Solving multimodal optimization problems by a knowledge-driven brain storm optimization algorithm

Multimodal optimization problem (MMOP) refers to the problem having more than one optima or satisfied solution in the decision space. The accuracy and diversity of solutions should be considered when solving MMOPs. In the brain storm optimization (BSO) algorithm, the information on current solutions is analyzed, but the information on previous solutions needs to be more effectively used to guide the search. A knowledge driven BSO in objective space (KBSOOS) algorithm is proposed to enhance the search performance and to maintain the diversity of the solutions for solving MMOPs. In addition, a diversity indicator is proposed as a quantitative measurement to measure the performance of various algorithms for solving MMOPs. The 30 nonlinear equation system (NES) problems are modeled as MMOPs and solved by six swarm intelligence algorithms to validate the proposed algorithm's performance. Based on the experimental results, the diversity indicator could give a good indication of the performance of algorithms, and the KBSOOS algorithm could enhance the performance of various BSO algorithms.