A Technique Based on Trade-off Maps to Visualise and Analyse Relationships Between Objectives in Optimisation Problems
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| Format: | Preprint |
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2025
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| _version_ | 1866909818687586304 |
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| author | Pinheiro, Rodrigo Lankaites Landa-Silva, Dario Atkin, Jason |
| author_facet | Pinheiro, Rodrigo Lankaites Landa-Silva, Dario Atkin, Jason |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_00877 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Technique Based on Trade-off Maps to Visualise and Analyse Relationships Between Objectives in Optimisation Problems Pinheiro, Rodrigo Lankaites Landa-Silva, Dario Atkin, Jason Neural and Evolutionary Computing Artificial Intelligence Human-Computer Interaction Optimization and Control 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. |
| title | A Technique Based on Trade-off Maps to Visualise and Analyse Relationships Between Objectives in Optimisation Problems |
| topic | Neural and Evolutionary Computing Artificial Intelligence Human-Computer Interaction Optimization and Control |
| url | https://arxiv.org/abs/2510.00877 |