Nowadays, multimodal multi-objective optimization problems (MMOPs) have received increasing attention from many researchers. In such problems, there are situations where two or more Pareto Sets (PSs) correspond to the same Pareto Front (PF). It is crucial to obtain as many PSs as possible without compromising the performance of the objective space. Therefore, this paper proposes an enhanced multimodal multi-objective genetic algorithm with a novel adaptive crossover mechanism, named AEDN_NSGAII. In the AEDN_NSGAII, the special crowding distance strategy can provide potential development opportunities for individuals with a larger crowding distance. An adaptive crossover mechanism is established by combining the simulated binary crossover (SBX) operator and the Laplace crossover (LP) operator, which adaptively improves the ability to obtain Pareto optimal solutions. Meanwhile, an elite selection mechanism can efficiently get more excellent individuals as parents to enhance the diversity of the decision space. Then, the proposed algorithm is evaluated on the CEC2019 test suite by the Friedman method and discussed for its feasibility through ablation experiments and boxplot analysis of PSP indicators. Experimental results show that AEDN_NSGAII can effectively search for more PSs without weakening the diversity and convergence of objective space. Finally, the performance of AEDN_NSGAII on the multimodal feature selection problem is compared with that of the other four algorithms. The statistical analysis demonstrates that the proposed algorithm has great potential for resolving this issue.
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