Solution approaches for equitable multiobjective integer programming problems

We consider multi-objective optimization problems where the decision maker (DM) has equity concerns. We assume that the preference model of the DM satisfies properties related to inequity-aversion, hence we focus on finding nondominated solutions in line with the properties of inequity-averse prefer...

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Veröffentlicht in:Annals of operations research Jg. 311; H. 2; S. 967 - 995
Hauptverfasser: Bashir, Bashir, Karsu, Özlem
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.04.2022
Springer
Springer Nature B.V
Schlagworte:
Algorithms
Analysis
Business and Management
Combinatorics
Decision making
Integer programming
Job shops
Knapsack problem
Mathematical optimization
Multiple objective analysis
Operations research
Operations Research/Decision Theory
Optimization
S.i.: Mopgp19
Theory of Computation
Utility functions
Turkey
Convex cones
Equitable efficiency
Interactive algorithm
Equitable dominance
Equitable preferences
Multiobjective integer programming
Generalized Lorenz dominance
Multi-objective knapsack problem
Fairness
ISSN:0254-5330, 1572-9338
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Zusammenfassung:We consider multi-objective optimization problems where the decision maker (DM) has equity concerns. We assume that the preference model of the DM satisfies properties related to inequity-aversion, hence we focus on finding nondominated solutions in line with the properties of inequity-averse preferences, namely the equitably nondominated solutions. We discuss two algorithms for finding good subsets of equitably nondominated solutions. The first approach is an extension of an interactive approach developed for finding the most preferred nondominated solution when the utility function is assumed to be quasiconcave. We find the most preferred equitably nondominated solution when the utility function is assumed to be symmetric quasiconcave. In the second approach we generate an evenly distributed subset of the set of equitably nondominated solutions to be considered further by the DM. We show the computational feasibility of the two algorithms on equitable multi-objective knapsack problem, in which projects in different categories are to be funded subject to a limited budget. We perform experiments to show and discuss the performances of the algorithms.
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ISSN:0254-5330
1572-9338
DOI:10.1007/s10479-020-03613-9