A distributed individuals based multimodal multi-objective optimization differential evolution algorithm

There may exist a one-to-many mapping between objective and decision spaces in multimodal multi-objective optimization problems (MMOPs), which requires the evolutionary algorithm to locate multiple non-dominated solution sets. In order to enhance the diversity of the population, we develop a multimodal multi-objective differential evolution algorithm based on distributed individuals and lifetime mechanism. First, every individual can be seen as a distributed unit to locate multiple non-dominated solutions. The solutions with the good diversity are generated by adopting virtual population, and the range of virtual population is adjusted by an adaptive adjustment strategy to locate more non-dominated solutions. Second, it is considered that each individual has a limited lifespan inspired by natural phenomenon. As the search area of individuals becoming adaptively smaller, the individuals with good quality are archived and they can reinitialize with a new lifespan for enhancing diversity of the search space. Then the probability selection strategy is applied in the environment selection to balance exploration and exploitation. The test results on 22 multimodal multi-objective benchmark test functions verify the superior performance of the proposed method.