- http://www.sciencedirect.com/science/journal/03050548
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**On finding representative non-dominated points for bi-objective integer network flow problems.** / Eusébio, Augusto; Figueira, José Rui; Ehrgott, Matthias.

Research output: Contribution to journal › Journal article › peer-review

Eusébio, A, Figueira, JR & Ehrgott, M 2014, 'On finding representative non-dominated points for bi-objective integer network flow problems', *Computers and Operations Research*, vol. 48, pp. 1-10. https://doi.org/10.1016/j.cor.2014.02.009

Eusébio, A., Figueira, J. R., & Ehrgott, M. (2014). On finding representative non-dominated points for bi-objective integer network flow problems. *Computers and Operations Research*, *48*, 1-10. https://doi.org/10.1016/j.cor.2014.02.009

Eusébio A, Figueira JR, Ehrgott M. On finding representative non-dominated points for bi-objective integer network flow problems. Computers and Operations Research. 2014 Aug 1;48:1-10. https://doi.org/10.1016/j.cor.2014.02.009

@article{9b624ae574854033b81874f4761445c9,

title = "On finding representative non-dominated points for bi-objective integer network flow problems",

abstract = "This paper proposes a new algorithm to find a representation of the set of all non-dominated points of the bi-objective integer network flow problem. The algorithm solves a sequence of ε-constraint problems with a branch-and-bound algorithm to find a subset of non-dominated points that represents the set of all non-dominated points well in the sense of coverage or uniformity. At each iteration of the algorithm, one non-dominated point, determined by solving one ε-constraint problem, is added to the representation until it is guaranteed that the representation has the desired quality. Computational experiments on different problem types show the efficacy of the algorithm.",

keywords = "Multi-objective optimisation, Network optimisation, Integer programming, ε-Constraint method, Bi-objective network flow problem, Representation",

author = "Augusto Eus{\'e}bio and Figueira, {Jos{\'e} Rui} and Matthias Ehrgott",

year = "2014",

month = aug,

day = "1",

doi = "10.1016/j.cor.2014.02.009",

language = "English",

volume = "48",

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journal = "Computers and Operations Research",

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AU - Eusébio, Augusto

AU - Figueira, José Rui

AU - Ehrgott, Matthias

PY - 2014/8/1

Y1 - 2014/8/1

N2 - This paper proposes a new algorithm to find a representation of the set of all non-dominated points of the bi-objective integer network flow problem. The algorithm solves a sequence of ε-constraint problems with a branch-and-bound algorithm to find a subset of non-dominated points that represents the set of all non-dominated points well in the sense of coverage or uniformity. At each iteration of the algorithm, one non-dominated point, determined by solving one ε-constraint problem, is added to the representation until it is guaranteed that the representation has the desired quality. Computational experiments on different problem types show the efficacy of the algorithm.

AB - This paper proposes a new algorithm to find a representation of the set of all non-dominated points of the bi-objective integer network flow problem. The algorithm solves a sequence of ε-constraint problems with a branch-and-bound algorithm to find a subset of non-dominated points that represents the set of all non-dominated points well in the sense of coverage or uniformity. At each iteration of the algorithm, one non-dominated point, determined by solving one ε-constraint problem, is added to the representation until it is guaranteed that the representation has the desired quality. Computational experiments on different problem types show the efficacy of the algorithm.

KW - Multi-objective optimisation

KW - Network optimisation

KW - Integer programming

KW - ε-Constraint method

KW - Bi-objective network flow problem

KW - Representation

U2 - 10.1016/j.cor.2014.02.009

DO - 10.1016/j.cor.2014.02.009

M3 - Journal article

VL - 48

SP - 1

EP - 10

JO - Computers and Operations Research

JF - Computers and Operations Research

SN - 0305-0548

ER -