A Technique Based on Trade-off Maps to Visualise and Analyse Relationships Between Objectives in Optimisation Problems
This work addresses the need for better decision support in real-world logistic optimization problems, though it appears incremental as it builds on existing correlation and mapping methods.
The paper tackles the challenge of understanding complex relationships between objectives in multiobjective optimization problems, particularly in combinatorial scenarios like logistics, by proposing a visualization technique based on trade-off maps, and results indicate it aids in gaining insights into problem difficulty.
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.