Leaders and followers — A new metaheuristic to avoid the bias of accumulated information

Finding good solutions on multi-modal optimization problems depends mainly on the efficacy of exploration. However, many search techniques applied to multi-modal problems were initially conceptualized with unimodal functions in mind, prioritizing exploitation over exploration. In this paper, we perform a study on the efficacy of exploration under random sampling, which leads to the identification of an important comparison bias that occurs when a solution which has benefited from local search is compared to the first (random) solution in a new search area. With the goal of eliminating this bias and improving the efficacy of exploration, we have developed a new search technique explicitly designed for multi-modal search spaces. “Leaders and Followers” aims to eliminate the negative effects of information accumulation and at the same time use the information from the best solutions in a way that they have controlled influence over the newly-sampled solutions. The proposed metaheuristic outperforms both Particle Swarm Optimization and Differential Evolution across a broad range of multi-modal optimization problems.