Hypercube-Based Crowding Differential Evolution with Neighborhood Mutation for Multimodal Optimization

1. Introduction

In practical optimization problems, it is not uncommon that multiple global and local optima need to be located for a given objective function. Therefore, multimodal optimization is proposed to deal with optimization tasks that involve finding multiple optima of a problem rather than a single best solution. Recently, in the field of optimization, there have been lots of theory and application researches on evolutionary algorithms (EAs) such as particle swarm optimization (PSO) (Jordehi, 2015; Jordehi et al., 2015), differential evolution (DE) (Storn et al., 1997; Das et al., 2011). Particularly, the research of evolutionary multimodal optimization algorithms (Wong, 2015; Das et al., 2011) is quite popular since most EAs are population-based and they are naturally excelling at parallel search to find multiple optima. Different evolutionary multimodal optimization algorithms have been developed based on different EAs, such as multimodal genetic algorithm (GA) (Yao et al., 2010; Kamyab et al., 2013, 2016), multimodal PSO (Chang, 2015; Li, 2011; Zhang et al., 2015), multimodal estimation of distribution algorithm (EDA) (Yang, et al., 2017) and multimodal DE (Liang et al., 2014; Qu et al., 2012; Zhang. et al., 2015). Among those EAs, DE has been widely researched and adopted to tackle optimization problems in various areas (Cheng et al., 2014; Pan et al., 2015; Rocca et al., 2011), due to its simplicity and high efficiency. Thus, in this study, we devote efforts to further research on DE for multimodal optimization.