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One of the most common approaches for multiobjective optimization is togenerate a solution set that well approximates the whole Pareto-optimalfrontier to facilitate the later decision-making process. However, how toevaluate and compare the quality of different solution sets remainschallenging. Existing measures typically require additional problem knowledgeand information, such as a reference point or a substituted set of thePareto-optimal frontier. In this paper, we propose a quality measure, calleddominance move (DoM), to compare solution sets generated by multiobjectiveoptimizers. Given two solution sets, DoM measures the minimum sum of movedistances for one set to weakly Pareto dominate the other set. DoM can be seenas a natural reflection of the difference between two solutions, capturing allaspects of solution sets' quality, being compliant with Pareto dominance, anddoes not need any additional problem knowledge and parameters. We present anexact method to calculate the DoM in the biobjective case. We show thenecessary condition of constructing the optimal partition for a solution set'sminimum move, and accordingly propose an efficient algorithm to recursivelycalculate the DoM. Finally, DoM is evaluated on several groups of artificialand real test cases as well as by a comparison with two well-establishedquality measures.

Dominance Move: A Measure of Comparing Solution Sets in Multiobjective Optimization