A Complex Search Technique for Solving the Quadratic Assignment Problem

An algorithm recently developed by Enkhbat et al. [3] based on continuous relaxation of the quadratic assignment problem generates suboptimal solution of good quality on average giving no sufficient enough verification on global optimality of the generated solution, whereas a branch and bound method provides a solution with verified global optimality, taking on input an upper bound close to global optimality. In this report we investigated possibility for combining these two techniques, so that firstly upper bound is obtained from the relaxed problem using a continuous global optimization, then a branch and bound procedure is taken to solve the problem completely. We had tested our approach in the case of test problems from the well known QAPLIB library. We consider that the combined search technique is competitive for solving problems with unknown upper bound.