Optimization by Simulated Annealing: An Experimental Evaluation; Part II, Graph Coloring and Number Partitioning

TLDR

This study is the second in a series of three papers that empirically evaluate simulated annealing’s competitiveness in well‑studied combinatorial optimization domains. The authors aim to adapt simulated annealing to graph coloring and number partitioning, problems previously deemed unsuitable for local optimization. Experiments employ multiple simulated annealing schemes tailored to each problem. In graph coloring, three simulated annealing schemes outperform traditional methods on certain graph classes given sufficient time, whereas in number partitioning they are only competitive on small instances and, when runtime is considered, cannot beat multiple random runs of local optimization, contrasting with their success on other problems.

Abstract

This is the second in a series of three papers that empirically examine the competitiveness of simulated annealing in certain well-studied domains of combinatorial optimization. Simulated annealing is a randomized technique proposed by S. Kirkpatrick, C. D. Gelatt and M. P. Vecchi for improving local optimization algorithms. Here we report on experiments at adapting simulated annealing to graph coloring and number partitioning, two problems for which local optimization had not previously been thought suitable. For graph coloring, we report on three simulated annealing schemes, all of which can dominate traditional techniques for certain types of graphs, at least when large amounts of computing time are available. For number partitioning, simulated annealing is not competitive with the differencing algorithm of N. Karmarkar and R. M. Karp, except on relatively small instances. Moreover, if running time is taken into account, natural annealing schemes cannot even outperform multiple random runs of the local optimization algorithms on which they are based, in sharp contrast to the observed performance of annealing on other problems.