Simulated Annealing with Extended Neighbourhood 1

Simulated Annealing (SA) is a powerful stochastic search method applicable to a wide range of problems for which little prior knowledge is available. It can produce very high quality solutions for hard combinatorial optimization problems. However, the computation time required by SA is very large. Various methods have been proposed to reduce the computation time, but they mainly deal with the careful tuning of SA's control parameters. This paper rst analyzes the impact of SA's neighbourhood on SA's performance and shows that SA with a larger neighbourhood is better than SA with a smaller one. The paper also gives a general model of SA, which has both dynamic generation probability and acceptance probability, and proves its convergence. All variants of SA can be uni ed under such a generalization. Finally, a method of extending SA's neighbourhood is proposed, which uses a discrete approximation to some continuous probability function as the generation function in SA, and several important corollaries of the general model are given.