Localized Distance and Time-based Differential Evolution for Multimodal Optimization Problems

Multimodal optimization problems (MMOPs) aim to find global multiple optimal solutions with high accuracy. Although many state-of-the-art algorithms are proposed to deal with MMOPs, there are still some challenges as how to avoid local optima and how to refine the solutions accuracy. Aim to these, this paper proposes a Localized Distance and Time-based Differential Evolution (LDTDE) for MMOPs, which includes three contributions. Firstly, a Random and Neighborhood-based Mutation (RNM) strategy is proposed to avoid local optima and refine the accuracy of found solutions. That is each individual not only performs random-based mutation operation but also performs neighborhood-based mutation operation by Euclidean distance. Secondly, a Locality-based Crowding Selection (LCS) strategy is introduced to accelerate the convergence and further approach the global optima. Thirdly, an Adaptive Parameter Control (APC) strategy is proposed to reduce the sensitivity of parameters, which can dynamically calculate the appropriate parameters for each individual based on the state of itself. The performance of LDTDE is tested on CEC'2013 and compared with state-of-the-art multimodal optimization algorithms.