  Niching is an important and widely used technique in evolutionary
multi-objective optimization. Its applications mainly focus on maintaining
diversity and avoiding early convergence to local optimum. Recently, a special
class of multi-objective optimization problems, namely, multi-modal
multi-objective optimization problems (MMOPs), started to receive increasing
attention. In MMOPs, a solution in the objective space may have multiple
inverse images in the decision space, which are termed as equivalent solutions.
Since equivalent solutions are overlapping (i.e., occupying the same position)
in the objective space, standard diversity estimators such as crowding distance
are likely to select one of them and discard the others, which may cause
diversity loss in the decision space. In this study, a general niching
mechanism is proposed to make standard diversity estimators more efficient when
handling MMOPs. In our experiments, we integrate our proposed niching diversity
estimation method into SPEA2 and NSGA-II and evaluate their performance on
several MMOPs. Experimental results show that the proposed niching mechanism
notably enhances the performance of SPEA2 and NSGA-II on various MMOPs.
