Minimum spanning tree niching-based differential evolution with knowledge-driven update strategy for multimodal optimization problems

Abstract

Multimodal optimization problems (MMOPs) aim to simultaneously locate as many global optima as possible with high accuracy. Recently, many niching strategies have been wildly used in evolutionary algorithms to solve MMOPs due to the advantage of maintaining the diversity of population. However, most multimodal algorithms are sensitive to the niching parameters and lack effective methods to update the “stagnant individuals”, including individuals that have trapped into local optima or converged to the same optima. In this paper, a minimum spanning tree niching-based differential evolution (TNDE) with knowledge-driven update (KDU) strategy is proposed to better solve the above challenges, where the “knowledge” includes historical evolutionary information, fitness distribution information, and individual distribution information. In TNDE, a minimum spanning tree niching (MSTN) strategy is proposed to adaptively divide the population, which can adjust the number of niches dynamically. Besides, the KDU strategy is proposed to utilize the knowledge to locate and update stagnant individuals. Lastly, an improved differential evolution with local stage-based mutation (LSM) and directional guidance selection (DGS) strategies is proposed to accelerate convergence and refine the accuracy of solutions, respectively. The comparison results with 16 state-of-the-art algorithms on CEC’2013 show that TNDE achieves significant advantages on high-dimensional problems or problems with many global optima.