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A New Method for Optimizing a Linear Function over the Efficient Set of a Multiobjective Integer Program

Natashia Boland (Natashia.Boland***at***newcastle.edu.au )
Hadi Charkhgard (hadi.charkhgard***at***uon.edu.au )
Martin Savelsbergh (martin.savelsbergh***at***isye.gatech.edu )

Abstract: We present a new algorithm for optimizing a linear function over the set of efficient solutions of a multiobjective integer program MOIP. The algorithmís success relies on the efficiency of a new algorithm for enumerating the nondominated points of a MOIP, which is the result of employing a novel criterion space decomposition scheme which (1) limits the number of subspaces that are created, and (2) limits the number of sets of disjunctive constraints required to define the single-objective IP that searches a subspace for a nondominated point. A extensive computational study shows that the efficacy of the algorithm. Finally, we show that the algorithm can be easily modified to efficiently compute the nadir point of a multiobjective integer program.

Keywords: multiobjective integer programming, nondominated points, extension of the L-shape search method, optimizing over the efficient set, nadir point

Category 1: Other Topics (Multi-Criteria Optimization )

Category 2: Integer Programming

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Entry Submitted: 05/22/2015
Entry Accepted: 05/22/2015
Entry Last Modified: 03/19/2016

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