Skip to main content
SpringerLink
Log in

Simulated Annealing

  • Chapter
  • First Online:
Handbook of Metaheuristics

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 146))

  • 13k Accesses

Abstract

Simulated annealing is a well-studied local search metaheuristic used to address discrete and, to a lesser extent, continuous optimization problems. The key feature of simulated annealing is that it provides a mechanism to escape local optima by allowing hill-climbing moves (i.e., moves which worsen the objective function value) in hopes of finding a global optimum. A brief history of simulated annealing is presented, including a review of its application to discrete, continuous, and multi-objective optimization problems. Asymptotic convergence and finite-time performance theory for simulated annealing are reviewed. Other local search algorithms are discussed in terms of their relationship to simulated annealing. The chapter also presents practical guidelines for the implementation of simulated annealing in terms of cooling schedules, neighborhood functions, and appropriate applications.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

References

  1. Aarts, E.H.L., Korst, J.: Simulated Annealing and Boltzmann Machines: A Stochastic Approach to Combinatorial Optimization and Neural Computing. Wiley, Chichester (1989)

    Google Scholar 

  2. Aarts, E.H.L., Lenstra, J.K.: Local Search in Combinatorial Optimization. Wiley, Chichester (1997)

    Google Scholar 

  3. Aarts, E.H.L., van Laarhoven, P.J.M.: Statistical cooling: A general approach to combinatorial optimization problems. Phillips J. Res. 40, 193–226 (1985)

    Google Scholar 

  4. Abramson, D., Krishnamoorthy, M., Dang, H.: Simulated annealing cooling schedules for the school timetabling problem. Asia-Pac. J. Oper. Res. 16, 1–22 (1999)

    Google Scholar 

  5. Ahmed, M.A.: A modification of the simulated annealing algorithm for discrete stochastic optimization. Eng. Optim. 39(6), 701–714 (2007)

    Google Scholar 

  6. Alkhamis, T.M., Ahmed, M.A., Tuan, V.K.: Simulated annealing for discrete optimization with estimation. Eur. J. Oper. Res. 116, 530–544 (1999)

    Google Scholar 

  7. Alrefaei, M.H., Andradottir, S.: A simulated annealing algorithm with constant temperature for discrete stochastic optimization. Manage. Sci. 45, 748–764 (1999)

    Google Scholar 

  8. Althofer, I., Koschnick, K.U.: On the convergence of threshold accepting. Appl. Math. Optim. 24, 183–195 (1991)

    Google Scholar 

  9. Aluffi-Pentini, F., Parisi, V., Zirilli, F.: Global optimization and stochastic differential equations. J. Optim. Theory Appl. 47, 1–16 (1985)

    Google Scholar 

  10. Anily, S., Federgruen, A.: Simulated annealing methods with general acceptance probabilities. J. Appl. Probab. 24, 657–667 (1987)

    Google Scholar 

  11. Azizi, N., Zolfaghari, S.: Adaptive temperature control for simulated annealing: A comparative study. Comput. Oper. Res. 31(14), 2439–2451 (2004)

    Google Scholar 

  12. Belisle, C.J.P.: Convergence theorems for a class of simulated annealing algorithms on RD. J. Appl. Probab. 29, 885–895 (1992)

    Google Scholar 

  13. Belisle, C.J.P., Romeijn, H.E., Smith, R.L.: Hit-and-run algorithms for generating multivariate distributions. Math. Oper. Res. 18, 255–266 (1993)

    Google Scholar 

  14. Ben-Ameur, W.: Computing the initial temperature of simulated annealing. Comput. Optim. Appl. 29, 369–385 (2004)

    Google Scholar 

  15. Bohachevsky, I.O., Johnson, M.E., Stein, M.L.: Generalized simulated annealing for function optimization. Technometrics 28, 209–217 (1986)

    Google Scholar 

  16. Borkar, V.S.: Pathwise recurrence orders and simulated annealing. J. Appl. Probab. 29, 472–476 (1992)

    Google Scholar 

  17. Bouffard, V., Ferland, J.: Improving simulated annealing with variable neighborhood search to solve resource-constrained scheduling problem. J. Sched. 10, 375–386 (2007)

    Google Scholar 

  18. Bratley, P., Fox, B.L., Schrage, L.: A guide to simulation. Springer, New York, NY (1987)

    Google Scholar 

  19. Cardoso, M.F., Salcedo, R.L., de Azevedo, S.F.: Nonequilibrium simulated annealing: A faster approach to combinatorial minimization. Ind. Eng. Chem. Res. 33, 1908–1918 (1994)

    Google Scholar 

  20. Catoni, O.: Metropolis, simulated annealing, and Iterated energy transformation algorithms: Theory and experiments. J. Complex. 12, 595–623 (1996)

    Google Scholar 

  21. Cerf, R.: Asymptotic convergence of genetic algorithms. Adv. Appl. Probab. 30, 521–550 (1998)

    Google Scholar 

  22. Chardaire, P., Lutton, J.L., Sutter, A.: Thermostatistical persistency: A powerful improving concept for simulated annealing algorithms. Eur. J. Oper. Res. 86, 565–579 (1995)

    Google Scholar 

  23. Charon, I., Hudry, O.: The noising method - a new method for combinatorial optimization. Oper. Res. Lett. 14, 133–137 (1993)

    Google Scholar 

  24. Charon, I., Hudry, O.: The Noising Methods - a generalization of some metaheuristics. Eur. J. Oper. Res. 135, 86–101 (2001)

    Google Scholar 

  25. Cheh, K.M., Goldberg, J.B., Askin, R.G.: A note on the effect of neighborhood-structure in simulated annealing. Comput. Oper. Res. 18, 537–547 (1991)

    Google Scholar 

  26. Chen, D., Lee, C., Park, C., Mendes, P.: Parallelizing simulated annealing algorithms based on high-performance computer. J. Global Optim. 39, 261–289 (2007)

    Google Scholar 

  27. Chen, S., Luk, B.L.: Adaptive simulated annealing for optimization in signal processing applications. Signal Process. 79, 117–128 (1999)

    Google Scholar 

  28. Chiang, T.S., Chow, Y.S.: On the convergence rate of annealing processes. SIAM J. Control Optim. 26, 1455–1470 (1988)

    Google Scholar 

  29. Chiang, T.S., Chow, Y.Y.: A limit-theorem for a class of inhomogeneous markov-processes. Ann. Probab. 17, 1483–1502 (1989)

    Google Scholar 

  30. Chiang, T.S., Chow, Y.Y.: The asymptotic-behavior of simulated annealing processes with absorption. SIAM J. Control. Optim. 32, 1247–1265 (1994)

    Google Scholar 

  31. Christoph, M., Hoffmann, K.H.: Scaling behavior of optimal simulated annealing schedules. J. Phys. A - Math. Gen. 26, 3267–3277 (1993)

    Google Scholar 

  32. Chu, K.W., Deng, Y.F., Reinitz, J.: Parallel simulated annealing by mixing of states. J. Comput. Phys. 148, 646–662 (1999)

    Google Scholar 

  33. Cinlar, E.: Introduction to Stochastic Processes. Prentice-Hall, Englewood Cliffs, NJ (1974)

    Google Scholar 

  34. Cohn, H., Fielding, M.: Simulated annealing: Searching for an optimal temperature schedule. SIAM J. Optim. 9, 779–802 (1999)

    Google Scholar 

  35. Connors, D.P., Kumar, P.R.: Simulated annealing type markov-chains and their order balance-equations. SIAM J. Control. Optim. 27, 1440–1461 (1989)

    Google Scholar 

  36. Czyzak, P., Hapke, M., Jaszkiewicz, A.: Application of the Pareto-Simulated Annealing to the Multiple Criteria Shortest Path Problem, Technical Report, Politechnika Poznanska Instytut Informatyki, Poland (1994)

    Google Scholar 

  37. Czyzak, P., Jaszkiewicz, A.: Pareto simulated annealing a metaheuristic technique for multiple-objective combinatorial optimization. J. Multicriteria Decis. Anal. 7, 34–47 (1998)

    Google Scholar 

  38. Davis, T.E.: Toward an extrapolation of the simulated annealing convergence theory onto the simple genetic algorithm. Doctoral Dissertation, University of Florida, Gainesville, FL (1991)

    Google Scholar 

  39. Davis, T.E., Principe, J.C.: A simulated annealing like convergence theory for the simple genetic algorithm. Proceedings of the Fourth International Conference on Genetic Algorithms in San Diego, CA, pp. 174–181. Morgan Kaufmann, San Francisco, CA (1991)

    Google Scholar 

  40. Dekkers, A., Aarts, E.: Global Optimization and Simulated Annealing, Math. Program. 50, 367–393 (1991)

    Google Scholar 

  41. Delport, V.: Parallel simulated annealing and evolutionary selection for combinatorial optimisation. Electron. Lett. 34, 758–759 (1998)

    Google Scholar 

  42. Del Moral, P., Miclo, L.: On the convergence and applications of generalized simulated annealing. SIAM J. Control. Optim. 37(4), 1222–1250 (1999)

    Google Scholar 

  43. Deng, J., Chen, H., Chang, C., Yang, Z.: A superior random number generator for visiting distribution in GSA. Int. J. Comput. Math. 81(1), 103–120 (2004)

    Google Scholar 

  44. Desai, M.P.: Some results characterizing the finite time behaviour of the simulated annealing algorithm. Sadhana-Acad. Proc. Eng. Sci. 24, 317–337 (1999)

    Google Scholar 

  45. Dueck, G., Scheuer, T.: Threshold accepting - a general-purpose optimization algorithm appearing superior to simulated annealing. J. Comput. Phys. 90, 161–175 (1990)

    Google Scholar 

  46. Eglese, R.W.: Simulated annealing: A tool for operational research. Eur. J. Oper. Res. 46, 271–281 (1990)

    Google Scholar 

  47. Emden-Weinert, T., Proksch, M.: Best practice simulated annealing for the airline crew scheduling problem. J. Heuristics 5, 419–436 (1999)

    Google Scholar 

  48. Fabian, V.: Simulated annealing simulated. Comput. Math. Appl. 33, 81–94 (1997)

    Google Scholar 

  49. Faigle, U., Kern, W.: Note on the convergence of simulated annealing algorithms. SIAM J. Control. Optim. 29, 153–159 (1991)

    Google Scholar 

  50. Faigle, U., Kern, W.: Some convergence results for probabilistic tabu search. ORSA J. Comput. 4, 32–37 (1992)

    Google Scholar 

  51. Faigle, U., Schrader, R.: On the convergence of stationary distributions in simulated annealing algorithms. Inf. Process. Lett. 27, 189–194 (1988)

    Google Scholar 

  52. Faigle, U., Schrader, R.: Simulated annealing - a case-study. Angew. Inform. 30(6), 259–263 (1988)

    Google Scholar 

  53. Fielding, M.: Simulated annealing with an optimal fixed temperature. SIAM J. Optim. 11, 289–307 (2000)

    Google Scholar 

  54. Fleischer, M.A.: Assessing the performance of the simulated annealing algorithm using information theory. Doctoral Dissertation, Department of Operations Research, Case Western Reserve University, Clevelend, Ohio (1993)

    Google Scholar 

  55. Fleischer, M.A.: Simulated annealing: Past, present, and future. In: Alexopoulos, C., Kang, K., Lilegdon, W.R., Goldsman, D., (eds.) Proceedings of the 1995 Winter Simulation Conference, pp. 155–161. IEEE Press, Arlington, Virginia (1995)

    Google Scholar 

  56. Fleischer, M.A.: Generalized cybernetic optimization: Solving continuous variable problems, In: Voss, S., Martello, S., Roucairol, C., Ibrahim, H., Osman, I.H., (eds.) Meta-heuristics: Advances and Trends in Local Search Paradigms for Optimization, pp. 403–418. Kluwer (1999)

    Google Scholar 

  57. Fleischer, M.A., Jacobson, S.H.: Cybernetic optimization by simulated annealing: An implementation of parallel processing using probabilistic feedback control, In: Osman, I.H., Kelly, J.P., (eds.) Meta-heuristics: Theory and applications, pp. 249–264. Kluwer (1996)

    Google Scholar 

  58. Fleischer, M.A., Jacobson, S.H.: Information theory and the finite-time behavior of the simulated annealing algorithm: Experimental results. INFORMS J. Comput. 11, 35–43 (1999)

    Google Scholar 

  59. Fox, B.L.: Integrating and accelerating tabu search, simulated annealing, and genetic algorithms. Ann. Oper. Res. 41, 47–67 (1993)

    Google Scholar 

  60. Fox, B.L.: Random restarting versus simulated annealing. Comput. Math. Appl. 27, 33–35 (1994)

    Google Scholar 

  61. Fox, B.L.: Faster Simulated Annealing. SIAM J. Optim. 5, 485–505 (1995)

    Google Scholar 

  62. Fox, B.L., Heine, G.W.: Simulated Annealing with Overrides, Technical, Department of Mathematics, University of Colorado, Denver, Colorado (1993)

    Google Scholar 

  63. Gelfand, S.B., Mitter, S.K.: Simulated annealing with noisy or imprecise energy measurements. J. Optim. Theory. Appl. 62, 49–62 (1989)

