arXiv:2510.00877cs.NEcs.AI2025-10被引 9

用四步法可视化多目标优化中的权衡关系,助力决策。

A Technique Based on Trade-off Maps to Visualise and Analyse Relationships Between Objectives in Optimisation Problems

  • 基于肯德尔相关与灰度码映射,分析目标间全局关系。
  • 在三个组合优化问题上验证,揭示目标间复杂权衡。
  • 适合需要理解多目标难题的优化研究者使用。

在多目标优化问题中理解目标间的相互关系,对设计高效求解方法至关重要。尤其在现实物流场景中出现的多目标组合优化问题,若能更深入理解复杂的适应度景观,可显著提升对决策者的辅助能力。本文提出一种新方法,用于可视化和分析多目标优化中目标间的局部与全局关系。该方法包含四个步骤:首先采用肯德尔相关法分析全局成对关系;其次估计并评估给定帕累托前沿上的取值范围;接着利用这些范围绘制类似卡诺图的灰度码地图,以突出多个目标间的权衡;最后通过散点图识别局部关系。实验针对三类组合优化问题:多目标多维背包问题、多目标护士排班问题、带时间窗的多目标车辆路径问题。结果表明,该技术有助于洞察由目标间关系引发的问题难度。

原文摘要 · Abstract (English)

Understanding the relationships between objectives in a multiobjective optimisation problem is important for developing tailored and efficient solving techniques. In particular, when tackling combinatorial optimisation problems with many objectives, that arise in real-world logistic scenarios, better support for the decision maker can be achieved through better understanding of the often complex fitness landscape. This paper makes a contribution in this direction by presenting a technique that allows a visualisation and analysis of the local and global relationships between objectives in optimisation problems with many objectives. The proposed technique uses four steps: First, the global pairwise relationships are analysed using the Kendall correlation method; then, the ranges of the values found on the given Pareto front are estimated and assessed; next, these ranges are used to plot a map using Gray code, similar to Karnaugh maps, that has the ability to highlight the trade-offs between multiple objectives; and finally, local relationships are identified using scatter plots. Experiments are presented for three combinatorial optimisation problems: multiobjective multidimensional knapsack problem, multiobjective nurse scheduling problem, and multiobjective vehicle routing problem with time windows . Results show that the proposed technique helps in the gaining of insights into the problem difficulty arising from the relationships between objectives.

多目标优化可视化权衡分析

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