A NEW FORMULATION OF THE QUADRATIC ASSIGNMENT PROBLEM ON R-DIMENSIONAL GRID

In this paper, we show that the quadratic assignment problem defined on the r-dimensional grid can be formalized using polynomial equations. Consequently, the problem can be classified into subgroups of the relaxed problems according to the degree of the polynomial equations. Since this problem has such feature that the behavior of the solution is almost determined by a few polynomial equations with rather low degree, and it is generally easier to solve the relaxed problem represented by the polynomial equations with lower degree, there is much possibility to be able to derive more efficient and effective methods than those based on the conventional formulations. We also discuss the solutions for the relaxed problem in which the degree is not more than two, and we introduce some applications of the present formulation to the other combinatorial problems, the floor planning problem of VLSI, and the graph partitioning problem.