A new distribution metric for comparing Pareto optimal solutions

Evolutionary multi-objective optimization has established itself a core field of research and application, with a proliferation of algorithms derived. During the multi-objective optimization processes, the discovered ideal solutions should be diversely distributed at the Pareto front. In order to measure and compare the performances of different multi-objective evolutionary algorithms, or provide a guidance for the search or a stopping criterion, various performance metrics are defined and used. In this paper, two of the most commonly used metrics, the spacing metric and the overall Pareto spread metric, which evaluate the uniformity and the range of the Pareto solutions' distribution are studied, respectively. A new distribution metric which potentially can combine these two metrics and resolve their deficiencies for comparing Pareto optimal solutions is then proposed. Five typical Pareto fronts and a real practical example are used to demonstrate the effectiveness of the proposed metric by comparing with the subject matter experts' ratings.