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...

Full description

Saved in:

Bibliographic Details
Published in:	Journal of multi-criteria decision analysis Vol. 28; no. 3-4; pp. 170 - 184
Main Authors:	Benabbou, Nawal, Martin, Hugo, Perny, Patrice
Format:	Journal Article
Language:	English
Published:	Chichester Wiley Periodicals Inc 01.05.2021 Wiley
Subjects:	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
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Description
Summary:	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.
Bibliography:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	1057-9214 1099-1360
DOI:	10.1002/mcda.1743