Dominance Move：多目标优化问题解集比较的度量
Dominance Move: A Measure of Comparing Solution Sets in Multiobjective Optimization
摘要：
多目标优化最常用的方法之一是生成一个很好地逼近整个帕累托最优边界的解集，以便于以后的决策过程。然而，如何评估和比较不同的解决方案集的质量仍然具有挑战性。现有的措施通常需要额外的问题知识和信息，如参考点或替代的帕累托最优边界集。在本文中，我们提出了一个质量的措施，称为优势移动（DoM），比较多目标优化生成的解决方案集。给定两个解集，DoM测量一个解集弱帕累托支配另一个解集的最小移动距离之和。DoM可以被视为两个解决方案之间差异的自然反映，捕获解决方案集质量的所有方面，符合Pareto优势，并且不需要任何额外的问题知识和参数。我们提出了一种精确的方法来计算双目标情况下的DoM。我们给出了构造解集最小移动的最优划分的必要条件，并据此提出了一个递归计算DoM的有效算法。最后，DoM的几组人工和真实的测试案例，以及通过比较两个完善的质量措施进行评估。
英文摘要：
One of the most common approaches for multiobjective optimization is to generate a solution set that well approximates the whole Pareto-optimal frontier to facilitate the later decision-making process. However, how to evaluate and compare the quality of different solution sets remains challenging. Existing measures typically require additional problem knowledge and information, such as a reference point or a substituted set of the Pareto-optimal frontier. In this paper, we propose a quality measure, called dominance move (DoM), to compare solution sets generated by multiobjective optimizers. Given two solution sets, DoM measures the minimum sum of move distances for one set to weakly Pareto dominate the other set. DoM can be seen as a natural reflection of the difference between two solutions, capturing all aspects of solution sets' quality, being compliant with Pareto dominance, and does not need any additional problem knowledge and parameters. We present an exact method to calculate the DoM in the biobjective case. We show the necessary condition of constructing the optimal partition for a solution set's minimum move, and accordingly propose an efficient algorithm to recursively calculate the DoM. Finally, DoM is evaluated on several groups of artificial and real test cases as well as by a comparison with two well-established quality measures.
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