A directed batch growing self-organizing map based niching differential evolution for multimodal optimization problems

Abstract

Many real-world optimization problems naturally result in multiple optimal solutions, thereby falling in the class of multimodal optimization problems (MMOPs). A task of finding a plurality of optimal solutions for MMOPs comes under the scope of multimodal optimization algorithms (MMOAs). To solve MMOPs, niching techniques are usually employed by proactively modifying standard evolutionary algorithms (EAs) to form stable subpopulations around multiple niches within their evolving populations. This way, each optimum can germinate and eventually help form a cloud of solutions around each optimum parallely, thereby finding multiple (but a finite number of) optima simultaneously. However, several existing niching techniques suffer from common drawbacks, such as sensitivity with niching parameters or poor performance on high-dimensional problems. An efficient niching technique needs an effective population partitioning method around distinct leading solutions representing each optimum. In this paper, we propose a directed batch growing self-organizing map based niching differential evolution (DBGSOM-NDE). For this purpose, a standard differential evolution (DE) method is divided into two overlapping phases: (i) population-wide search (PS) and (ii) niche-wide search (NS). PS executes neighborhood search around each individual, promoting exploration, while NS explores only the leaders, thus reducing the effect of exploration for a better search intensification around the leaders using a Cauchy-distribution based local search to improve them. We evaluate the role of each operator of the proposed approach DBGSOM-NDE and compare its performance with a number of state-of-the-art niching techniques demonstrating its competitiveness and superiority, especially on high-dimensional and nonlinear problems taken from the existing literature. Finally, a hyper-parametric study is provided demonstrating weak dependence of them to the algorithm’s performance.