An interactive approximation algorithm for multi-objective integer programs

Lokman, Banu
Korhonen, Pekka J.
Wallenius, Jyrki
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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We develop an interactive algorithm for biobjective integer programs that finds the most preferred solution of a decision maker whose preferences are consistent with a quasiconvex preference function to be minimized. During the algorithm, preference information is elicited from the decision maker. Based on this preference information and the properties of the underlying quasiconvex preference function, the algorithm reduces the search region and converges to the most preferred solution progressively. Findin...
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An interactive algorithm to find the most preferred solution of multi-objective integer programs
LOKMAN, BANU; Köksalan, Mustafa Murat; Korhonen, Pekka J.; Wallenius, Jyrki (Springer Science and Business Media LLC, 2016-10-01)
In this paper, we develop an interactive algorithm that finds the most preferred solution of a decision maker (DM) for multi-objective integer programming problems. We assume that the DM's preferences are consistent with a quasiconcave value function unknown to us. Based on the properties of quasiconcave value functions and pairwise preference information obtained from the DM, we generate constraints to restrict the implied inferior regions. The algorithm continues iteratively and guarantees to find the mos...
An Interactive partitioning approach for multiobjective decision making under a general monotone utility function
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We develop an interactive partitioning approach for solving the multiobjective decision making problem of a decision maker (DM) who has an implicit general monotone utility function. The approach reduces feasible solution space using the DM's preferences. Hypothetical solutions called partition ideals (PIs) that dominate portions of the efficient frontier are generated and those that are inferior to a feasible solution are used to eliminate the dominated regions. We investigate the issues in representation ...
Citation Formats
B. Lokman, P. J. Korhonen, and J. Wallenius, “An interactive approximation algorithm for multi-objective integer programs,” COMPUTERS & OPERATIONS RESEARCH, pp. 80–90, 2018, Accessed: 00, 2020. [Online]. Available: