational search algorithm (GSA), slap swarm algorithm (SSA), differential evolution (DE), self-adaptive differential evolution (SADE), basic GWO and its three recently improved variants. Statistical analysis and Friedman tests have been conducted to thoroughly compare their performance. The obtained results demonstrate that the proposed GWO outperforms the algorithms compared for the benchmark functions and engineering case studies tested. [ABSTRACT FROM AUTHOR]

• This paper proposes an enhanced SCA algorithm variant, called ARSCA. • ARSCA improves the convergence accuracy and avoids premature convergence. • This paper compares ARSCA with classical algorithms, variations of other algorithms. • ARSCA is applied to six engineering design problems and its results are satisfactory. The sine cosine algorithm (SCA) is a well-known meta-heuristic optimization algorithm. SCA has received much attention in various optimization fields due to its simple structure and excellent optimization capabilities. However, the dimension of objective function also increases with the increasing complexity of optimization tasks. This makes the original SCA appear to have insufficient optimization capability and likely to fall into premature convergence. A multi-mechanism acting variant of SCA, called ARSCA, is proposed to address the above deficiencies. ARSCA is an enhanced SCA algorithm based on the adaptive quadratic interpolation mechanism (AQIM) and Rounding mechanism (RM). RM enables a more balanced state between exploration and exploitation of the ARSCA. AQIM enhances local exploitation capabilities. To verify the performance of ARSCA, we compared ARSCA with some advanced traditional optimization algorithms and variants of algorithms for 30 consecutive benchmark functions of IEEE CEC2014. In addition, ARSCA was applied to 6 constrained engineering optimization problems. These six algorithms include the tension–compression spring design problem, the welded beam design problem, the pressure vessel design problem, the I-beam design problem, the speed reducer design problem, and the three-bar design problem. Experimental results show that ARSCA outperforms its competitors in both the solution quality and the ability to jump out of the local optimum. The relevant codes for the paper are publicly available at https://github.com/YangXiao9799/paper_ARSCA. [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]

This paper proposes a novel nature-inspired meta-heuristic optimization algorithm, called Whale Optimization Algorithm (WOA), which mimics the social behavior of humpback whales. The algorithm is inspired by the bubble-net hunting strategy. WOA is tested with 29 mathematical optimization problems and 6 structural design problems. Optimization results prove that the WOA algorithm is very competitive compared to the state-of-art meta-heuristic algorithms as well as conventional methods. The source codes of the WOA algorithm are publicly available at http://www.alimirjalili.com/WOA.html [ABSTRACT FROM AUTHOR]

A novel swarm intelligence optimization technique is proposed called dragonfly algorithm (DA). The main inspiration of the DA algorithm originates from the static and dynamic swarming behaviours of dragonflies in nature. Two essential phases of optimization, exploration and exploitation, are designed by modelling the social interaction of dragonflies in navigating, searching for foods, and avoiding enemies when swarming dynamically or statistically. The paper also considers the proposal of binary and multi-objective versions of DA called binary DA (BDA) and multi-objective DA (MODA), respectively. The proposed algorithms are benchmarked by several mathematical test functions and one real case study qualitatively and quantitatively. The results of DA and BDA prove that the proposed algorithms are able to improve the initial random population for a given problem, converge towards the global optimum, and provide very competitive results compared to other well-known algorithms in the literature. The results of MODA also show that this algorithm tends to find very accurate approximations of Pareto optimal solutions with high uniform distribution for multi-objective problems. The set of designs obtained for the submarine propeller design problem demonstrate the merits of MODA in solving challenging real problems with unknown true Pareto optimal front as well. Note that the source codes of the DA, BDA, and MODA algorithms are publicly available at . [ABSTRACT FROM AUTHOR]

This paper proposes a novel population-based optimization algorithm called Sine Cosine Algorithm (SCA) for solving optimization problems. The SCA creates multiple initial random candidate solutions and requires them to fluctuate outwards or towards the best solution using a mathematical model based on sine and cosine functions. Several random and adaptive variables also are integrated to this algorithm to emphasize exploration and exploitation of the search space in different milestones of optimization. The performance of SCA is benchmarked in three test phases. Firstly, a set of well-known test cases including unimodal, multi-modal, and composite functions are employed to test exploration, exploitation, local optima avoidance, and convergence of SCA. Secondly, several performance metrics (search history, trajectory, average fitness of solutions, and the best solution during optimization) are used to qualitatively observe and confirm the performance of SCA on shifted two-dimensional test functions. Finally, the cross-section of an aircraft's wing is optimized by SCA as a real challenging case study to verify and demonstrate the performance of this algorithm in practice. The results of test functions and performance metrics prove that the algorithm proposed is able to explore different regions of a search space, avoid local optima, converge towards the global optimum, and exploit promising regions of a search space during optimization effectively. The SCA algorithm obtains a smooth shape for the airfoil with a very low drag, which demonstrates that this algorithm can highly be effective in solving real problems with constrained and unknown search spaces. Note that the source codes of the SCA algorithm are publicly available at http://www.alimirjalili.com/SCA.html . [ABSTRACT FROM AUTHOR]

