Optimization by Simulated Annealing: Quantitative Studies

Simulated annealing is a stochastic optimization procedure which is widely applicable and has been found effective in several problems arising in computeraided circuit design. This paper derives the method in the context of traditional optimization heuristics and presents experimental .studies of its computational efficiency when applied to graph partitioning and traveling salesman problems. Dan Gelatt and I, with help from several of our colleagues, have explored a general framework for optimization which uses computer simulation methods from condensed matter physics and an equivalence (which can be made rigorous) between the many undetermined parameters of the system being optimized and the particles in an imaginary physical system. The energy of the physical system is given by the objective function of the optimization problem. States of low energy in the imaginary physical system are thus the near-global optimum configurations sought in the optimization problem. The trick we have used to find these is to model statistically the evolution of the physical system at a series of temperatures which allow it to "anneal" into a state of high order and very low energy. Arguments for the validity of this approach, and some ideas which help in understanding how to use it effectively, are given in a paper which