    Google Scholar 

  64. Gemen, S., Hwang, C.R.: Diffusions for global optimization. SIAM J. Control. Optim. 24, 1031–1043 (1986)

    Google Scholar 

  65. Gidas, B.: Nonstationary Markov Chains and Convergence of the Annealing Algorithm, J. Stat. Phys. 39, 73–131 (1985)

    Google Scholar 

  66. Glover, F.: Tabu search for nonlinear and parametric optimization (with Links to Genetic Algorithms). Discrete Appl. Math. 49, 231–255 (1994)

    Google Scholar 

  67. Glover, F., Hanafi, S.: Tabu search and finite convergence. Discrete Appl. Math. 119(1–2), 3–36 (2002)

    Google Scholar 

  68. Goldstein, L., Waterman, M.: Neighborhood size in the simulated annealing algorithm. Am. J. Math. Manage. Sci. 8, 409–423 (1988)

    Google Scholar 

  69. Gong, G., Liu, Y., Quin, M.: An adaptive simulated annealing algorithm. Stoch. Processes. Appl. 94, 95–103 (2001)

    Google Scholar 

  70. Granville, V., Krivanek, M., Rasson, J.P.: Simulated annealing - a proof of convergence. IEEE Trans. Pattern Anal. Mach. Intell. 16, 652–656 (1994)

    Google Scholar 

  71. Gutjahr, W.J., Pflug, G.C.: Simulated annealing for noisy cost functions. J. Global Optim. 8, 1–13 (1996)

    Google Scholar 

  72. Hajek, B.: Cooling schedules for optimal annealing. Math. Oper. Res. 13, 311–329 (1988)

    Google Scholar 

  73. Hamma, B., Viitanen, S., Torn, A.: Parallel continuous simulated annealing for global optimization. Optim. Methods. Softw. 13, 95–116 (2000)

    Google Scholar 

  74. Hammersley, J.M., Handscomb, D.C.: Monte Carlo Methods, Methuen, Wiley, London, New York (1964)

    Google Scholar 

  75. Henderson, D., Jacobson, S.H., Johnson, A.W.: Handbook of Metaheuristics, Kluwer, Boston, MA (2003)

    Google Scholar 

  76. Herault, L.: Rescaled simulated annealing - accelerating convergence of simulated annealing by rescaling the state energies. J. Heuristics, 6, 215–252 (2000)

    Google Scholar 

  77. Hu, T.C., Kahing, A.B., Tsao, C.W.A.: Old bachelor acceptance: A new class of non-monotone threshold accepting methods. ORSA J. Comput. 7, 417–425 (1995)

    Google Scholar 

  78. Isaacson, D.L., Madsen, R.W.: Markov Chains, Theory and Applications, Wiley, New York (1976)

    Google Scholar 

  79. Jacobson, S.H.: Analyzing the performance of local search algorithms using generalized hill climbing algorithms. In: Hansen, P., Ribeiro C.C. (eds.) Chapter 20 in Essays and Surveys on Metaheuristics, pp. 441–467. Kluwer, Norwell, MA (2002)

    Google Scholar 

  80. Jacobson, S.H., Sullivan, K.A., Johnson, A.W.: Discrete manufacturing process design optimization using computer simulation and generalized hill climbing algorithms. Eng. Optim. 31, 247–260 (1998)

    Google Scholar 

  81. Jacobson, S.H., Yucesan, E.: Global optimization performance measures for generalized hill climbing algorithms. J. Global Optim. 29(2), 173–190 (2004)

    Google Scholar 

  82. Jacobson, S.H., Yucesan, E.: Analyzing the performance of generalized hill climbing algorithms. J. Heuristics 10(4), 387–405 (2004)

    Google Scholar 

  83. Jacobson, S.H., Hall, S.N., McLay, L.A., Orosz, J.E.: Performance analysis of cyclical simulated annealing algorithms. Methodol. Comput. Appl. Probab. 7, 183–201 (2005)

    Google Scholar 

  84. Johnson, A.W., Jacobson, S.H.: A class of convergent generalized hill climbing algorithms. Appl. Math. Comput. 125(2–3), 359–373 (2002a)

    Google Scholar 

  85. Johnson, A.W., Jacobson, S.H.: On the convergence of generalized hill climbing algorithms. Discrete Appl. Math., 119(1–2), 37–57 (2002b)

