Rescaled simulated annealing

This paper presents a new metaheuristics called rescaled simulated annealing (RSA). It is based on a generic modification of the Metropolis procedure inside the simulated annealing (SA) algorithm. This modification consists in rescaling, before applying the Metropolis criterion, the energies of the states candidate to a transition. The direct consequence is an acceleration of convergence, by avoiding to dive and escape from high energy local minima. Asymptotic results are established and favorably compared to the famous ones due to Mitra and al. for SA [13]. Some practical implementations are presented for the Traveling Salesman Problem and results are compared to those obtained with SA. Less transitions need to be tested with RSA to obtain results of similar quality. As a corollary, within a limited computational effort, RSA provides better quality solutions than SA.