Simplex Search Based Brain Storm Optimization

TL;DR

This paper introduces Simplex-BSO, a hybrid algorithm combining Brain Storm Optimization with Nelder-Mead Simplex to improve convergence and accuracy in global optimization tasks.

Contribution

It proposes a novel hybrid approach that balances exploration and exploitation, effectively addressing the degenerated L-curve phenomenon in BSO.

Findings

Eliminates the L-curve phenomenon on unimodal functions.

Significantly alleviates the L-curve issue on multimodal functions.

Demonstrates promising results in global optimization experiments.

Abstract

Through modeling human's brainstorming process, the brain storm optimization (BSO) algorithm has become a promising population-based evolutionary algorithm. However, BSO is pointed out that it possesses a degenerated L-curve phenomenon, i.e., it often gets near optimum quickly but needs much more cost to improve the accuracy. To overcome this question in this paper, an excellent direct search based local solver, the Nelder-Mead Simplex (NMS) method is adopted in BSO. Through combining BSO's exploration ability and NMS's exploitation ability together, a simplex search based BSO (Simplex-BSO) is developed via a better balance between global exploration and local exploitation. Simplex-BSO is shown to be able to eliminate the degenerated L-curve phenomenon on unimodal functions, and alleviate significantly this phenomenon on multimodal functions. Large number of experimental results show that Simplex-BSO is a promising algorithm for global optimization problems.