Mathematical formulations for the K clusters with fixed cardinality problem

G. M. Gonçalves; L. L. Lourenço

doi:10.1016/j.cie.2019.06.028

Mathematical formulations for the K clusters with fixed cardinality problem

G. M. Gonçalves, L. L. Lourenço

CMA - Centro de Matemática e Aplicações

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

In this paper we propose some mixed integer linear programming formulations for the K clusters with fixed cardinality problem. These formulations are strengthened by valid inequalities and all the mixed integer linear models are compared from a theoretical and practical point of view. The continuous linear relaxation bounds of the developed models are tested on randomly generated instances, by using standard software, with promising results.

Original language	English
Pages (from-to)	593-600
Number of pages	8
Journal	Computers & Industrial Engineering
Volume	135
DOIs	https://doi.org/10.1016/j.cie.2019.06.028
Publication status	Published - 1 Sept 2019

Keywords

Clusters with fixed cardinality
Combinatorial optimization
Mixed integer linear formulations
Upper bounds
Valid inequalities

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10.1016/j.cie.2019.06.028Licence: CC BY-NC-ND

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title = "Mathematical formulations for the K clusters with fixed cardinality problem",

abstract = "In this paper we propose some mixed integer linear programming formulations for the K clusters with fixed cardinality problem. These formulations are strengthened by valid inequalities and all the mixed integer linear models are compared from a theoretical and practical point of view. The continuous linear relaxation bounds of the developed models are tested on randomly generated instances, by using standard software, with promising results.",

keywords = "Clusters with fixed cardinality, Combinatorial optimization, Mixed integer linear formulations, Upper bounds, Valid inequalities",

author = "Gon{\c c}alves, {G. M.} and Louren{\c c}o, {L. L.}",

note = "This work is partially supported by the Funda{\c c}{\~a}o para a Ci{\^e}ncia e Tecnologia (Portuguese Foundation for Science and Technology) through the project UID/MAT/00297/2019 (Centro de Matem{\'a}tica e Aplica{\c c}a{\~o}es).",

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AU - Lourenço, L. L.

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PY - 2019/9/1

Y1 - 2019/9/1

N2 - In this paper we propose some mixed integer linear programming formulations for the K clusters with fixed cardinality problem. These formulations are strengthened by valid inequalities and all the mixed integer linear models are compared from a theoretical and practical point of view. The continuous linear relaxation bounds of the developed models are tested on randomly generated instances, by using standard software, with promising results.

AB - In this paper we propose some mixed integer linear programming formulations for the K clusters with fixed cardinality problem. These formulations are strengthened by valid inequalities and all the mixed integer linear models are compared from a theoretical and practical point of view. The continuous linear relaxation bounds of the developed models are tested on randomly generated instances, by using standard software, with promising results.

KW - Clusters with fixed cardinality

KW - Combinatorial optimization

KW - Mixed integer linear formulations

KW - Upper bounds

KW - Valid inequalities

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DO - 10.1016/j.cie.2019.06.028

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VL - 135

SP - 593

EP - 600

JO - Computers & Industrial Engineering

JF - Computers & Industrial Engineering

ER -

Mathematical formulations for the K clusters with fixed cardinality problem

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Keywords

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