Simulated annealing and its problems to color graphs

Abstract

Simulated Annealing is a very successful heuristic for various problems in combinatorial optimization. In this paper an application of Simulated Annealing to the 3-coloring problem is considered. In contrast to many good empirical results we will show for a certain class of graphs, that the expected first hitting time of a proper coloring, given an arbitrary cooling scheme, is of exponential size. Furthermore a new proof of the convergence of Simulated Annealing with a logarithmic cooling schedule by considering the conductance of the underlying transition graph is given. With this proof technique it is possible to show that Simulated Annealing converges to an optimal solution in exponential time.