Finding a representative nondominated set for multi-objective mixed integer programs

•Representative sets are found for multi-objective mixed integer programs.•A desired level of quality is guaranteed in representing the nondominated frontier.•The methods are computationally efficient based on extensive computational tests. In this paper, we develop algorithms to find small represen...

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Vydané v:European journal of operational research Ročník 272; číslo 1; s. 61 - 77
Hlavní autori: Ceyhan, Gökhan, Köksalan, Murat, Lokman, Banu
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier B.V 01.01.2019
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ISSN:0377-2217, 1872-6860
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Abstract •Representative sets are found for multi-objective mixed integer programs.•A desired level of quality is guaranteed in representing the nondominated frontier.•The methods are computationally efficient based on extensive computational tests. In this paper, we develop algorithms to find small representative sets of nondominated points that are well spread over the nondominated frontiers for multi-objective mixed integer programs. We evaluate the quality of representations of the sets by a Tchebycheff distance-based coverage gap measure. The first algorithm aims to substantially improve the computational efficiency of an existing algorithm that is designed to continue generating new points until the decision maker (DM) finds the generated set satisfactory. The algorithm improves the coverage gap value in each iteration by including the worst represented point into the set. The second algorithm, on the other hand, guarantees to achieve a desired coverage gap value imposed by the DM at the outset. In generating a new point, the algorithm constructs territories around the previously generated points that are inadmissible for the new point based on the desired coverage gap value. The third algorithm brings a holistic approach considering the solution space and the number of representative points that will be generated together. The algorithm first approximates the nondominated set by a hypersurface and uses it to plan the locations of the representative points. We conduct computational experiments on randomly generated instances of multi-objective knapsack, assignment, and mixed integer knapsack problems and show that the algorithms work well.
AbstractList •Representative sets are found for multi-objective mixed integer programs.•A desired level of quality is guaranteed in representing the nondominated frontier.•The methods are computationally efficient based on extensive computational tests. In this paper, we develop algorithms to find small representative sets of nondominated points that are well spread over the nondominated frontiers for multi-objective mixed integer programs. We evaluate the quality of representations of the sets by a Tchebycheff distance-based coverage gap measure. The first algorithm aims to substantially improve the computational efficiency of an existing algorithm that is designed to continue generating new points until the decision maker (DM) finds the generated set satisfactory. The algorithm improves the coverage gap value in each iteration by including the worst represented point into the set. The second algorithm, on the other hand, guarantees to achieve a desired coverage gap value imposed by the DM at the outset. In generating a new point, the algorithm constructs territories around the previously generated points that are inadmissible for the new point based on the desired coverage gap value. The third algorithm brings a holistic approach considering the solution space and the number of representative points that will be generated together. The algorithm first approximates the nondominated set by a hypersurface and uses it to plan the locations of the representative points. We conduct computational experiments on randomly generated instances of multi-objective knapsack, assignment, and mixed integer knapsack problems and show that the algorithms work well.
Author Köksalan, Murat
Ceyhan, Gökhan
Lokman, Banu
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Issue 1
Keywords Mixed integer programming
Representative subset
Nondominated point
Multiple objective programming
Language English
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Snippet •Representative sets are found for multi-objective mixed integer programs.•A desired level of quality is guaranteed in representing the nondominated...
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SubjectTerms Mixed integer programming
Multiple objective programming
Nondominated point
Representative subset
Title Finding a representative nondominated set for multi-objective mixed integer programs
URI https://dx.doi.org/10.1016/j.ejor.2018.06.012
Volume 272
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