A Fitness Spatially Informed Evolutionary Algorithm for Deceptive Multi-Modal Multi-Objective Optimization

Evolutionary Algorithms (EAs) are effective for solving Multi-Modal Multi-Objective Optimization Problems which optimal solutions subsets distributed regularly in the decision space. Existing EAs, however, are hard to achieve good diversity in the decision space due to their lack of thinking-in-space when solving deceptive multi-modal multi-objective problems, and one manifestation of the deceptiveness is that global optima are composed of unconnected small optimal solution subsets that randomly distributed in the decision space with many local optima subsets mixed among. In this study, for enabling EAs to continuously search without trapping, a solving pathway is proposed that identifies information-rich historical data and constructs structured spatial representation based on high-quality evolutionary data. Furthermore, a moderate region-oriented solution set update methodology is proposed for the detection of ultra-small optimal modalities, and two novel environmental selection and archive update mechanisms are designed. A Memory-aiding Search Multi-Modal Multi-Objective Optimization EA, i.e., MS-MMOEA, is instantiated. The experimental results on 27 deceptive instances and a real-world problem demonstrate MS-MMOEA’s competitiveness over the state-of-the-art.