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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Final published version
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
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 -