A Lower Bound for the Quadratic Assignment Problem Based on a Level-2 Reformulation-Linearization Technique

This paper should be of interest to the combinatorial optimization community and especially to those interested in the Quadratic Assignment Problem (QAP). The QAP has application in the assignment of facilities to locations (to minimize the cost of intrafacility transportation), the placement of electronic components (to minimize the length of interconnecting wire), the placement of blades in a turbine (to minimize rotor imbalance), and many other analogous problems. The advances described herein are mainly computational. The authors demonstrate the efficacy of their new exact solution algorithm by timing it on series of especially difficult test cases and comparing the results with those of the two competing algorithms for this purpose. For the largest case tested, the new algorithm is an order of magnitude faster than the only other algorithm to have solved this problem. More importantly, the increase in computation time appears to be much slower with problem size than in the case of the two competing algorithms. Sufficient theory is presented to give an understanding of the underlying principles of the algorithm.