A technique based on trade-off maps to visualise and analyse relationships between objectives in optimisation problems
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...
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| Format: | Article |
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Wiley
2017
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| Online Access: | https://eprints.nottingham.ac.uk/41541/ |
| _version_ | 1848796298824646656 |
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| author | Pinheiro, Rodrigo Lankaites Landa-Silva, Dario Atkin, Jason |
| author_facet | Pinheiro, Rodrigo Lankaites Landa-Silva, Dario Atkin, Jason |
| author_sort | Pinheiro, Rodrigo Lankaites |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T19:45:46Z |
| format | Article |
| id | nottingham-41541 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:45:46Z |
| publishDate | 2017 |
| publisher | Wiley |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-415412020-05-04T18:36:55Z https://eprints.nottingham.ac.uk/41541/ 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 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. Wiley 2017-03-06 Article PeerReviewed Pinheiro, Rodrigo Lankaites, Landa-Silva, Dario and Atkin, Jason (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). pp. 37-56. ISSN 1057-9214 multiobjective fitness landscape analysis; trade-off region maps; fitness landscape visualisation; multiobjective combinatorial problems http://onlinelibrary.wiley.com/doi/10.1002/mcda.1604/abstract doi:10.1002/mcda.1604 doi:10.1002/mcda.1604 |
| spellingShingle | multiobjective fitness landscape analysis; trade-off region maps; fitness landscape visualisation; multiobjective combinatorial problems Pinheiro, Rodrigo Lankaites Landa-Silva, Dario Atkin, Jason A technique based on trade-off maps to visualise and analyse relationships between objectives in optimisation problems |
| title | A technique based on trade-off maps to visualise and analyse relationships between objectives in optimisation problems |
| title_full | A technique based on trade-off maps to visualise and analyse relationships between objectives in optimisation problems |
| title_fullStr | A technique based on trade-off maps to visualise and analyse relationships between objectives in optimisation problems |
| title_full_unstemmed | A technique based on trade-off maps to visualise and analyse relationships between objectives in optimisation problems |
| title_short | A technique based on trade-off maps to visualise and analyse relationships between objectives in optimisation problems |
| title_sort | technique based on trade-off maps to visualise and analyse relationships between objectives in optimisation problems |
| topic | multiobjective fitness landscape analysis; trade-off region maps; fitness landscape visualisation; multiobjective combinatorial problems |
| url | https://eprints.nottingham.ac.uk/41541/ https://eprints.nottingham.ac.uk/41541/ https://eprints.nottingham.ac.uk/41541/ |