Multimodal and multi-objective optimization algorithm based on two-stage search framework

The problem that multiple Pareto solution sets correspond to the same Pareto front is called multimodal multi-objective optimization problem. Solving all Pareto solution sets in this kind of problem can provide decision makers with more convenient and accurate choices. However, the traditional multi-objective optimization algorithm often ignores the distribution of solutions in the decision space when solving such problems, resulting in poor diversity of Pareto solution sets.To solve this problem, a two-stage search algorithm framework is proposed. This framework divides the optimization process into two parts: global search and local search to balance the search ability of the algorithm. When searching globally, locate as many approximate locations with the optimal solution as possible, providing a good population distribution for subsequent local searches. In local search, DBSCAN clustering method with adaptive neighborhood radius is used to divide the population into several subpopulations, so as to enhance the local search ability with the algorithm. At the same time, an individual selection mechanism based on the farthest-candidate approach with two spaces is proposed to keep the diversity of the population in the objective space and decision space. The algorithm is compared with five state-of-the-art algorithms on 22 multimodal and multi-objective optimization test functions. The experimental results indicate that the proposed algorithm can search more Pareto solution sets while maintaining the diversity of solutions in the objective space.