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A two phase method for multi-objective integer programming and its application to the assignment problem with three objectives

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A two phase method for multi-objective integer programming and its application to the assignment problem with three objectives. / Przybylski, Anthony; Gandibleux, Xavier; Ehrgott, Matthias.
In: Discrete Optimization, Vol. 7, No. 3, 01.08.2010, p. 149-165.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Przybylski, A, Gandibleux, X & Ehrgott, M 2010, 'A two phase method for multi-objective integer programming and its application to the assignment problem with three objectives', Discrete Optimization, vol. 7, no. 3, pp. 149-165. https://doi.org/10.1016/j.disopt.2010.03.005

APA

Przybylski, A., Gandibleux, X., & Ehrgott, M. (2010). A two phase method for multi-objective integer programming and its application to the assignment problem with three objectives. Discrete Optimization, 7(3), 149-165. https://doi.org/10.1016/j.disopt.2010.03.005

Vancouver

Przybylski A, Gandibleux X, Ehrgott M. A two phase method for multi-objective integer programming and its application to the assignment problem with three objectives. Discrete Optimization. 2010 Aug 1;7(3):149-165. doi: 10.1016/j.disopt.2010.03.005

Author

Przybylski, Anthony ; Gandibleux, Xavier ; Ehrgott, Matthias. / A two phase method for multi-objective integer programming and its application to the assignment problem with three objectives. In: Discrete Optimization. 2010 ; Vol. 7, No. 3. pp. 149-165.

Bibtex

@article{3ad2d7a57dfe4dbf8c289706b4757f34,
title = "A two phase method for multi-objective integer programming and its application to the assignment problem with three objectives",
abstract = "In this paper, we present a generalization of the two phase method to solve multi-objective integer programmes with p>2p>2 objectives. We apply the method to the assignment problem with three objectives.We have recently proposed an algorithm for the first phase, computing all supported efficient solutions. The second phase consists in the definition and the exploration of the search area inside of which nonsupported nondominated points may exist. This search area is not defined by trivial geometric constructions in the multi-objective case, and is therefore difficult to describe and to explore. The lower and upper bound sets introduced by Ehrgott and Gandibleux in 2001 are used as a basis for this description.Experimental results on the three-objective assignment problem where we use a ranking algorithm to explore the search area show the efficiency of the method.",
keywords = "Multi-objective combinatorial optimization, Two phase method , Assignment problem , Ranking",
author = "Anthony Przybylski and Xavier Gandibleux and Matthias Ehrgott",
year = "2010",
month = aug,
day = "1",
doi = "10.1016/j.disopt.2010.03.005",
language = "English",
volume = "7",
pages = "149--165",
journal = "Discrete Optimization",
issn = "1572-5286",
publisher = "Elsevier",
number = "3",

}

RIS

TY - JOUR

T1 - A two phase method for multi-objective integer programming and its application to the assignment problem with three objectives

AU - Przybylski, Anthony

AU - Gandibleux, Xavier

AU - Ehrgott, Matthias

PY - 2010/8/1

Y1 - 2010/8/1

N2 - In this paper, we present a generalization of the two phase method to solve multi-objective integer programmes with p>2p>2 objectives. We apply the method to the assignment problem with three objectives.We have recently proposed an algorithm for the first phase, computing all supported efficient solutions. The second phase consists in the definition and the exploration of the search area inside of which nonsupported nondominated points may exist. This search area is not defined by trivial geometric constructions in the multi-objective case, and is therefore difficult to describe and to explore. The lower and upper bound sets introduced by Ehrgott and Gandibleux in 2001 are used as a basis for this description.Experimental results on the three-objective assignment problem where we use a ranking algorithm to explore the search area show the efficiency of the method.

AB - In this paper, we present a generalization of the two phase method to solve multi-objective integer programmes with p>2p>2 objectives. We apply the method to the assignment problem with three objectives.We have recently proposed an algorithm for the first phase, computing all supported efficient solutions. The second phase consists in the definition and the exploration of the search area inside of which nonsupported nondominated points may exist. This search area is not defined by trivial geometric constructions in the multi-objective case, and is therefore difficult to describe and to explore. The lower and upper bound sets introduced by Ehrgott and Gandibleux in 2001 are used as a basis for this description.Experimental results on the three-objective assignment problem where we use a ranking algorithm to explore the search area show the efficiency of the method.

KW - Multi-objective combinatorial optimization

KW - Two phase method

KW - Assignment problem

KW - Ranking

U2 - 10.1016/j.disopt.2010.03.005

DO - 10.1016/j.disopt.2010.03.005

M3 - Journal article

VL - 7

SP - 149

EP - 165

JO - Discrete Optimization

JF - Discrete Optimization

SN - 1572-5286

IS - 3

ER -