Historical knowledge-based MBO for global optimization problems and its application to clustering optimization
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METHODOLOGIES AND APPLICATION
Historical knowledge-based MBO for global optimization problems and its application to clustering optimization Mahdi Rahbar1 • Samaneh Yazdani1
Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Monarch butterfly optimization (MBO), which is a simple and widely used algorithm, has some limitations, such as utilizing the obtained experiential knowledge about the search space inefficiently, the lack of exploration, and being rotational variance. This paper proposes a new variation of MBO, which is called knowledge-based MBO (KMBO), to address these limitations. KMBO is proposed by introducing new operators that are linearized and can utilize the population’s experimental knowledge. Furthermore, KMBO adopts the re-initialization operator to enhance the exploration ability and increase the diversity of the population. To verify KMBO’s performance, it is tested on 23 well-known optimization benchmark functions and compared with MBO and five other state-of-the-art evolutionary algorithms. Experimental results confirm the superior performance of our proposed algorithm compared with MBO in terms of solution accuracy and convergence speed. Also, results demonstrate that KMBO performs better than or provides competitive performance with the other six algorithms. In addition, the real-world application of KMBO on clustering optimization is presented. The results prove that KMBO is applicable to solve real-world problems and achieve superior results. Keywords Monarch butterfly optimization Numerical optimization Clustering optimization Experiential knowledge
1 Introduction Mathematical optimization is the process of achieving the best solution for minimizing or maximizing a given function (Wang et al. 2019a). Swarm intelligence (SI) and EAs are a branch of optimization techniques that have shown considerable success in solving complex optimization problems in which traditional mathematical methods sometimes can’t obtain good solutions (Wang et al. 2019a; Engelbrecht 2007). The performance of SI algorithms depends on the exploration–exploitation trade-off, which is affected by SI algorithms’ operators, and the way in which their parameters are adjusted. Several improved approaches
Communicated by V. Loia. & Samaneh Yazdani [email protected] Mahdi Rahbar [email protected] 1
Department of Electrical and Computer Engineering, North Tehran Branch, Islamic Azad University, Tehran, Iran
have been presented for each proposed SI algorithms by modifying their operators and adjusting their parameters. MBO (Wang et al. 2019b) is one of the recently developed SI algorithms, which is presented by emulating the monarch butterflies’ behavior. A distinct feature of MBO, which is a population-based metaheuristic algorithm, is that it divides the population into two subpopulations (Subpopulation 1 and Subpopulation 2). It applies migration and adjusting operators for updating individuals of Subpopulation 1 and Subpopulation 2,
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