Probabilistic asymptotic properties of some combinatorial optimization problems

Abstract

A class of combinatorial optimization problems with sum- and bottleneck objective function is described, having the following probabilistic asymptotic behaviour: With probability tending to one the ratio between worst and optimal objective function value approaches one as the size of the problem tends to infinity. Problems belonging to this class are among others quadratic assignment problems, as well as certain combinatorial and graph theoretical optimization problems. The obtained results suggest that even very simple heuristic algorithms incline to yield good solutions for high dimensional problems of this class.