Journal of Heuristics

, Volume 14, Issue 6, pp 627–654 | Cite as

Simulated annealing in the presence of noise

  • Jürgen Branke
  • Stephan Meisel
  • Christian Schmidt


In many practical optimization problems, evaluation of a solution is subject to noise, e.g., due to stochastic simulations or measuring errors. Therefore, heuristics are needed that are capable of handling such noise. This paper first reviews the state-of-the-art in applying simulated annealing to noisy optimization problems. Then, two new algorithmic variants are proposed: an improved version of stochastic annealing that allows for arbitrary annealing schedules, and a new approach called simulated annealing in noisy environments (SANE). The latter integrates ideas from statistical sequential selection in order to reduce the number of samples required for making an acceptance decision with sufficient statistical confidence. Finally, SANE is shown to significantly outperform other state-of-the-art simulated annealing techniques on a stochastic travelling salesperson problem.


Simulated annealing Uncertainty Noise Sequential sampling 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Ahmed, M.A., Alkhamis, T.M.: Simulation-based optimization using simulated annealing with ranking and selection. Comput. Oper. Res. 29(4), 387–402 (2002) zbMATHCrossRefGoogle Scholar
  2. Alkhamis, T.M., Ahmed, M.A.: Simulation-based optimization using simulated annealing with confidence interval. In: Ingalls, R.G. et al. (eds.) Winter Simulation Conference, pp. 514–519 (2004) Google Scholar
  3. Alkhamis, T.M., Ahmed, M.A., Tuan, V.K.: Simulated annealing for discrete optimization with estimation. Eur. J. Oper. Res. 116(3), 530–544 (1999) zbMATHCrossRefGoogle Scholar
  4. Alrefaei, M.H., Andradóttir, S.: A simulated annealing algorithm with constant temperature for discrete stochastic optimization. Manag. Sci. 45(5), 748–764 (1999) CrossRefGoogle Scholar
  5. Ball, R.C., Fink, T.M.A., Bowler, N.E.: Stochastic annealing. Phys. Rev. Lett. 91(3), 030201 (2003a) CrossRefGoogle Scholar
  6. Ball, R.C., Fink, T.M.A., Bowler, N.E.: Characterization of the probabilistic traveling salesman problem. Phys. Rev. E 68(3), 036703 (2003b) CrossRefGoogle Scholar
  7. Bowler, N.E.: The role of noise in optimisation and diffusion limited aggregation. Ph.D. thesis, University of Warwick (2001) Google Scholar
  8. Branke, J., Chick, S., Schmidt, C.: New developments in ranking and selection: an empirical comparison of the three main approaches. In: Kuhl, N.E., Steiger, M.N., Armstrong, F.B., Joines, J.A. (eds.) Winter Simulation Conference, pp. 708–717. IEEE, New York (2005) CrossRefGoogle Scholar
  9. Bulgak, A.A., Sanders, J.L.: Integrating a modified simulated annealing algorithm with the simulation of a manufacturing system to optimize buffer sizes in automatic assembly systems. In: Winter Simulation Conference, pp. 684–690. IEEE, New York (1988) Google Scholar
  10. Ceperley, D.M., Dewing, M.: The penalty method for random walks with uncertain energies. J. Chem. Phys. 110(20), 9812–9820 (1999) CrossRefGoogle Scholar
  11. Cheh, K.M., Goldberg, J.B., Askin, R.G.: A note on the effect of neighborhood structure in simulated annealing. Comput. Oper. Res. 18(6), 537–548 (1991) zbMATHCrossRefGoogle Scholar
  12. Fink, T.M.A.: Inverse protein folding, hierarchical optimisation and tie knots. Ph.D. thesis, University of Cambridge (1998) Google Scholar
  13. Fox, B.L., Heine, G.W.: Probabilistic search with overrides. Ann. Appl. Probab. 5(4), 1087–1094 (1995) zbMATHCrossRefMathSciNetGoogle Scholar
  14. Gelfand, S.B., Mitter, S.K.: Simulated annealing with noisy or imprecise energy measurements. J. Optim. Theory Appl. 62(1), 49–62 (1989) zbMATHCrossRefMathSciNetGoogle Scholar
  15. Glauber, R.J.: Time-dependent statistics of the Ising model. J. Math. Phys. 4(2), 294–307 (1963) zbMATHCrossRefMathSciNetGoogle Scholar
  16. Gutjahr, W.J., Pflug, G.C.: Simulated annealing for noisy cost functions. J. Glob. Optim. 8(1), 1–13 (1996) zbMATHCrossRefMathSciNetGoogle Scholar
  17. Haddock, J., Mittenthal, J.: Simulation optimization using simulated annealing. Comput. Ind. Eng. 20(4), 387–395 (1992) CrossRefGoogle Scholar
  18. Hajek, B.: Cooling schedules for optimal annealing. Math. Oper. Res. 13(2), 311–329 (1988) zbMATHCrossRefMathSciNetGoogle Scholar
  19. Hastings, W.K.: Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57(1), 97–109 (1970) zbMATHCrossRefGoogle Scholar
  20. Hertz, J., Krogh, A., Palmer, R.G.: Introduction to the Theory of Neural Computation. Addison-Wesley, Reading (1991) Google Scholar
  21. Kennedy, A.D., Kuti, J.: Noise without noise: a new Monte Carlo method. Phys. Rev. Lett. 54(23), 2473–2476 (1985) CrossRefGoogle Scholar
  22. Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 220(4598), 671–680 (1983) CrossRefMathSciNetGoogle Scholar
  23. Kushner, H.J.: Asymptotic global behavior for stochastic approximation and diffusions with slowly decreasing noise effects: global minimization via Monte Carlo. SIAM J. Appl. Math. 47(1), 169–185 (1987) zbMATHCrossRefMathSciNetGoogle Scholar
  24. Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., Teller, E.: Equation of state calculations by fast computing machines. J. Chem. Phys. 21(6), 1087–1092 (1953) CrossRefGoogle Scholar
  25. Nourani, Y., Andresen, B.: A comparison of simulated annealing cooling strategies. J. Phys. A: Math. Gen. 31, 8373–8385 (1998) zbMATHCrossRefGoogle Scholar
  26. Painton, L., Diwekar, U.: Stochastic annealing for synthesis under uncertainty. Eur. J. Oper. Res. 83(3), 489–502 (1995) zbMATHCrossRefGoogle Scholar
  27. Prudius, A.A., Andradottir, S.: Two simulated annealing algorithms for noisy objective functions. In: Kuhl, M.E. et al. (eds.) Winter Simulation Conference, pp. 797–802. IEEE, New York (2005) CrossRefGoogle Scholar
  28. Rees, S., Ball, R.C.: Criteria for an optimum simulated annealing schedule for problems of the travelling salesman type. J. Phys. A: Math. Gen. 20(5), 1239–1249 (1987) CrossRefMathSciNetGoogle Scholar
  29. van Laarhoven, P.J.M., Aarts, E.H.L.: Simulated Annealing: Theory and Applications. Reidel, Dordrecht (1987) zbMATHGoogle Scholar
  30. Wang, L., Zhang, L.: Stochastic optimization using simulated annealing with hypothesis test. Appl. Math. Comput. 174(2), 1329–1342 (2006) zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Jürgen Branke
    • 1
  • Stephan Meisel
    • 2
  • Christian Schmidt
    • 1
  1. 1.Institute AIFBUniversity of KarlsruheKarlsruheGermany
  2. 2.Dept. of Management StudiesUniv. of BraunschweigBraunschweigGermany

Personalised recommendations