Rescaled Simulated Annealing—Accelerating Convergence of Simulated Annealing by Rescaling the States Energies

• Authors: L. Herault
• Venue: Journal of Heuristics
• Year: 2000

This paper presents a new metaheuristic, called rescaled simulated annealing (RSA) which is particularly adapted tocombinatorial problems where the available computational effort tosolve it is limited. Asymptotic convergence on optimal solutions isestablished and the results are favorably compared to the famous onesdue to Mitra, Romeo, and Sangiovanni-Vincentelli (Mitra, Romeo, andSangiovanni-Vincentelli. (1986). Adv. Appl. Prob. 18,747–771.) for simulated annealing (SA). It is based on ageneralization of the Metropolis procedure used by the SA algorithm.This generalization consists in rescaling the energies of the statescandidate for a transition, before applying the Metropolis criterion.The direct consequence is an acceleration of convergence, by avoidingdives and escapes from high energy local minima. Thus, practicallyspeaking, less transitions need to be tested with RSA to obtain agood quality solution. As a corollary, within a limited computationaleffort, RSA provides better quality solutions than SA and the gain ofperformance of RSA versus SA is all the more important since theavailable computational effort is reduced. An illustrative exampleis detailed on an instance of the Traveling Salesman Problem.