Uniformity assessment for evolutionary multi-objective optimization

Uniformity assessment of approximations of the Pareto-optimal set is an important issue in comparing the performance of multi-objective evolutionary algorithms. Although a number of performance metrics existed, many are applicable to low objective problems (2–3 objectives). In addition, most of the existed metrics are only applied to the final non-dominated set. In this paper, we suggest a running metric which evaluates the uniformity of solutions at every generation of a MOEA run. In particular, this metric can compare the uniformity of population with different size in any number of objectives. With an agglomeration of generation-wise populations, the metric reveals the change of uniformity in a MOEA run or helps provide a comparative evaluation of two or more MOEAs.