A theoretical study on the behavior of simulated annealing leading to a new cooling schedule

Abstract

This paper presents an empirical study on the efficiency of the simulated annealing (SA) algorithm. It considers various parameters such as landscape and neighborhood. The need for a better understanding of SA, with the additional goal of implementing the algorithm efficiently, motivated this study. The method selected to conduct that study was to carry out experiments to obtain practical data, which could be utilized to carry out a theoretical study simultaneously. Experiments on such a stochastic algorithm as SA were initiated following the observation that it is possible to calculate the exact probability for SA to reach any point in the landscape, provided that the number of solutions and the number of neighbors per solution are small enough. An efficient development of a SA simulator has enabled us to study the influence of the tuning of all the main parameters of SA as well as theoretical concepts such as thermodynamic equilibrium and optimal temperature decrement rules. Interesting results have been obtained in the field of adaptive cooling schedules that enable us to demonstrate that the classical cooling schedules are all equivalent. Finally a new schedule has been proposed that exhibits some useful properties. The proposed cooling schedule has been successfully implemented in the SA algorithm to solve the well known traveling salesman problem.