The Effect of State Space Clustering on the Performance of Simulated Annealing and Its Topology-Aware Variant

Abstract

Simulated annealing is one of the most widely used algorithms for global optimization. Due to its success, several variants of classical simulated annealing have been proposed. These variants may use more sophisticated neighborhood selection strategies or may employ different acceptance probabilities. Topology-aware simulated annealing is one such variant that takes into consideration the branching factor of states when performing uphill moves. The experimental evaluation done on topology-aware simulated annealing suggests the potential effect of clustering on performance. In this paper, we experimentally investigate the effect of the state space clustering on the performance of classical simulated annealing and its topology-aware variant. This is achieved through the use of networks with different degrees of clustering as search spaces. These networks are generated using the hidden metric model, a recently proposed complex network model. The results show that the effects are indeed nontrivial, and that there exist certain clustering levels that cause an improvement in the performance. These results are more pronounced in spaces with multiple deep local minima, where the performance falls off if the clustering of the network is made smaller or larger than a certain optimal value.