    Google Scholar 

  86. Johnson, D.S., Aragon, C.R., McGeoch, L.A., Schevon, C.: Optimization by simulated annealing - an experimental evaluation; Part 1, graph partitioning. Oper. Res., 37, 865–892 (1989)

    Google Scholar 

  87. Johnson, D.S., Aragon, C.R., McGeoch, L.A., Schevon, C.: Optimization by simulated annealing - an experimental evaluation; Part 2, graph-coloring and number partitioning. Ope. Res., 39, 378–406 (1991)

    Google Scholar 

  88. Kiatsupaibul, S., Smith, R.L.: A General Purpose Simulated Annealing Algorithm for Integer Linear Programming, Technical Report, Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, Michigan (2000)

    Google Scholar 

  89. Kirkpatrick, S., Gelatt, Jr., C.D., Vecchi, M.P.: Optimization by simulated annealing. Science, 220, 671–680 (1983)

    Google Scholar 

  90. Koulamas, C., Antony, S.R., Jaen, R.: A survey of simulated annealing applications to operations- research problems. OMEGA-Int. J. Manage. Sci. 22, 41–56 (1994)

    Google Scholar 

  91. Leite, J.P.B., Topping, B.H.V.: Parallel simulated annealing for structural optimization. Comput. Struct. 73, 545–564 (1999)

    Google Scholar 

  92. Liepins, G.E., Hilliard, M.R.: Genetic algorithms: Foundations and applications. Ann. Oper. Res. 21, 31–58 (1989)

    Google Scholar 

  93. Lin, C.K.Y., Haley, K.B., Sparks, C.: A comparative study of both standard and adaptive versions of threshold accepting and simulated annealing algorithms in three scheduling problems. Eur. J. Oper. Res. 83, 330–346 (1995)

    Google Scholar 

  94. Locatelli, M.: Convergence properties of simulated annealing for continuous global optimization. J. Appl. Probab. 33, 1127–1140 (1996)

    Google Scholar 

  95. Locatelli, M.: Simulated annealing algorithms for continuous global optimization: Convergence conditions. J. Optim. Theory. Appl. 104, 121–133 (2000)

    Google Scholar 

  96. Locatelli, M.: Convergence and first hitting time of simulated annealing algorithms for continuous global optimization. Math. Methods. Oper. Res. 54, 171–199 (2001)

    Google Scholar 

  97. Lundy, M., Mees, A.: Convergence of an annealing algorithm. Math. Program. 34, 111–124 (1986)

    Google Scholar 

  98. Ma, J., Straub, J.E.: Simulated annealing using the classical density distribution. J. Chem. Phy. 101, 533–541 (1994)

    Google Scholar 

  99. Mantegna, R.N.: Fast, accurate algorithm for numerical simulation of Levy stable stochastic processes. Phys. Rev. E, 49(5), 4677–4683 (1994)

    Google Scholar 

  100. Mazza, C.: Parallel simulated annealing, Random Struct. Algorithms, 3, 139–148 (1992)

    Google Scholar 

  101. Metropolis, N., Rosenbluth, A., Rosenbluth, M., Teller, A., Teller, E.: Equation of state calculations by fast computing machines. J. Chem. Phys., 21, 1087–1092 (1953)

    Google Scholar 

  102. Meyer, C.D.: The condition of a finite markov chain and perturbation bounds for the limiting probabilities. SIAM J. Algebraic. Discrete Methods 1, 273–283 (1980)

    Google Scholar 

  103. Mingjun, J., Huanwen, T.: Application of chaos in simulated annealing. Chaos, Solitions. Fractals 21, 933–941 (2003)

    Google Scholar 

  104. Mitra, D., Romeo, F., Sangiovanni-Vincentelli, A.L.: Convergence and finite time behavior of simulated annealing. Adv. Appl. Probab. 18, 747–771 (1986)

    Google Scholar 

  105. Moscato, P.: An introduction to population approaches for optimization and hierarchical objective functions: A discussion on the role of tabu search. Ann. Oper. Res. 41, 85–121 (1993)

    Google Scholar 

  106. Moscato, P., Fontanari, J.F.: Convergence and finite-time behavior of simulated annealing. Adv. Appl. Probab. 18, 747–771 (1990)

    Google Scholar 

  107. Muhlenbein, H.: Genetic algorithms, In: Aarts, E., Lenstra, J.K., (eds.) Local search in combinatorial optimization, pp. 137–172. Wiley, New York, NY (1997)

    Google Scholar 

  108. Munakata, T., Nakamura, Y.: Temperature control for simulated annealing. Phys. Rev. E Stat. Nonlin. and Soft Matter Phys. 64(4II), 461271–461275 (2001)

