Solving quadratic assignment problems using convex quadratic programming relaxations

Abstract

We describe a branch-and-bound algorithm for the quadratic assignment problem (QAP) that uses a convex quadratic programming (QP) relaxation to obtain a bound at each node. The QP subproblems are approximately solved using the Frank-Wolfe algorithm, which in this case requires the solution of a linear assignment problem on each iteration. Our branching strategy makes extensive use of dual information associated with the QP subproblems. We obtain state-of-the-art computational results on large benchmark QAPs

Keywords:

• Quadratic assignment problem
• Branch-and-bound
• Quadratic programming
• Frank-Wolfe algorithm