Efficient hybrid algorithm based on moth search and fireworks algorithm for solving numerical and constrained engineerin

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Efficient hybrid algorithm based on moth search and fireworks algorithm for solving numerical and constrained engineering optimization problems Xiaoxia Han1   · Lin Yue1 · Yingchao Dong1 · Quanxi Xu1 · Gang Xie1,2 · Xinying Xu1

© Springer Science+Business Media, LLC, part of Springer Nature 2020

Abstract The moth search algorithm (MS) is a novel intelligent optimization algorithm based on moth population behavior, which can solve many problems in different fields. However, the algorithm is easy to fall into local optimization when solving complex optimization problems. This study develops a new hybrid moth search-fireworks algorithm (MSFWA) to solve numerical and constrained engineering optimization problems. The explosion and mutation operators from the fireworks algorithm are introduced into the MS, which not only preserves the advantages of fast convergence and strong exploitation capability of the algorithm, but also significantly enhances the exploration capability. The performance of the MSFWA is tested using 23 benchmark functions. The hybrid algorithm is superior to other highly advanced metaheuristic algorithms for most benchmark functions, demonstrating the characteristics of fast convergence and high stability. Finally, the ability of the MSFWA to solve practical constrained problems is evaluated on six well-known engineering application problems. Compared with other optimization algorithms, the MSFWA is very competitive in its solution of these complex and constrained practical problems. Keywords  Constrained engineering optimization problem · Moth search-fireworks algorithm · Exploitation · Exploration · Explosion and mutation operators

* Xiaoxia Han [email protected] 1

College of Electrical and Power Engineering, Department of Automation, Taiyuan University of Technology, No. 79 Yingze West Street, Taiyuan 030024, Shanxi, China

2

School of Electronic and Information Engineering, Taiyuan University of Science and Technology, Taiyuan 030024, Shanxi, China



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1 Introduction Optimization refers to the process of finding the optimal solution under specific conditions   [1, 2]. Although a lot of research shows that traditional mathematical methods can solve continuous, unimodal, differential, and linear problems, optimization problems in the real world are often nonlinear, discontinuous, non-differentiable, and multimodal  [3]. Moreover, some complex optimization problems cannot be solved in sufficient time or accuracy by classical methods  [4]. Therefore, many researchers have proposed a new solution, i.e., metaheuristic algorithms. Compared with traditional mathematical methods, metaheuristic algorithms do not rely on gradient information and are applicable to different problems and fields  [2, 5, 6]. In recent years, many metaheuristic algorithms based on some mechanisms and principles of nature have been proposed by researchers and are widely used in practical engineering optimization problems. According to different search mechanisms, researchers div