Superior relation‐based firefly algorithm for superior solution set search problem

In this paper, we analyze the properties of the superior solution set search (SSSS) problem and point out the structural similarities between it and the multiobjective optimization problem. Based on the analyzed properties, we propose a new Firefly algorithm (FA) based on superior relations, which can search for the superior solution set by using the user's quantitative desire level as a search strategy. By introducing the distance of the problem space into the moving mechanism, FA makes it possible to search for multiple local optimal solutions by dividing the solution set into multiple groups. By analyzing this property of FA, we clarify the affinity between FA and the SSSS problem. We subsequently analyze the SSSS problem and FA, and discuss their properties together in a similar problem setting. We propose an FA based on superior relations as a new optimization technique for the superior solution set problem based on these analyses. Numerical experiments are then conducted using the SSSS problem and demonstrate the usefulness of the proposed method by comparing the performance of the proposed method with the conventional FA. © 2019 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.