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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Vydané v:Trends in Computational and Applied Mathematics Ročník 19; číslo 3
Hlavní autori: Hugo José Lara, Abel Soares Siqueira, Jinyun Yuan
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Sociedade Brasileira de Matemática Aplicada e Computacional 17.12.2018
Predmet:
Integer quadratic programming. Semidefinite programming
Sports scheduling
ISSN:2676-0029
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Shrnutí: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