Min cost improvement and max gain stability in multicriteria sorting methods on combinatorial domains

Various multicriteria sorting methods have been proposed in the literature to assign the feasible alternatives into predefined categories. We consider here problems involving a set of totally ordered categories representing different achievement levels in the satisfaction of criteria. As in many exi...

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Veröffentlicht in:Journal of multi-criteria decision analysis Jg. 28; H. 3-4; S. 170 - 184
Hauptverfasser: Benabbou, Nawal, Martin, Hugo, Perny, Patrice
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Chichester Wiley Periodicals Inc 01.05.2021
Wiley
Schlagworte:
Computer Science
max gain stability
min cost improvement
multicriteria sorting method
multi‐objective combinatorial optimization
Multi-Objective Combinatorial Optimization
Max Gain Stability
Min Cost Improvement
Multicriteria Sorting Method
ISSN:1057-9214, 1099-1360
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Zusammenfassung:Various multicriteria sorting methods have been proposed in the literature to assign the feasible alternatives into predefined categories. We consider here problems involving a set of totally ordered categories representing different achievement levels in the satisfaction of criteria. As in many existing methods, the assignment rule of an alternative to a category is based on the comparison of its performance vector to reference profiles defining lower bounds of the categories. Within this standard setting we address a new problem that consists in finding how to modify a given solution, within a combinatorial set of alternatives, to upgrade it in the upper category (or higher) at minimum cost. We also consider the problem of identifying the sequence of solutions that minimize the total cost while satisfying some budget constraint at every step, and the problem of determining how to modify the current solution to save money while staying in the same category. We first propose a general approach based on mixed integer (linear or quadratic) programming to solve these problems. Then, we implement this approach on various multiobjective combinatorial problems, such as multi‐agent assignment problems and multiobjective knapsack problems. Numerical tests are provided to establish the feasibility of the approach on instances of different sizes.
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ISSN:1057-9214
1099-1360
DOI:10.1002/mcda.1743