Continuous Optimization Methods for the Quadratic Assignment Problem

TAO HUANG: Continuous Optimization Methods for the Quadratic Assignment Problem (Under the direction of Jon W. Tolle) In this dissertation we have studied continuous optimization techniques as they are applied in nonlinear 0-1 programming. Specifically, the methods of relaxation with a penalty function have been carefully investigated. When the strong equivalence properties hold, we are guaranteed an integer solution to the original 0-1 problem. The quadratic assignment problem (QAP) possesses such properties and consequently we have developed an algorithm for the QAP based on the method of relaxation using the quadratic penalty function. In our algorithm we have applied two pre-conditioning techniques that enables us to devise a scheme to find a good initial point and hence obtain good solutions to the QAP. Furthermore, we have shown how quadratic cuts can be used to improve on the current solutions. Extensive numerical results on several sets of QAP test problems (including the QAPLIB) have been reported and these results show our algorithm produces good solutions for certain classes of problems in a small amount of time.