    Google Scholar 

  109. Nishimori, H., Inoue, J.: Convergence of simulated annealing using the generalized transition probability. J. Phys. A, 31, 5661–5672 (1998)

    Google Scholar 

  110. Nissen, V., Paul, H.: A modification of threshold accepting and its application to the quadratic assignment problem. OR Spektrum 17, 205–210 (1995)

    Google Scholar 

  111. Nolte, A., Schrader R.: A note on finite time behavior of simulated annealing. Math. Oper. Res. 25(3), 476–484 (2000)

    Google Scholar 

  112. Nourani, Y., Andresen, B.: A comparison of simulated annealing cooling strategies. J. Phys. A-Math. Gen. 31, 8373–8385 (1998)

    Google Scholar 

  113. Ogbu, F.A., Smith, D.K.: The application of the simulated annealing algorithm to the solution of the N/M/Cmax flowshop problem. Comput. Oper. Res. 17, 243–253 (1990)

    Google Scholar 

  114. Ohlmann, J.W., Bean, J.C., Henderson, S.G.: Convergence in probability of compressed annealing. Math. Oper. Res. 29(4), 837–860 (2004)

    Google Scholar 

  115. Orosz, J.E., Jacobson, S.H.: Finite-time performance analysis of static simulated annealing algorithms. Comput. Optim. Appl. 21, 21–53 (2002a)

    Google Scholar 

  116. Orosz, J.E., Jacobson, S.H.: Analysis of static simulated annealing algorithms. J. Optim. Theory. Appl. 115(1), 165–182 (2002b)

    Google Scholar 

  117. Pepper, J.W., Golden, B.L., Wasil, E.A.: Solving the traveling salesman problem with annealing-based Heuristics: A computational study. IEEE Trans. Syst. Manufacturing and Cybernetics, Part A: Syst. Humans, 32(1), 72–77 (2002)

    Google Scholar 

  118. Rajasekaran, S.: On simulated annealing and nested annealing. J. Global Optim. 16, 43–56 (2000)

    Google Scholar 

  119. Romeijn, H.E., Zabinsky, Z.B., Graesser, D.L., Noegi, S.: New reflection generator for simulated annealing in mixed-integer/continuous global optimization. J. Optim. Theory. Appl. 101, 403–427 (1999)

    Google Scholar 

  120. Romeo, F., Sangiovanni-Vincentelli, A.: A theoretical framework for simulated annealing. Algorithmica 6, 302–345 (1991)

    Google Scholar 

  121. Rosenthal, J.S.: Convergence rates for markov chains. SIAM Rev. 37, 387–405 (1995)

    Google Scholar 

  122. Ross, S.M.: Stochastic processes, J Wiley, New York, NY (1996)

    Google Scholar 

  123. Rossier, Y., Troyon, M., Liebling, T.M.: Probabilistic exchange algorithms and euclidean traveling salesman problems. OR Spektrum 8, 151–164 (1986)

    Google Scholar 

  124. Rudolph, G.: Convergence analysis of cononical genetic algorithms. IEEE Trans. Neural Net. Special Issue on Evolutional Computing, 5, 96–101 (1994)

    Google Scholar 

  125. Scheermesser, T., Bryngdahl, O.: Threshold accepting for constrained half-toning. Opt. Commun. 115, 13–18 (1995)

    Google Scholar 

  126. Schuur, P.C.: Classification of acceptance criteria for the simulated annealing algorithm. Math. Oper. Res. 22, 266–275 (1997)

    Google Scholar 

  127. Seneta, E.: Non-Negative Matrices and Markov Chains, Springer, New York, NY (1981)

    Google Scholar 

  128. Serafini, P.: Mathematics of Multiobjective Optimization, p. 289. CISM Courses and Lectures, Springer, Berlin (1985)

    Google Scholar 

  129. Serafini, P.: Simulated Annealing for Multiple Objective Optimization Problems, Proceedings of the Tenth International Conference on Multiple Criteria Decision Making, pp. 87–96, Taipei (1992)

    Google Scholar 

  130. Serafini, P.: Simulated Annealing for Multiple Objective Optimization Problems, Multiple Criteria Decision Making. Expand and Enrich the Domains of Thinking and Application pp. 283–292, Springer, Berlin, (1994)

    Google Scholar 

  131. Siarry, P., Berthiau, G., Durbin, F., Haussy, J.: Enhanced simulated annealing for globally minimizing functions of many-continuous variables. ACM Trans. Math. Softw. 23, 209–228 (1997)

