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 different 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.

中文翻译：

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一种基于折衷图的技术，可以可视化和分析优化问题中目标之间的关系

了解多目标优化问题中目标之间的关系对于开发量身定制的有效求解技术非常重要。特别是，当解决现实世界中后勤场景中出现的许多目标的组合优化问题时，可以通过更好地理解通常复杂的适应状况来为决策者提供更好的支持。本文通过提出一种技术，可以对具有多个目标的优化问题中的目标之间的局部和全局关系进行可视化和分析，从而对此方向做出了贡献。所提出的技术分四个步骤：首先使用Kendall相关方法分析全局成对关系。然后估计和评估在给定的帕累托前沿找到的值的范围；接下来，这些范围用于使用格雷代码绘制类似于卡诺图的地图，该图能够突出显示多个目标之间的取舍。最后使用散点图确定局部关系。针对三个不同的组合优化问题提出了实验：多目标多维背包问题，多目标护士调度问题和带时间窗的多目标车辆路径问题。结果表明，所提出的技术有助于获得对由目标之间的关系引起的问题难度的见识。针对三个不同的组合优化问题提出了实验：多目标多维背包问题，多目标护士调度问题和带时间窗的多目标车辆路径问题。结果表明，所提出的技术有助于获得对由目标之间的关系引起的问题难度的见识。针对三个不同的组合优化问题提出了实验：多目标多维背包问题，多目标护士调度问题和带时间窗的多目标车辆路径问题。结果表明，所提出的技术有助于获得对由目标之间的关系引起的问题难度的见识。