A Weakly Pareto Compliant Quality Indicator

Abstract: In multi-objective optimization problems, the optimization target is to obtain a set of non-dominated solutions. Comparing solution sets is crucial in evaluating the performances of different optimization algorithms. The use of performance indicators is common in comparing those sets and, subsequently, optimization algorithms. A good solution set must be close to the Pareto-optimal front, well-distributed, maximally extended and fully filled. Therefore, an effective performance indicator must encompass these features as a whole and must be Pareto dominance compliant. Unfortunately, some of the known indicators often fail to properly reflect the quality of a solution set or cost a lot to compute. This paper demonstrates that the Degree of Approximation (DOA) quality indicator, is a weakly Pareto compliant unary indicator that gives a good estimation of the match between the approximated front and the Pareto-optimal front. Moreover, DOA computation is easy and fast.