Some results characterizing the finite time behaviour of the simulated annealing algorithm

Abstract

TheSimulated Annealing algorithm is a probabilistic search technique for finding the minimum cost state in a set Ω. The algorithm has been successfully used to obtain near-optimal solutions for problems for which no other effective algorithms exist. For example, problems in integrated circuit layout and in finite impulse response (FIR) filter design have been solved using annealing. In most applications, Ω is finite set, and the annealing algorithm may be modelled as a time-inhomogeneous Markov chain on Ω with transition probabilities that are powers of a time varying parameter e. It has been shown by several researchers that if e is driven to 0 sufficiently slowly, then the algorithm will eventually find a minimum cost state in Ω with probability 1. In this paper, we will focus on the finite-time behaviour of the annealing algorithm. In particular, we will summarize some results relating the number of steps taken by the algorithm to the quality of the solutions obtained. These results provide qualitative as well as quantitative information about the status of the annealing algorithm after a finite number of steps. This will be illustrated using some examples.