The palm tree optimization: Algorithm and applications

Metaheuristic algorithms are constructed to solve optimization problems, but they cannot solve all the problems with best solutions. This work proposes a novel self-adaptive metaheuristic optimization algorithm, named Optimal Stochastic Process Optimizer (OSPO), which can solve different kinds of optimization problems with promising performance. Specifically, OSPO regards the procedure of optimization as a realization of stochastic process, and with the help of Subjective Probability Distribution Function (SPDF) and Receding Sampling Strategy proposed in this paper, OSPO can control the exploration-exploitation property online by the adaptive modification of the parameters in SPDF. This adaptive exploration-exploitation property of OSPO contributes to dealing with different kinds of problems; thus, it makes OSPO have the potential to solve at least a vast majority of optimization problems. The proposed algorithm is first benchmarked on uni-modal, multi-modal and composite test functions both in low and high dimensions. The results are verified by comparative studies with seven well-performed metaheuristic algorithms. Then, 21 real-world optimization problems are used to further investigate the effectiveness of OSPO. The winners of CEC2020 Competition on Real-World Single Objective Constrained Optimization, SASS algorithm, sCMAgES algorithm, EnMODE algorithm and COLSHADE algorithm are used as four comparative algorithms in real-world optimization problems. The analysis of simulations demonstrates that OSPO is able to provide very competitive performance compared to the comparative meta-heuristics both in benchmark functions and in real-world optimization problems; thus, the potential of OSPO to solve at least a vast majority of optimization problems is verified. A corresponding MATLAB APP demo is available on https://github.com/JiahongXu123/OSPO-algorithm.git.

<p>In last decade, numerous meta-heuristic algorithms have been proposed for dealing the complexity and difficulty of numerical optimization problems in the realworld which is growing continuously recently, but only a few algorithms have caught researchers’ attention. In this study, a new swarm-based meta-heuristic algorithm called Rhizostoma optimization algorithm (ROA) is proposed for solving the optimization problems based on simulating the social movement of Rhizostoma octopus (barrel jellyfish) in the ocean. ROA is intended to mitigate the two optimization problems of trapping in local optima and slow convergence. ROA is proposed with three different movement strategies (simulated annealing (SA), fast simulated annealing (FSA), and Levy walk (LW)) and tested with 23 standard mathematical benchmark functions, two classical engineering problems, and various real-world datasets including three widely used datasets to predict the students’ performance. Comparing the ROA algorithm with the latest meta-heuristic optimization algorithms and a recent published research proves that ROA is a very competitive algorithm with a high ability in optimization performance with respect to local optima avoidance, the speed of convergence and the exploration/exploitation balance rate, as it is effectively applicable for performing optimization tasks.</p>

Bare-Bones Based Sine Cosine Algorithm for global optimization

Biochemical parameter estimation vs. benchmark functions: A comparative study of optimization performance and representation design

Optimization is a crucial part of every field that requires computation and plays an important role in modern optimization. Metaheuristics algorithms are stochastic algorithms designed in such a way that they don't require the calculation of gradient for optimization. Hence they can be used for optimizing non-linear functions too. Since most real-world optimization problems are non-linear in nature, algorithms provide a sufficiently good solution (close to actual solution) for such optimization problems. This paper is aimed to explain the Genetic Algorithm(GA), Simulated Annealing(SA), and Particle Swarm Optimization(PSO) and compare their performance on benchmark functions. Benchmark functions provides a baseline measurement of the performance of algorithms and allows the algorithm to be compared to some other algorithms in the same manner. The algorithm runs on these functions with an aim to locate an optimal position. The performance and the results obtained can be affected by the parameter setting or operations inside each method. Based on the results, PSO performed better compared to GA and SA in obtaining best minimum fitness.

The Sailfish Optimizer: A novel nature-inspired metaheuristic algorithm for solving constrained engineering optimization problems

