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

Abstract

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.

Citation

Pinheiro, R. L., Landa-Silva, D., & Atkin, J. (2017). A technique based on trade-off maps to visualise and analyse relationships between objectives in optimisation problems. Journal of Multi-Criteria Decision Analysis, 24(1-2), 37-56. https://doi.org/10.1002/mcda.1604

• Journal Article Type: Article
• Acceptance Date: Nov 27, 2016
• Publication Date: Mar 6, 2017
• Deposit Date: Mar 24, 2017
• Publicly Available Date: Mar 7, 2019
• Journal: Journal of Multi-criteria Decision Analysis
• Print ISSN: 1057-9214
• Electronic ISSN: 1057-9214
• Publisher: Wiley
• Peer Reviewed: Peer Reviewed
• Volume: 24
• Issue: 1-2
• Pages: 37-56
• DOI: https://doi.org/10.1002/mcda.1604
• Keywords: multiobjective fitness landscape analysis; trade-off region maps; fitness landscape visualisation; multiobjective combinatorial problems
• Public URL: https://nottingham-repository.worktribe.com/output/849135
• Publisher URL: http://onlinelibrary.wiley.com/doi/10.1002/mcda.1604/abstract
• Additional Information: This is the peer reviewed version of the following article: Lankaites Pinheiro R, Landa-Silva D, Atkin J. A technique based on trade-off maps to visualise and analyse relationships between objectives in optimisation problems. J Multi-Crit Decis Anal. 2017;24:37–56, which has been published in final form at https://doi.org/10.1002/mcda.1604. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving