Speeding up IP-based algorithms for constrained quadratic 0-1 optimization

Beitrag in einer Fachzeitschrift

Details zur Publikation

Autorinnen und Autoren: Buchheim C, Liers F, Oswald M
Zeitschrift: Mathematical Programming
Verlag: Springer Verlag (Germany)
Jahr der Veröffentlichung: 2010
Band: 124
Seitenbereich: 513-535
ISSN: 0025-5610


In many practical applications, the task is to optimize a non-linear objective function over the vertices of a well-studied polytope as, e.g., the matching polytope or the travelling salesman polytope (TSP). Prominent examples are the quadratic assignment problem and the quadratic knapsack problem; further applications occur in various areas such as production planning or automatic graph drawing. In order to apply branch-and-cut methods for the exact solution of such problems, the objective function has to be linearized. However, the standard linearization usually leads to very weak relaxations. On the other hand, problem-specific polyhedral studies are often time-consuming. Our goal is the design of general separation routines that can replace detailed polyhedral studies of the resulting polytope and that can be used as a black box. As unconstrained binary quadratic optimization is equivalent to the maximum-cut problem, knowledge about cut polytopes can be used in our setting. Other separation routines are inspired by the local cuts that have been developed by Applegate, Bixby, Chvátal and Cook for faster solution of large-scale traveling salesman instances. Finally, we apply quadratic reformulations of the linear constraints as proposed by Helmberg, Rendl and Weismantel for the quadratic knapsack problem. By extensive experiments, we show that a suitable combination of these methods leads to a drastic speedup in the solution of constrained quadratic 0-1 problems. We also discuss possible generalizations of these methods to arbitrary non-linear objective functions. © 2010 Springer and Mathematical Programming Society.

FAU-Autorinnen und Autoren / FAU-Herausgeberinnen und Herausgeber

Liers-Bergmann, Frauke Prof. Dr.
Professur für Angewandte Mathematik (Ganzzahlige und robuste Optimierung)

Einrichtungen weiterer Autorinnen und Autoren

Ruprecht-Karls-Universität Heidelberg
Universität zu Köln


Buchheim, C., Liers, F., & Oswald, M. (2010). Speeding up IP-based algorithms for constrained quadratic 0-1 optimization. Mathematical Programming, 124, 513-535. https://dx.doi.org/10.1007/s10107-010-0377-3

Buchheim, Christoph, Frauke Liers, and Marcus Oswald. "Speeding up IP-based algorithms for constrained quadratic 0-1 optimization." Mathematical Programming 124 (2010): 513-535.


Zuletzt aktualisiert 2018-23-10 um 21:50