Abstract
Methods of stochastic optimization are designed to find the maximum/minimum of some complex cost function within a defined search space using stochastic methods. The simplest, most transparent but also very inefficient method is the method of hill climbing. It resembles a controlled random walk. More elaborate is the method of simulated annealing which is based on Markov-chain Monte-Carlo and uses the Metropolis algorithm (or one of its variations) to generate new configurations within the search space. A ‘cooling’ strategy reduces the search space slowly until it has been restricted to the immediate vicinity of the global minimum. Various flavors of this method are discussed and the algorithm is tested against the traveling salesperson problem. A different class of algorithms is established by genetic algorithms. They are borrowed from nature’s concept of the survival of the fittest. The applicability of such an algorithm is tested against the traveling salesperson problem.
Notes
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Note that in the real world the environment (in particular the natural enemies of a species) develop as well. Moreover, we do not consider any communication within a species, like the formation of societies, learning, and related processes.
References
Panos, M.P., Resende, M.G.C. (eds.): Handbook of Applied Optimization. Oxford University Press, New York (2002)
Hartmann, A.H., Rieger, H.: Optimization Algorithms in Physics. Wiley – VCH, Berlin (2002)
Locatelli, M., Schoen, F.: Global Optimization. MPS-SIAM Series on Optimization. Cambridge University Press, Cambridge (2013)
Scholz, D.: Deterministic Global Optimization. Springer, Berlin/Heidelberg (2012)
Schneider, J.J., Kirkpatrick, S. (eds.): Stochastic Optimization. Springer, Berlin/Heidelberg (2006)
Lawler, E.L., Lenstra, K.K., Rinnooy Kan, A.H.G., Shmoys, D.B.: The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization. Wiley, New York (1985)
Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes in C++, 2nd edn. Cambridge University Press, Cambridge (2002)
Kundu, S., Acharyya, S.: Stochastic local search approaches in solving the nurse scheduling problem. In: Chaki, N., Cortesi, A. (eds.) Computer Information Systems – Analysis and Technologies, Communications in Computer and Information Science, vol. 245, pp. 202–211. Springer, Berlin/Heidelberg (2011)
Marinari, E., Parisi, G., Ritort, F.: On the 3d Ising spin glass. J. Phys. A: Math. Gen. 27, 2687 (1994). doi:10.1088/0305-4470/27/8/008
Watkins, J.J.: Across the Board: The Mathematics of Chessboard Problems. Princeton University Press, Princeton (2012)
Skiena, S.S.: The Algorithm Design Manual. Springer, Berlin/Heidelberg (2008)
Marsaglia, G.: Choosing a point from the surface of a sphere. Ann. Math. Stat. 43, 645–646 (1972). doi:10.1214/aoms/1177692644
Bertsimas, D., Tsitsiklis, J.: Simulated annealing. Stat. Sci. 8, 10–15 (1993)
Salamon, P., Sibani, P., Frost, R.: Facts, Conjectures, and Improvements for Simulated Annealing. Cambridge University Press, Cambridge (2002)
Kirkpatrik, S., Gellat, C.D., Jr., Vecchi, M.P.: Simulated annealing. Science 220, 671 (1983)
Tsallis, C.: Introduction to Nonextensive Statistical Mechanics. Springer, Berlin/Heidelberg (2009)
Man, K.F., Tang, K.S., Kwong, S.: Genetic Algorithms. Springer, Berlin/Heidelberg (1999)
Bäck, T.: Evolutionary Algorithms in Theory and Practice. Oxford University Press, New York (1996)
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Stickler, B.A., Schachinger, E. (2016). Stochastic Optimization. In: Basic Concepts in Computational Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-27265-8_20
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