Fitness and distance based local search with adaptive differential evolution for multimodal optimization problems

Local search has been regarded as a promising technique in multimodal algorithms to refine the accuracy of found multiple optima. However, how to execute the local search operations precisely on the found global optima and avoid the meaningless local search operations on local optima or found similar areas is still a challenge. In this paper, we propose a novel local search technique based on the individual information from two aspects, termed as fitness and distance based local search (FDLS). The fitness information can avoid the ineffective local search operations on the local optima, while the distance information can avoid the meaningless local search operations on the similar areas. These two kinds of information act in different roles and complement each other, which ensures that the local search is executed in different (ensured by distance information) and promising (ensured by fitness information) areas, leading to successful local search. Based on this, we design an adaptive DE (ADE) with adaptive parameters scheme and apply FDLS to ADE, termed as FDLS-ADE. Experimental results on the CEC2015 multimodal competition show the effectiveness and superiority of the FDLS-ADE, including comparisons with the winner of the CEC2015 multimodal competition. Furthermore, compared with other multimodal algorithms, the performance of the FDLS-ADE is seen relatively insensitive to niching parameters. Besides, experiments conducted also show that the FDLS can be applied to other multimodal algorithms easily and can further improve their performance. Finally, an application to a real-world nonlinear equations system further illustrates the applicability of the FDLS-ADE.