A Landscape-Aware Differential Evolution for Multimodal Optimization Problems

Abstract

How to simultaneously locate multiple global peaks and achieve certain accuracy on the found peaks are two key challenges in solving multimodal optimization problems (MMOPs). In this article, a landscape-aware differential evolution (LADE) algorithm is proposed for MMOPs, which utilizes landscape knowledge to maintain sufficient diversity and provide efficient search guidance. In detail, the landscape knowledge is efficiently utilized in the following three aspects. First, a landscape-aware peak exploration helps each individual evolve adaptively to locate a peak and simulates the regions of the found peaks according to search history to avoid an individual re-locating an already found peak. Second, a landscape-aware peak distinction distinguishes whether an individual locates a new global peak, a new local peak, or an already found peak. Accuracy refinement can thus only be conducted on the global peaks to enhance the search efficiency. Third, a landscape-aware reinitialization specifies the initial position of an individual adaptively according to the distribution and distinction of the found peaks, which helps explore more peaks. The experiments are conducted on the widely-used benchmark MMOPs and multimodal nonlinear equation system problems. Experimental results show that LADE obtains generally better or competitive performance compared with seven well-performing recent algorithms and four winner algorithms in the IEEE CEC competitions for multimodal optimization.