Sampling Reference Points on the Pareto Fronts of Benchmark Multi-Objective Optimization Problems

The effectiveness of evolutionary algorithms have been verified on multi-objective optimization, and a large number of multi-objective evolutionary algorithms have been proposed during the last two decades. To quantitatively compare the performance of different algorithms, a set of uniformly distributed reference points sampled on the Pareto fronts of benchmark problems are needed in the calculation of many performance metrics. However, not much work has been done to investigate the method for sampling reference points on Pareto fronts, even though it is not an easy task for many Pareto fronts with irregular shapes. More recently, an evolutionary multi-objective optimization platform was proposed by us, called PlatEMO, which can automatically generate reference points on each Pareto front and use them to calculate the performance metric values. In this paper, we report the reference point sampling methods used in PlatEMO for different types of Pareto fronts. Experimental results show that the reference points generated by the proposed sampling methods can evaluate the performance of algorithms more accurately than randomly sampled reference points.