An Adjustable Diversity Metric for Multimodal Multi-objective Evolutionary Algorithms

AbstractThe performance of multimodal multi-objective evolutionary algorithms (MMEAs) is determined by not only the convergence to the Pareto front in the objective space, but also the distribution spread to the Pareto set in the decision space. Comparing with the performance matrix applied in the objective space, the performance assessment in the decision space should pay more attention to the distribution spread of solutions. This paper presents a novel diversity metric (PSCR) to reveal the distribution spread of a solution set to the pareto set in the decision space. In addition, in order to avoid the influence of boundary individuals, the grid-partition method is adopted. Through adjusting the scale of the grid, the proposed PSCR could evaluate the MMEAs on both coarse-grained and fine-grained way. The test is carried out on 6 test functions and the reasonable range of parameters is discussed. Moreover, the results of 21 experiments were measured with metrics, and PSCR was compared with other metrics. It was proved that PSCR could not only accurately measure the performance of the algorithm, but also had a higher degree of differentiation than the other metrics.KeywordsMultimodal multi-objective optimizationMetricDiversity