    Google Scholar 

  132. Solla, S.A., Sorkin, G.B., White, S.R.: Configuration space analysis for optimization problems. In: Bienenstock, E., Fogelmansoulie, F., Weisbuch, G. (eds.) Disordered Systems and Biological Organization, pp. 283–292. Springer, New York (1986)

    Google Scholar 

  133. Srichander, R.: Efficient schedules for simulated annealing. Eng. Optim. 24, 161–176 (1995)

    Google Scholar 

  134. Steinhofel, K., Albrecht, A., Wong, C.K.: The convergence of stochastic algorithms solving flow shop scheduling. Theor. Comput. Sci. 285, 101–117 (2002)

    Google Scholar 

  135. Stern, J.M.: Simulated annealing with a temperature dependent penalty function, ORSA J. Comput. 4, 311–319 (1992)

    Google Scholar 

  136. Storer, R.H., Wu, S.D., Vaccari, R.: New Search Spaces for Sequencing Problems with Application to Job Shop Scheduling, Manage. Sci. 38, 1495–1509 (1992)

    Google Scholar 

  137. Straub, J.E., Ma, J., Amara, P.: Simulated annealing using coarse grained classical dynamics: Smouuchowski Dynamics in the Gaussian Density Approximation. J. Chem. Phys. 103, 1574–1581 (1995)

    Google Scholar 

  138. Strenski, P.N., Kirkpatrick, S.: Analysis of finite length annealing schedules. Algorithmica, 6, 346–366 (1991)

    Google Scholar 

  139. Sullivan, K.A., Jacobson, S.H.: Ordinal hill climbing algorithms for discrete manufacturing process design optimization problems. Discrete Event Dyn. Syst. 10, 307–324 (2000)

    Google Scholar 

  140. Sullivan, K.A., Jacobson, S.H.: A convergence analysis of generalized hill climbing algorithms. IEEE Trans. Automatic Control 46, 1288–1293 (2001)

    Google Scholar 

  141. Suman, B.: Multiobjective simulated annealing a metaheuristic technique for multiobjective optimization of a constrained problem. Found. Comput. Decis. Sci., 27, 171–191 (2002)

    Google Scholar 

  142. Suman, B.: Simulated annealing based multiobjective algorithm and their application for system reliability. Eng. Optim., 35, 391–416 (2003)

    Google Scholar 

  143. Suman, B.: Self-stopping PDMOSA and performance measure in simulated annealing based multiobjective optimization algorithms. Comput. Chem. Eng. 29, 1131–1147 (2005)

    Google Scholar 

  144. Suman, B., Kumar, P.: A survey of simulated annealing as a tool for single and multiobjective optimization. J. Oper. Res. Soc. 57, 1143–1160 (2006)

    Google Scholar 

  145. Suppapitnarm, A., Parks, T.: Simulated Annealing: An Alternative Approach to True Multiobjective Optimization, Genetic and Evolutionary Computation Conference, Conference Workshop Program pp. 406–407, Orlando, FL (1999)

    Google Scholar 

  146. Tekinalp, O., Karsli, G.: A new multiobjective simulated annealing algorithm. J. Global Optim. 39, 49–77 (2007)

    Google Scholar 

  147. Tian, P., Ma, J., Zhang, D.M.: Application of the simulated annealing algorithm to the combinatorial optimisation problem with permutation property: An investigation of generation mechanism. Eur. J. Oper. Res. 118, 81–94 (1999)

    Google Scholar 

  148. Tovey, C.A.: Simulated simulated annealing. Am. J. Math. Manage. Sci., 8, 389–407 (1988)

    Google Scholar 

  149. Tsallis, C., Stariolo, D.A.: Generalized simulated annealing. Physica A, 233, 395–406 (1996)

    Google Scholar 

  150. Tsitsiklis, J.N.: Markov chains with rare transitions and simulated annealing. Math. Oper. Res. 14, 70–90 (1989)

    Google Scholar 

  151. Triki, E., Collette, Y., Siarry, P.: A theoretical study on the behavior of simulated annealing leading to a new cooling schedule. Eur. J. Oper. Res. 166, 77–92 (2005)

    Google Scholar 

  152. Ulungu, L.E., Teghem, J.: Multiobjective combinatorial optimization problems: A survey. J. Multicriteria Decis. Anal. 3, 83–104 (1994)