In this paper a novel nature-inspired optimization paradigm is proposed called Moth-Flame Optimization (MFO) algorithm. The main inspiration of this optimizer is the navigation method of moths in nature called transverse orientation. Moths fly in night by maintaining a fixed angle with respect to the moon, a very effective mechanism for travelling in a straight line for long distances. However, these fancy insects are trapped in a useless/deadly spiral path around artificial lights. This paper mathematically models this behaviour to perform optimization. The MFO algorithm is compared with other well-known nature-inspired algorithms on 29 benchmark and 7 real engineering problems. The statistical results on the benchmark functions show that this algorithm is able to provide very promising and competitive results. Additionally, the results of the real problems demonstrate the merits of this algorithm in solving challenging problems with constrained and unknown search spaces. The paper also considers the application of the proposed algorithm in the field of marine propeller design to further investigate its effectiveness in practice. Note that the source codes of the MFO algorithm are publicly available at http://www.alimirjalili.com/MFO.html . [ABSTRACT FROM AUTHOR]

• A novel method to improve the performance of population-based optimizers. • The combination lock algorithm used as a pre-processing optimization method. • The combination lock algorithm produces an elite individual. • The elite individual is inserted into the initial population of optimizers. • The new algorithm significantly improves the performance of optimizers. Nature-inspired population-based metaheuristics are promising search methods for solving optimization problems. In this paper, a novel systematic pre-processing approach, called the combination lock algorithm, for obtaining a good starting point for population-based algorithms is proposed. The proposed algorithm is tested on 32 benchmark unconstrained multidimensional optimization problems of different characteristics that are either unimodal or multimodal, continuous or non-continuous, separable or non-separable, differentiable or non-differentiable. The tests also include four engineering constrained optimization benchmark problems. The experimental results of applying the proposed algorithm for the Particle Swarm Optimization, the Ant Colony Optimization for Continuous Domain, and the Grey Wolf Optimization were compared with the results obtained from the conventional approach of initializing the starting population of population-based metaheuristic methods. The simulation results show the potential of the proposed algorithm as an efficient and reliable approach to enhance the performance of population-based optimization algorithms such that, overall, 50% and up to 100% of the tested problems "across various population size" settings, had either improved or equalled the optimal values when the proposed algorithm was applied. [ABSTRACT FROM AUTHOR]

Nature-Inspired Metaheuristics (NIM) have emerged as a potent tool for solving complex and difficult optimization problems, arising in various industries, which otherwise become quite difficult (if not impossible) to solve by the classical methods based on gradient search. Further, NIM techniques are more likely to obtain a global optimal solution, often desired and sometimes a necessity in several real life situations. In this study we employ SABC, a variant of Artificial Bee Colony (ABC), a relatively newer NIM algorithm, for solving four typical processes of a paper mill where optimization can be applied. We have also considered two chemical process problems that can be related to paper industry. Numerical results show that the proposed SABC scheme is efficient in dealing with these problems. [ABSTRACT FROM AUTHOR]

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]

The Particle Swarm Optimization algorithm is a metaheuristic based on populations of individuals in which solution candidates evolve through simulation of a simplified model of social adaptation. By aggregating robustness, efficiency and simplicity, PSO has gained great popularity. Modified PSO algorithms have been proposed to solve optimization problems with domain, linear and nonlinear constraints. Other algorithms that use multi-objective optimization to deal with constrained problems face the problem of not being able to guarantee finding feasible solutions. Current PSO algorithms that deal with constraints only treat domain constraints by controlling the velocity of particle displacement in the swarm, or do so inefficiently by randomly resetting each infeasible particle. This approach may make it infeasible to optimize certain problems, especially real ones. This work presents a new particle swarm optimization algorithm, called PSO+, capable of solving problems with linear and nonlinear constraints in order to solve these deficiencies. The proposed algorithm uses a feasibility repair operator and two swarms to ensure there will always be a swarm whose particles fully respect every constraint. A new particle update method is also proposed to insert diversity into the swarm and improve search-space coverage, allowing the search-space border to be exploited as well, which is particularly convenient when the optimization involves active constraints in global optimum. Two heuristics are proposed to initialize a feasible swarm with the purpose of speeding up the initialization mechanism and ensuring diversity at the starting point of the optimization process. Furthermore, a neighborhood topology is proposed to minimize premature convergence. The proposed algorithm was tested for twenty-four benchmark functions, as well as in a real reservoir drainage plan optimization problem. Results attest that the new algorithm is competitive, since it increases the efficiency of the PSO and the speed of convergence. • The algorithm ensures there will always be particles fully respecting constraints. • The proposed update method improves diversity in the swarm. • The proposed update method allows the search-space border to be exploited. • The Metropolis–Hastings algorithm improved the particle swarms initialization. • PSO+ performed well in a real reservoir drainage plan optimization problem. [ABSTRACT FROM AUTHOR]