Nonconvex continuous models for combinatorial optimization problems with application to satisfiability and node packing problems

We show how a large class of combinatorial optimization problems can be reformulated as a nonconvex minimization problem over the unit hyper cube with continuous variables. No additional constraints are required; all constraints are incorporated in the n onconvex objective function, which is a polynomial function. The application of the general transform to satisfiability and node packing problems is discussed, and various approximation algorithms are briefly reviewed. To give an indication of the strength of the proposed approaches, we conclude with some computational results on instances of the graph coloring problem

A potential reduction approach to the frequency assignment problem

AbstractThe frequency assignment problem is the problem of assigning frequencies to transmission links such that either no interference occurs, or the amount of interference is minimized. We present an approximation algorithm for this problem that is inspired by Karmarkar's interior point potential reduction approach to combinatorial optimization problems. A non convex quadratic model of the problem is developed, that is very compact as all interference constraints are incorporated in the objective function. Moreover, optimizing this model may result in finding multiple solutions to the problem simultaneouly. Several preprocessing techniques are discussed. We report on computational experience with both real-life and randomly generated instances