An Adaptive Memetic Differential Evolution with Virtual Population and Multi-Mutation Strategies for Multimodal Optimization Problems

Multimodal optimization is characterized by the dual imperative of achieving global peak diversity and local precision enhancement for discovered solutions. An adaptive memetic differential evolution is proposed in this work based on the virtual population mechanism and multi-mutation strategy to tackle these problems. Firstly, the virtual population mechanism (VPM) is designed to support the maintenance of population diversity, taking advantage of the distribution of a current population to obtain a virtual population. In this mechanism, the virtual population is used to provide certain requirements for the population evolution, but it does not participate in the evolution operation itself. The multi-mutation strategy (MMS) is further executed on the joint virtual and current populations, with the explicit aim of assigning promising candidates to exploitation tasks and less promising ones to exploration tasks during the creation of offspring. Additionally, a probabilistic local search (PLS) scheme is introduced to enhance the precision of elite solutions. This scheme specifically targets the fittest-and-farthest individuals, effectively addressing solution inaccuracies on the identified peaks. Through comprehensive benchmarking on standard test problems, the proposed algorithm demonstrates performance that is either superior or on par with existing methods, confirming its overall competitiveness.