The Research On Diversity Metric Of Multi-Objective Evolutionary Algorithm

In the research of MOEA (Multi-Objective Evolutionary Algorithm), many algorithms for multi-objective optimization have been proposed. MOEAs don't guarantee to identify the Pareto optimal solutions but try to find a good approximation. Therefore, the questions arise of how to evaluate the quality of approximation results for a given problem. For this purpose, various performance metrics for measuring the quality of observed Pareto optimal sets have been proposed to compare the performance of different MOEAs. By realizing that there are two main functional goals of MOEAs, efforts can be made in devising two metrics: (i) one for measuring the convergence of solutions to the Pareto-optimal front and (ii) the other for measuring the diversity of solutions. Because the diversity of solutions is an important measure, it is significant how to evaluate the diversity of an MOEA. In this paper, we not only introduce briefly the history of MOEA and the several representative MOEAs, but also analyze the research works that experts and scholars are going along within the aspect of diversity metric. From the features of current diversity metrics, we discuss the K-means clustering algorithm of the distances between individuals, and put forward the diversity metric based on clustering. Implying this metric, we compare several popular multi-objective evolutionary algorithms. It is shown by experimental results that the method can evaluate the diversity of algorithms more exactly, especially helps to provide a comparative evaluation of two or more MOEAs.