An interactive approximation algorithm for multi-objective integer programs

•An interactive algorithm for multi-objective integer programs is developed.•The algorithm finds the most preferred point at a desired level of accuracy.•The decision maker is assumed to have an underlying quasiconcave value function.•Extensive computational experiments show the algorithm works very...

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Bibliographic Details
Published in:Computers & operations research Vol. 96; pp. 80 - 90
Main Authors: Lokman, Banu, Köksalan, Murat, Korhonen, Pekka J., Wallenius, Jyrki
Format: Journal Article
Language:English
Published: New York Elsevier Ltd 01.08.2018
Pergamon Press Inc
Subjects:
Algorithms
Approximation
Approximation algorithm
Combinatorial analysis
Cones
Decision making
Integer programming
Interactive algorithm
Multi-objective integer programming
Multiple objective analysis
Operations research
Studies
Multi-objective integer programming
Approximation algorithm
Interactive algorithm
ISSN:0305-0548, 1873-765X, 0305-0548
Online Access:Get full text
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Summary:•An interactive algorithm for multi-objective integer programs is developed.•The algorithm finds the most preferred point at a desired level of accuracy.•The decision maker is assumed to have an underlying quasiconcave value function.•Extensive computational experiments show the algorithm works very well. We develop an interactive algorithm that approximates the most preferred solution for any multi-objective integer program with a desired level of accuracy, provided that the decision maker's (DM's) preferences are consistent with a nondecreasing quasiconcave value function. Using pairwise comparisons of the DM, we construct convex cones and eliminate the inferior regions that are close to being dominated by the cones in addition to the regions dominated by the cones. The algorithm allows the DM to change the desired level of accuracy during the solution process. We test the performance of the algorithm on a set of multi-objective combinatorial optimization problems. It performs very well in terms of the quality of the solution found, the solution time, and the required preference information.
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ISSN:0305-0548
1873-765X
0305-0548
DOI:10.1016/j.cor.2018.04.005