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Graphical exploration of the weight space in three-objective mixed integer linear programs

Maria João Alves and João Costa

European Journal of Operational Research, 2016, vol. 248, issue 1, 72-83

Abstract: In this paper we address the computation of indifference regions in the weight space for multiobjective integer and mixed-integer linear programming problems and the graphical exploration of this type of information for three-objective problems. We present a procedure to compute a subset of the indifference region associated with a supported nondominated solution obtained by the weighted-sum scalarization. Based on the properties of these regions and their graphical representation for problems with up to three objective functions, we propose an algorithm to compute all extreme supported nondominated solutions adjacent to a given solution and another one to compute all extreme supported nondominated solutions to a three-objective problem. The latter is suitable to characterize solutions in delimited nondominated areas or to be used as a final exploration phase. A computer implementation is also presented.

Keywords: Multiple objective programming; Mixed integer linear programming; Weighted-sum scalarization; Weight space; Extreme supported nondominated solutions (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1016/j.ejor.2015.06.072

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