Multimodal multi-objective differential evolution algorithm based on spectral clustering

In recent years, in the face of the same problem in industrial production and life, decision-makers often hope to have a variety of different solutions to deal with. In other words, we hope to locate more different Pareto solutions under the condition of finding Pareto front. However, there are few researches in this field. For this reason, we propose a multimodal multi-objective differential evolution algorithm based on spectral clustering (SC-MMODE), which mainly uses some mechanisms to divide the solutions in the decision space into several mutually independent subpopulations. First, SC-MMODE uses a spectral clustering algorithm to control the decision space and form multiple sub-populations with good neighbourhood relations. Secondly, a special crowding distance mechanism is used to balance the distribution of solutions in the decision space and objective space. In addition, the classical differential evolution algorithm can effectively prevent premature convergence. Then, in 17 test problems, the SC-MMODE algorithm and some new multimode multi-objective algorithms are tested simultaneously. Finally, through the analysis of experimental data, the SC-MMODE algorithm can find more Pareto optimal sets in the decision space, so it can effectively solve such problems.