In this paper, a completely different metaheuristic algorithm called the Orangutan Optimization Algorithm (OOA) is introduced, which replicates the complex and adaptive behaviors of Orangutans in their natural habitat. The main inspiration for OOA lies in the strategic foraging techniques of Orangutans, alongside their highly developed nesting abilities. More words are used to provide a detailed theoretical explanation of OOA, followed by a comprehensive modeling of the algorithm’s implementation in two key phases: exploration and exploitation. These phases are mathematically structured to ensure the balance required for optimal search processes. The performance of OOA is rigorously evaluated using twenty-nine benchmark functions from the CEC 2017 test suite, with problem dimensions of 10, 30, 50, and 100. More sentences are included to elaborate on the optimization outcomes, which reveal that OOA effectively balances the exploration and exploitation stages, yielding suitable and competitive solutions across the benchmark functions. Additionally, to further validate its quality, the results from OOA are compared against twelve other well-established metaheuristic algorithms. The analysis of these simulation results demonstrates that OOA consistently outperforms competing algorithms by achieving superior results across most benchmark functions. Furthermore, to assess its real-world applicability, OOA is implemented on a set of twenty-two constrained optimization problems drawn from the CEC 2011 test suite. The extended simulation results clearly indicate that OOA is highly efficient in solving real-world optimization challenges, consistently delivering a superior performance when compared to other competitor algorithms.

Nature-inspired metaheuristic algorithms have been a topic of interest for researchers to solve optimization problems in engineering designs and real-world applications, due to their simplicity and flexibility. This paper presents a new nature-inspired search algorithm called Woodpecker Mating Algorithm (WMA) and applies it to challenging problems in structural optimization. The WMA is a population-based metaheuristic algorithm that mimics the mating behavior of woodpeckers. It was inspired by the drumming sound intensity. In WMA, the population of woodpeckers is divided into male and female groups. The female woodpeckers approach the male woodpeckers based on the intensity of their drum sound. An efficiency comparison was drawn between the WMA algorithm and other metaheuristic algorithms by employing 19 benchmark functions(including unimodal, multimodal and composite functions). Moreover, the performance of WMA is compared with 8 of the best meta-heuristic algorithms using 13 high dimensional multimodal and unimodal benchmark functions. The assessments and statistical results indicate that the WMA algorithm offers promising results and is capable of outperforming the most recent and popular algorithms proposed in the literature in most of the employed benchmark functions. Moreover, a statistically significant difference was observed compared to the other assessed algorithms. The proposed algorithm produced significant results for a non-convex, inseparable, and scalable problems.

Marine Predators Algorithm (MPA) is a recent efficient metaheuristic algorithm that is enlightened by the biological behavior of ocean predators and prey. This algorithm simulates the Levy and Brownian movements of prevalent foraging strategy and has been applied to many complex optimization problems. However, the algorithm has defects such as a low diversity of the solutions, ease into the local optimal solutions, and decreasing convergence speed in dealing with complex problems. A modified version of this algorithm called ODMPA is proposed based on the tent map, the outpost mechanism, and the differential evolution mutation with simulated annealing (DE-SA) mechanism. The tent map and DE-SA mechanism are added to enhance the exploration capability of MPA by increasing the diversity of the search agents, and the outpost mechanism is mainly used to improve the convergence speed of MPA. To validate the outstanding performance of the ODMPA, a series of global optimization problems are selected as the test sets, including the standard IEEE CEC2014 benchmark functions, which are the authoritative test set, three well-known engineering problems, and photovoltaic model parameters tasks. Compared with some famous algorithms, the results reveal that ODMPA has achieved better performance than its counterparts in CEC2014 benchmark functions. And in solving real-world optimization problems, ODMPA could get higher accuracy than other metaheuristic algorithms. These practical results demonstrate that the mechanisms introduced positively affect the original MPA, and the proposed ODMPA can be a widely effective tool in tackling many optimization problems.

In many real-world optimization problems, multimodal function optimization is considered, in fact, we are faced with a multimodal optimization problem. Particle swarm optimization (PSO) and continuous ant colony optimization (ACOR) are two population-based optimization techniques that work based on probability laws. The main problem of PSO and ACOR algorithms is premature convergence and falling into local optima. One way to solve the problems is to use combinational methods. This paper presents a combinational method including PSO and ACOR in order to improve the search process. The proposed algorithm tries to solve the problem. Standard benchmark functions are used in order to evaluate the proposed algorithm, proposed method was compared with ACOR, PSO and sequential approach with the enlarged pheromone-particle table of the composition of PSO and ACOR Introduced in [8]. Results show that the proposed method is superior.

