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Search Methodologies pp 265–285Cite as

Simulated Annealing

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Abstract

Many problems in engineering, planning and manufacturing can be modeled as that of minimizing or maximizing a cost function over a finite set of discrete variables. This class of so-called combinatorial optimization problems has received much attention over the years and major achievements have been made in its analysis (Ausiello et al.

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Notes

  1. 1.

    Let A and A ′ ⊂ A be two sets. Then the characteristic function \(\chi _{({A}^{{\prime}})}: A \rightarrow \{ 0, 1\}\) of the set A ′ is defined as χ (A′) (a) = 1 if a ∈ A ′ , and \(\chi _{({A}^{{\prime}})}(a) = 0\) otherwise.

References

  • Aarts EHL, Korst JHM (1989) Simulated annealing and Boltzmann machines. Wiley, Chichester

    Google Scholar 

  • Aarts EHL, van Laarhoven PJM (1985) Statistical cooling: a general approach to combinatorial optimization problems. Philips J Res 40:193–226

    Google Scholar 

  • Aarts EHL, Lenstra JK (eds) (2003) Local search in combinatorial optimization. Princeton University Press, Princeton

    Google Scholar 

  • Aarts EHL, Korst JHM, van Laarhoven PJM (1988) A quantitative analysis of the simulated annealing algorithm: a case study for the traveling salesman problem. J Stat Phys 50:189–206

    Article  Google Scholar 

  • Andersen B (1996) Finite-time thermodynamics and simulated annealing. In: Shiner JS (ed) Entropy and entropy generation. Kluwer, Dordrecht, pp 111–127

    Google Scholar 

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

    Article  Google Scholar 

  • Arora S, Barak B (2009) Computational complexity: a modern approach. Cambridge University Press, Cambridge/New York

    Book  Google Scholar 

  • Ausiello G, Crescenzi P, Gambosi G, Kann V, Marchetti-Spaccamela A, Protasi M (1999) Complexity and approximation: combinatorial optimization problems and their approximability properties. Springer, Berlin

    Google Scholar 

  • Azencott R (1992) Simulated annealing: parallelization techniques. Wiley, Chichester

    Google Scholar 

  • Binder K (1978) Monte Carlo methods in statistical physics. Springer, Berlin

    Google Scholar 

  • Černý V (1985) Thermodynamical approach to the traveling salesman problem: an efficient simulation algorithm. J Optim Theory Appl 45:41–51

    Article  Google Scholar 

  • Collins NE, Eglese RW, Golden BL (1988) Simulated annealing: an annotated bibliography. Am J Math Manage Sci 8:209–307

    Google Scholar 

  • Connors DP, Kumar PR (1987) Simulated annealing and balance of recurrence order in time-inhomogeneous Markov chains. In: Proceedings of the 26th IEEE conference on decision and control, Los Angeles, pp 2261–2263

    Google Scholar 

  • Eglese RW (1990) Simulated annealing: a tool for operational research. Eur J Oper Res 46:271–281

    Article  Google Scholar 

  • Feller W (1950) An introduction to probability theory and its applications, vol 1. Wiley, New York

    Google Scholar 

  • Fox BL (1993) Integrating and accelerating tabu search, simulated annealing, and genetic algorithms. In: Glover F et al (eds) Tabu search. Annals of operations research, vol 41. Baltzer, Basel, pp 47–67

    Google Scholar 

  • Garey MR, Johnson DS (1979) Computers and intractability: a guide to the theory of NP-completeness. Freeman, San Francisco

    Google Scholar 

  • Gidas B (1985) Nonstationary Markov chains and convergence of the annealing algorithm. J Stat Phys 39:73–131

    Article  Google Scholar 

  • Hajek B (1985) A tutorial survey of the theory and application of simulated annealing. In: Proceedings of the 24th IEEE conference on decision and control, Fort Lauderdale, pp 755–760

    Google Scholar 

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

    Article  Google Scholar 

  • Isaacson D, Madsen R (1976) Markov chains. Wiley, New York

    Google Scholar 

  • Kernighan BW, Lin S (1970) An efficient heuristic procedure for partitioning graphs. Bell Syst Tech J 49:291–307

    Article  Google Scholar 

  • Kirkpatrick S, Gelatt CD Jr, Vecchi MP (1983) Optimization by simulated annealing. Science 220:671–680

    Article  Google Scholar 

  • Lin S (1965) Computer solutions of the traveling salesman problem. Bell Syst Tech J 44:2245–2269

    Article  Google Scholar 

  • Lin S, Kernighan BW (1973) An effective heuristic algorithm for the traveling salesman problem. Oper Res 21:498–516

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Michiels W, Aarts E, Korst J (2007) Theoretical aspects of local search. Springer, Berlin

    Google Scholar 

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

    Article  Google Scholar 

  • Nourani Y, Andersen B (1998) A comparison of simulated annealing cooling strategies. J Phys A 31:8373–8385

    Article  Google Scholar 

  • Orosz JE, Jacobson SH (2002) Finite-time performance analysis of static simulated annealing algorithms. Comput Optim Appl 21:21–53

    Article  Google Scholar 

  • Park M-W, Kim Y-D (1998) A systematic procedure for setting parameters in simulated annealing algorithms. Comput Oper Res 25:207–217

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Salamon P, Sibani P, Frost R (2002) Facts, conjectures, and improvements for simulated annealing. SIAM Monographs, Philadelphia

    Book  Google Scholar 

  • Seneta E (1981) Non-negative matrices and Markov chains, 2nd edn. Springer, New York

    Book  Google Scholar 

  • Steinhöfel K, Albrecht A, Wong CK (1998) On various cooling schedules for simulated annealing applied to the job shop problem. In: Luby M et al (eds) Randomization and approximation techniques in computer science. Lecture notes in computer science, vol 1518. Springer, Berlin, pp 260–279

    Chapter  Google Scholar 

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

    Article  Google Scholar 

  • van Laarhoven PJM (1988) Theoretical and computational aspects of simulated annealing. PhD thesis, Erasmus University Rotterdam

    Google Scholar 

  • van Laarhoven PJM, Aarts EHL (1987) Simulated annealing: theory and applications. Reidel, Dordrecht

    Book  Google Scholar 

  • van Laarhoven PJM, Aarts EHL, Lenstra JK (1992) Job shop scheduling by simulated annealing. Oper Res 40:185–201

    Google Scholar 

  • Vidal RVV (ed) (1993) Applied simulated annealing. Lecture notes in economics and mathematical systems, vol 396. Springer, Berlin

    Google Scholar 

  • Villalobos-Arias M, Coello CA, Hernandez-Lerma O (2006) Asymptotic convergence of a simulated annealing algorithm for multiobjective optimization problems. Math Methods Oper Res 64:353–362

    Article  Google Scholar 

  • White SR (1984) Concepts of scale in simulated annealing. In: Proceedings of the IEEE international conference on computer design, New York, pp 646–651

    Google Scholar 

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Author information

Authors and Affiliations

  1. Eindhoven University of Technology, Eindhoven, The Netherlands

    Emile Aarts

  2. Philips Research Laboratories, Eindhoven, The Netherlands

    Jan Korst

  3. NXP, Eindhoven, The Netherlands

    Wil Michiels

Authors
  1. Emile Aarts
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  2. Jan Korst
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  3. Wil Michiels
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Corresponding author

Correspondence to Wil Michiels .

Editor information

Editors and Affiliations

  1. Computing Science and Mathematics, University of Stirling, Scotland, United Kingdom

    Edmund K. Burke

  2. Research and Knowledge Transfer, University of Nottingham, Malaysia & UK, Semenyih, Malaysia

    Graham Kendall

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Aarts, E., Korst, J., Michiels, W. (2014). Simulated Annealing. In: Burke, E., Kendall, G. (eds) Search Methodologies. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-6940-7_10

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