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

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 s...

• Type: Journal
• Year: 2010
• Where: MP
• Authors: Christoph Buchheim, Frauke Liers, Marcus Oswald
• Keywords: MP 2010, Objective Functions, Quadratic Knapsack, Quadratic Knapsack Problem, Security Privacy