Abstract
Simulated Annealing (SA) is one of the simplest and best-known metaheuristic method for addressing difficult black box global optimization problems whose objective function is not explicitly given and can only be evaluated via some costly computer simulation. It is massively used in real-life applications. The main advantage of SA is its simplicity. SA is based on an analogy with the physical annealing of materials that avoids the drawback of the Monte-Carlo approach (which can be trapped in local minima), thanks to an efficient Metropolis acceptance criterion. When the evaluation of the objective-function results from complex simulation processes that manipulate a large-dimension state space involving much memory, population-based algorithms are not applicable and SA is the right answer to address such issues. This chapter is an introduction to the subject. It presents the principles of local search optimization algorithms, of which simulated annealing is an extension, and the Metropolis algorithm, a basic component of SA. The basic SA algorithm for optimization is described together with two theoretical properties that are fundamental to SA: statistical equilibrium (inspired from elementary statistical physics) and asymptotic convergence (based on Markov chain theory). The chapter surveys the following practical issues of interest to the user who wishes to implement the SA algorithm for its particular application: finite-time approximation of the theoretical SA, polynomial-time cooling, Markov-chain length, stopping criteria, and simulation-based evaluations. To illustrate these concepts, this chapter presents the straightforward application of SA to two classical and simple classical NP-hard combinatorial optimization problems: the knapsack problem and the traveling salesman problem. The overall SA methodology is then deployed in detail on a real-life application: a large-scale aircraft trajectory planning problem involving nearly 30,000 flights at the European continental scale. This exemplifies how to tackle nowadays complex problems using the simple scheme of SA by exploiting particular features of the problem, by integrating astute computer implementation within the algorithm, and by setting user-defined parameters empirically, inspired by the SA basic theory presented in this chapter.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
E. Aarts, J. Korst, Simulated Annealing and Boltzmann Machines: A Stochastic Approach to Combinatorial Optimization and Neural Computing (Wiley, New York, 1989)
E. Aarts, P. Van Laarhoven, A new polynomial time cooling schedule, in Proceedings of the IEEE International Conference on Computer-Aided Design, Santa Clara (1985), pp. 206–208
E. Aarts, P. Van Laarhoven, Statistical cooling: a general approach to combinatorial problems. Philips J. Res. 40, 193–226 (1985)
H. Bayram, R. Sahin, A new simulated annealing approach for travelling salesman problem. Math. Comput. Appl. 18(3), 313–322 (2013)
S. Chaimatanan, D. Delahaye, M. Mongeau, A hybrid metaheuristic optimization algorithm for strategic planning of 4D aircraft trajectories at the continental scale. IEEE Comput. Intell. Mag. 9(4), 46–61 (2014)
M. Chams, A. Hertz, D. de Werra, Some experiments with simulated annealing for coloring graphs. Eur. J. Oper. Res. 32(2), 260–266 (1987)
Y. Crama, M. Schyns, Simulated annealing for complex portfolio selection problems. Eur. J. Oper. Res. 150(3), 546–571 (2003)
T. Emden-Weiner, M. Proksch, Best practice simulated annealing for the airline crew scheduling problem. J. Heuristics 5(4), 419–436 (1999)
R. Hanafi, E. Kozan, A hybrid constructive heuristic and simulated annealing for railway crew scheduling. Comput. Ind. Eng. 70, 11–19 (2014)
A. Islami, S. Chaimatanan, D. Delahaye, Large-scale 4D trajectory planning, in Air Traffic Management and Systems II, ed. by Electronic Navigation Research Institute. Lecture Notes in Electrical Engineering, vol. 420 (Springer, Tokyo, 2017), pp. 27–47
S. Kirkpatrick, C.D. Gelatt, M.P. Vecchi, Optimization by simulated annealing. IBM Research Report RC 9355, Acts of PTRC Summer Annual Meeting (1982)
S. Kirkpatrick, C.D. Gelatt, M.P. Vecchi, Optimization by simulated annealing. Science 220(4598), 671 (1983)
P. Laarhoven, E. Aarts (eds.), Simulated Annealing: Theory and Applications (Kluwer, Norwell, 1987)
W.F. Mahmudy, Improved simulated annealing for optimization of vehicle routing problem with time windows (VRPTW). Kursor J. 7(3), 109–116 (2014)
N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, E. Teller, Equation of state calculation by fast computing machines. J. Chem. Phys. 21(6), 1087–1092 (1953)
P. Siarry, G. Berthiau, F. Durdin, J. Haussy, Enhanced simulated annealing for globally minimizing functions of many continuous variables. ACM Trans. Math. Softw. 23(2), 209–228 (1997)
D.F. Wong, H.W. Leong, C.L. Liu, Simulated Annealing for VLSI Design (Kluwer Academic, Boston, 1988)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Delahaye, D., Chaimatanan, S., Mongeau, M. (2019). Simulated Annealing: From Basics to Applications. In: Gendreau, M., Potvin, JY. (eds) Handbook of Metaheuristics. International Series in Operations Research & Management Science, vol 272. Springer, Cham. https://doi.org/10.1007/978-3-319-91086-4_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-91086-4_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-91085-7
Online ISBN: 978-3-319-91086-4
eBook Packages: Business and ManagementBusiness and Management (R0)