A theoretical framework for simulated annealing

Simulated Annealing has been a very successful general algorithm for the solution of large, complex combinatorial optimization problems. Since its introduction, several applications in different fields of engineering, such as integrated circuit placement, optimal encoding, resource allocation, logic synthesis, have been developed. In parallel, theoretical studies have been focusing on the reasons for the excellent behavior of the algorithm. This paper reviews most of the important results on the theory of Simulated Annealing, placing them in a unified framework. New results are reported as well.

[1]  R. H. J. M. Otten,et al.  The Annealing Algorithm , 1989 .

[2]  Brian D. Ripley,et al.  Stochastic Simulation , 2005 .

[3]  W. R. Stahl,et al.  An Elementary Introduction to the Theory of Probability. , 1962 .

[4]  M. E. Johnson,et al.  Generalized simulated annealing for function optimization , 1986 .

[5]  Richard W. Madsen,et al.  Markov Chains: Theory and Applications , 1976 .

[6]  Saul B. Gelfand,et al.  Analysis of simulated annealing type algorithms , 1987 .

[7]  S. Mitter,et al.  Simulated annealing with noisy or imprecise energy measurements , 1989 .

[8]  B. Gidas Nonstationary Markov chains and convergence of the annealing algorithm , 1985 .

[9]  Alberto L. Sangiovanni-Vincentelli,et al.  A Parallel Simulated Annealing Algorithm for the Placement of Macro-Cells , 1987, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[10]  W. Rudin Principles of mathematical analysis , 1964 .

[11]  Bruce E. Hajek,et al.  Cooling Schedules for Optimal Annealing , 1988, Math. Oper. Res..

[12]  W. Daniel Hillis,et al.  The connection machine , 1985 .

[13]  Alistair I. Mees,et al.  Convergence of an annealing algorithm , 1986, Math. Program..

[14]  Dean Isaacson,et al.  Markov Chains: Theory and Applications , 1976 .

[15]  Henk Tijms,et al.  Stochastic modelling and analysis: a computational approach , 1986 .

[16]  John G. Kemeny,et al.  Finite Markov chains , 1960 .

[17]  W. Dixon,et al.  Introduction to Mathematical Statistics. , 1964 .

[18]  W. Reiher Hammersley, J. M., D. C. Handscomb: Monte Carlo Methods. Methuen & Co., London, and John Wiley & Sons, New York, 1964. VII + 178 S., Preis: 25 s , 1966 .

[19]  D. Mitra,et al.  Convergence and finite-time behavior of simulated annealing , 1986, Advances in Applied Probability.

[20]  S. Dreyfus,et al.  Thermodynamical Approach to the Traveling Salesman Problem : An Efficient Simulation Algorithm , 2004 .

[21]  Donald Geman,et al.  Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images , 1984 .

[22]  Rob A. Rutenbar,et al.  Multiprocessor-Based Placement by Simulated Annealing , 1986, DAC 1986.

[23]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[24]  Huang,et al.  AN EFFICIENT GENERAL COOLING SCHEDULE FOR SIMULATED ANNEALING , 1986 .

[25]  Mark Howard Jones,et al.  A parallel simulated annealing algorithm for standard cell placement on a hypercube computer , 1987 .

[26]  A. Federgruen,et al.  Simulated annealing methods with general acceptance probabilities , 1987, Journal of Applied Probability.

[27]  T. Liebling,et al.  Probabilistic exchange algorithms and Euclidean traveling salesman problems , 1986 .

[28]  Wilbur B. Davenport Probability and Random Processes: An Introduction for Applied Scientists and Engineers , 1975 .

[29]  V. Cerný Thermodynamical approach to the traveling salesman problem: An efficient simulation algorithm , 1985 .

[30]  Gregory B. Sorkin Simulated annealing on fractals: theoretical analysis and relevance for combinatorial optimization , 1990 .

[31]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[32]  J. Hammersley,et al.  Monte Carlo Methods , 1965 .

[33]  Ehl Emile Aarts,et al.  Statistical cooling : a general approach to combinatorial optimization problems , 1985 .

[34]  Dean Isaacson,et al.  Strongly Ergodic Behavior for Non-Stationary Markov Processes , 1973 .

[35]  Gerard T. Barkema,et al.  Monte Carlo Methods in Statistical Physics , 1999 .

[36]  D. R. Cox,et al.  An Elementary Introduction to the Theory of Probability. , 1963 .

[37]  Gregory B. Sorkin,et al.  Efficient simulated annealing on fractal energy landscapes , 1991, Algorithmica.

[38]  D. Stroock,et al.  Simulated annealing via Sobolev inequalities , 1988 .

[39]  Valerie Isham,et al.  Non‐Negative Matrices and Markov Chains , 1983 .

[40]  Philip N. Strenski,et al.  Analysis of finite length annealing schedules , 2005, Algorithmica.

[41]  Sanjoy Mitter,et al.  Analysis of simulated annealing for optimization , 1985, 1985 24th IEEE Conference on Decision and Control.

[42]  P. Peskun,et al.  Optimum Monte-Carlo sampling using Markov chains , 1973 .

[43]  Emile H. L. Aarts,et al.  Simulated Annealing: Theory and Applications , 1987, Mathematics and Its Applications.

[44]  John N. Tsitsiklis,et al.  Markov Chains with Rare Transitions and Simulated Annealing , 1989, Math. Oper. Res..

[45]  P. R. Kumar,et al.  Balance of Recurrece Order in Time-Inhomogenous Markov Chains with Application to Simulated Annealing , 1988, Probability in the Engineering and Informational Sciences.

[46]  R. A. Fox,et al.  Introduction to Mathematical Statistics , 1947 .

[47]  Nulton,et al.  Statistical mechanics of combinatorial optimization. , 1988, Physical review. A, General physics.

[48]  Jean-Marc Delosme,et al.  Simulated annealing: a fast heuristic for some generic layout problems , 1988, [1988] IEEE International Conference on Computer-Aided Design (ICCAD-89) Digest of Technical Papers.

[49]  Rainer Schrader,et al.  On the Convergence of Stationary Distributions in Simulated Annealing Algorithms , 1988, Inf. Process. Lett..

[50]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .