A Complex Search Technique for Solving the Quadratic Assignment Problem Ider Tseveendorj 1 Catherine Roucairol 1 Bazarragchaa Barsbold 2 Enkhbat Rentsen 2 Bertrand Le Cun 1 and Franc ¸ois Galea 1 1 Laboratoire PRiSM, Universit´ e de Versailles, Versailles, France 2 The School of Mathematics and Computer Science, National University of Mongolia, Mongolia Abstract 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 aver- age 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 pro- cedure 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. 1 Introduction The Quadratic Assignment Problems (QAP) is one of the most challenging combinatorial opti- mization problem in existence. It was first introduced by Koopmans and Beckmann [6] in 1957 as a mathematical model for assigning a set of economic activities to a set of locations. Since then, the number of real-life problems which are mathematically modeled by QAPs has been continuously increasing and the variety of the fields they belong to is astonishing. To recall just a restricted number among the applications of the QAP let us mention placement problems, scheduling, manufacturing, VLSI design, statistical data analysis, and parallel and distributed computing. For more complete list of applications we refer to [5]. There is not only one reason explaining this popularity of the QAP. Besides, practical importance of the QAP, its mathematical challenge and computational com- plexity had been making it atractive. Sahni and Gonzalez [8] had proved that the QAP is NP hard. Moreover, they proved that any method that finds even an ε-approximate solution is also NP complete. Several other NP hard combinatorial optimization problems, as the traveling salesman problem, the bin-packing problem, the max clique problem and the isomorphism of 1