A Reduced Semidefinite Programming Formulation for HA Assignment Problems in Sport Scheduling

Home-Away Assignment problems are naturally cast as quadraticpro gramming models in binary variables. In this work we compare alternative formulations for this kind of problems. First, write a quadratic programming formulation with linear constraints, and then a quadratically constrained version. We...

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Bibliographic Details
Published in:	Trends in Computational and Applied Mathematics Vol. 19; no. 3
Main Authors:	Hugo José Lara, Abel Soares Siqueira, Jinyun Yuan
Format:	Journal Article
Language:	English
Published:	Sociedade Brasileira de Matemática Aplicada e Computacional 17.12.2018
Subjects:	Integer quadratic programming. Semidefinite programming Sports scheduling
ISSN:	2676-0029
Online Access:	Get full text
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Summary:	Home-Away Assignment problems are naturally cast as quadraticpro gramming models in binary variables. In this work we compare alternative formulations for this kind of problems. First, write a quadratic programming formulation with linear constraints, and then a quadratically constrained version. We also propose another formulation by manipulating their special structure to obtain versions with 1/4 of the original size. The quadratic programming formulations leads to semidefinite relaxations, which allows us to approximately solve the models. We compare our SDP relaxation with the MIN-RES-CUT based formulation. Numerical experiments exhibit the characteristics of each model.
ISSN:	2676-0029
DOI:	10.5540/tema.2018.019.03.471