Niching Diversity Estimation for Multi-modal Multi-objective Optimization
This work addresses a specific bottleneck in evolutionary optimization for multi-modal problems, offering an incremental improvement to existing methods.
The paper tackles the problem of maintaining decision-space diversity in multi-modal multi-objective optimization, where standard diversity estimators fail due to overlapping solutions in objective space. The proposed niching mechanism, integrated into SPEA2 and NSGA-II, notably enhances performance on various MMOPs, as shown in experiments.
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.