Many real-world optimization problems can be solved very efficiently by evolutionary algorithms. There exist many solutions in this field to solve multi-dimensional optimization problems, which is an important issue in today’s world. Swarm-based algorithms are very popular to solve these types of problems because of its effectiveness and quality of solutions. All swarm-based algorithms have different advantages and disadvantages. This paper has discussed two such mostly used algorithms, i.e., particle swarm optimization (PSO) and artificial bee colony (ABC). A fair comparison has been done between these two algorithms by implementing those to minimize five different standard benchmark functions. Results have been recorded and the performance of both the algorithms is analyzed with corresponding to the quality of solutions. It has been observed from the simulation results that ABC outperforms PSO in most of the cases corresponding to solution quality but it requires more time to converge than PSO.

This paper presents a new bio-inspired metaheuristic algorithm called Red Panda Optimization (RPO) that imitates the natural behaviors of red pandas in nature. The main design idea of RPO is derived from two characteristic natural behaviors of red pandas: (i) foraging strategy, and (ii) climbing trees to rest. The proposed RPO approach is mathematically modeled in two phases of exploration based on the simulation of red pandas’ foraging strategy and exploitation based on the simulation of red pandas’ movement in climbing trees. The main advantage of the proposed approach is that there is no control parameter in its mathematical modeling, and for this reason, it does not need a parameter adjustment process. The performance of RPO is evaluated on fifty-two standard benchmark functions including unimodal, high-dimensional multimodal, and fixed-dimensional multimodal types as well as CEC 2017 test suite. The optimization results obtained by the proposed RPO approach are compared with the performance of twelve well-known metaheuristic algorithms. The simulation results show that RPO, by maintaining the balance between exploration and exploitation, is effective in solving optimization problems and its performance is superior over competitor algorithms. Based on the analysis of the optimization results, RPO has provided more successful performance compared to the competitor algorithms in 100% of unimodal functions, 100% of high-dimensional multimodal functions, 100% of fixed-dimensional multimodal functions, and 86.2% of CEC 2017 test suite benchmark functions. Also, the statistical analysis of the Wilcoxon rank sum test shows that the superiority of RPO in the competition with the compared algorithms is significant from a statistical point of view. In addition, the results of implementing RPO on four engineering design problems confirms the ability of the proposed approach to handle real-world optimization applications.

Classical optimization methods often face great difficulties while dealing with several engineering applications. Under such conditions, the use of computational intelligence approaches has been recently extended to address challenging real-world optimization problems. On the other hand, the interesting and exotic collective behavior of social insects have fascinated and attracted researchers for many years. The collaborative swarming behavior observed in these groups provides survival advantages, where insect aggregations of relatively simple and “unintelligent” individuals can accomplish very complex tasks using only limited local information and simple rules of behavior. Swarm intelligence, as a computational intelligence paradigm, models the collective behavior in swarms of insects or animals. Several algorithms arising from such models have been proposed to solve a wide range of complex optimization problems. In this chapter, a novel swarm algorithm called the Social Spider Optimization (SSO) is proposed for solving optimization tasks. The SSO algorithm is based on the simulation of cooperative behavior of social-spiders. In the proposed algorithm, individuals emulate a group of spiders which interact to each other based on the biological laws of the cooperative colony. The algorithm considers two different search agents (spiders): males and females. Depending on gender, each individual is conducted by a set of different evolutionary operators which mimic different cooperative behaviors that are typically found in the colony. In order to illustrate the proficiency and robustness of the proposed approach, it is compared to other well-known evolutionary methods. The comparison examines several standard benchmark functions that are commonly considered within the literature of evolutionary algorithms. The outcome shows a high performance of the proposed method for searching a global optimum with several benchmark functions.

In this paper, a new optimization algorithm called the search and rescue optimization algorithm (SAR) is proposed for solving single‐objective continuous optimization problems. SAR is inspired by the explorations carried out by humans during search and rescue operations. The performance of SAR was evaluated on fifty‐five optimization functions including a set of classic benchmark functions and a set of modern CEC 2013 benchmark functions from the literature. The obtained results were compared with twelve optimization algorithms including well‐known optimization algorithms, recent variants of GA, DE, CMA‐ES, and PSO, and recent metaheuristic algorithms. The Wilcoxon signed‐rank test was used for some of the comparisons, and the convergence behavior of SAR was investigated. The statistical results indicated SAR is highly competitive with the compared algorithms. Also, in order to evaluate the application of SAR on real‐world optimization problems, it was applied to three engineering design problems, and the results revealed that SAR is able to find more accurate solutions with fewer function evaluations in comparison with the other existing algorithms. Thus, the proposed algorithm can be considered an efficient optimization method for real‐world optimization problems.

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.