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    Rights statement: This is the author’s version of a work that was accepted for publication in Computers and Operations Research. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Computers and Operations Research, 120, 2020 DOI: 10.1016/j.cor.2020.104975

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Using ℓp-norms for fairness in combinatorial optimisation

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Using ℓp-norms for fairness in combinatorial optimisation. / Bektas, Tolga; Letchford, Adam.

In: Computers and Operations Research, Vol. 120, 104975, 01.08.2020.

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Bektas, Tolga ; Letchford, Adam. / Using ℓp-norms for fairness in combinatorial optimisation. In: Computers and Operations Research. 2020 ; Vol. 120.

Bibtex

@article{af39ec7648334a5c9e83f20c0b4c49e7,
title = "Using ℓp-norms for fairness in combinatorial optimisation",
abstract = "The issue of fairness has received attention from researchers in many fields, including combinatorial optimisation. One way to drive the solution toward fairness is to use a modified objective function that involves so-called ℓp-norms. If done in a naive way, this approach leads to large and symmetric mixed-integer nonlinear programs (MINLPs), that may be difficult to solve. We show that, for some problems, one can obtain alternative MINLP formulations that are much smaller, do not suffer from symmetry, and have a reasonably tight continuous relaxation. We give encouraging computational results for certain vehicle routing, facility location and network design problems.",
keywords = "fairness, mixed-integer nonlinear programming, vehicle routing, facility location",
author = "Tolga Bektas and Adam Letchford",
note = "This is the author{\textquoteright}s version of a work that was accepted for publication in Computers and Operations Research. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Computers and Operations Research, 120, 2020 DOI: 10.1016/j.cor.2020.104975",
year = "2020",
month = aug,
day = "1",
doi = "10.1016/j.cor.2020.104975",
language = "English",
volume = "120",
journal = "Computers and Operations Research",
issn = "0305-0548",
publisher = "Elsevier Ltd",

}

RIS

TY - JOUR

T1 - Using ℓp-norms for fairness in combinatorial optimisation

AU - Bektas, Tolga

AU - Letchford, Adam

N1 - This is the author’s version of a work that was accepted for publication in Computers and Operations Research. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Computers and Operations Research, 120, 2020 DOI: 10.1016/j.cor.2020.104975

PY - 2020/8/1

Y1 - 2020/8/1

N2 - The issue of fairness has received attention from researchers in many fields, including combinatorial optimisation. One way to drive the solution toward fairness is to use a modified objective function that involves so-called ℓp-norms. If done in a naive way, this approach leads to large and symmetric mixed-integer nonlinear programs (MINLPs), that may be difficult to solve. We show that, for some problems, one can obtain alternative MINLP formulations that are much smaller, do not suffer from symmetry, and have a reasonably tight continuous relaxation. We give encouraging computational results for certain vehicle routing, facility location and network design problems.

AB - The issue of fairness has received attention from researchers in many fields, including combinatorial optimisation. One way to drive the solution toward fairness is to use a modified objective function that involves so-called ℓp-norms. If done in a naive way, this approach leads to large and symmetric mixed-integer nonlinear programs (MINLPs), that may be difficult to solve. We show that, for some problems, one can obtain alternative MINLP formulations that are much smaller, do not suffer from symmetry, and have a reasonably tight continuous relaxation. We give encouraging computational results for certain vehicle routing, facility location and network design problems.

KW - fairness

KW - mixed-integer nonlinear programming

KW - vehicle routing

KW - facility location

U2 - 10.1016/j.cor.2020.104975

DO - 10.1016/j.cor.2020.104975

M3 - Journal article

VL - 120

JO - Computers and Operations Research

JF - Computers and Operations Research

SN - 0305-0548

M1 - 104975

ER -