An enhanced fast non-dominated solution sorting genetic algorithm for multi-objective problems

Multi-modal multi-objective optimization problem (MMOPs) has attracted more and more attention in evolutionary computing recently. It is not easy to solve these problems using the existing evolutionary algorithms. The non-dominated solution sorting genetic algorithm (NSGA-II) has poor PS distribution and convergence. In this paper, an enhanced fast NSGA-II based on a special congestion strategy and adaptive crossover strategy, namely ASDNSGA-II is proposed. In the ASDNSGA-II, the strategy with a special congestion degree is used to improve the selection strategy. Then a new adaptive crossover strategy is designed by evaluating the advantages and disadvantages of the SBX crossover strategy with the ability to solve high dimensions and the BLX-α with the ability of Pareto solution to produce offspring solutions. These can ensure the generation of offspring solutions around individuals with large crowding degrees and balance the convergence and diversity of decision space and object space. It can improve PS distribution and convergence and maintain PF precision. Eight functions of MMF1-MMF8 from the CEC2020 are selected to prove the effectiveness of the ASDNSGA-II. By comparing several latest multi-modal multi-objective evolutionary algorithms, the results show that the ASDNSGA-II can effectively find the global Pareto solution set and improve the distribution and convergence of PS.