    Google Scholar 

  153. Ulungu, L.E., Teghem, J., Ost, C.: Interactive simulated annealing in a multiobjective framework: Application to an industrial problem. J. Oper. Res. Soc. 49, 1044–1050 (1998)

    Google Scholar 

  154. Ulungu, L.E., Teghem, J., Fortemps, P.H., Tuyttens, D.: MOSA method: A tool for solving multiobjective combinatorial optimization problems. J. Multicriteria Decis. Anal., 8, 221–236 (1999)

    Google Scholar 

  155. van Laarhoven, P.J.M.: Theoretical and Computational Aspects of Simulated Annealing, Centrum voor Wiskunde en Informatica, Amsterdam, Netherlands (1988)

    Google Scholar 

  156. van Laarhoven, P.J.M., Aarts, E.H.L.: Simulated annealing: Theory and applications, D. Reidel; Kluwer, Dordrecht, Boston, Norwell, MA (1987)

    Google Scholar 

  157. Varanelli, J.M., Cohoon, J.P.: A fast method for generalized starting temperature determination in homogeneous two-stage simulated annealing systems. Comput. Oper. Res. 26, 481–503 (1999)

    Google Scholar 

  158. Vaughan, D., Jacobson, S.H.: Tabu guided generalized hill climbing algorithms. Methodol. Comput. Appl. Probab. 6, 343–354 (2004)

    Google Scholar 

  159. Villalobos-Arias, M., Coello, C.A.C., Hernandez-Lerma, O.: Foundations of genetic algorithms. Lecture Notes in Comput. Sci. 3469, 95–111 (2005)

    Google Scholar 

  160. Villalobos-Arias, M., Coello, C.A.C., Hernandez-Lerma, O.: Asymptotic Convergence of a Simulated Annealing Algorithm for Multiobjective Optimization Problems, Math. Methods. Oper. Res., 64, 353–362 (2006)

    Google Scholar 

  161. Wood, G.R., Alexander, D.L.J., Bulger, D.W.: J. Global Optim., 22, 271–284 (2002)

    Google Scholar 

  162. Yan, D., Mukai, H.: Stochastic discrete optimization. SIAM J. Control Optim., 30, 594–612 (1992)

    Google Scholar 

  163. Yang, R.L.: Convergence of the simulated annealing algorithm for continuous global optimization. J. Optim. Theory. Appl. 104, 691–716 (2000)

    Google Scholar 

  164. Yao, X.: A new simulated annealing algorithm. Int. J. Comput. Math. 56, 161–168 (1995)

    Google Scholar 

  165. Yao, X., Li, G.: General simulated annealing. J. Comput. Sci. Tech. 6, 329–338 (1991)

    Google Scholar 

  166. Zabinsky, Z.B., Smith, R.L., McDonald, J.F., Romeijn, H.E., Kaufman, D.E.: Improving hit-and-run for global optimization. J. Global Optim. 3, 171–192 (1993)

    Google Scholar 

  167. Zolfaghari, S., Liang, M.: Comparative study of simulated annealing, genetic algorithms and tabu Search for solving binary and comprehensive machine-grouping problems. Int. J. Prod. Resour. 40(9), 2141–2158 (2002)

    Google Scholar 

Download references

Acknowledgments

This work is supported in part by the Air Force Office of Scientific Research (FA9550-07-1-0232). The authors wish to thank the anonymous referees for their feedback on this chapter.

Author information

Authors and Affiliations

  1. Industrial and Systems Engineering, University at Buffalo, Buffalo, NY, 14260-2050, USA

    Alexander G. Nikolaev

  2. Department of Computer Science, University of Illinois, Urbana, IL, USA, 61801-2302

    Sheldon H. Jacobson

Authors
  1. Alexander G. Nikolaev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sheldon H. Jacobson
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Alexander G. Nikolaev or Sheldon H. Jacobson .

Editor information

Editors and Affiliations

  1. , Département de mathématiques et génie in, École Polytechnique Montréal, Montreal, H3C 3A7, Québec, Canada

    Michel Gendreau

  2. Dépt. Informatique et Recherche, Opérationnelle, Université de Montreal, Pavillon André-Aisenstadt, Montreal, H3C 3J7, Québec, Canada

    Jean-Yves Potvin

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Nikolaev, A.G., Jacobson, S.H. (2010). Simulated Annealing. In: Gendreau, M., Potvin, JY. (eds) Handbook of Metaheuristics. International Series in Operations Research & Management Science, vol 146. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-1665-5_1

Download citation

Publish with us

Policies and ethics

Search

Navigation