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Stochastic Optimization

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Basic Concepts in Computational Physics

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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.

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Notes

  1. 1.

    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.

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Authors and Affiliations

  1. Faculty of Physics, University of Duisburg-Essen, Duisburg, Germany

    Benjamin A. Stickler

  2. Institute of Theoretical and Computational Physics, Graz University of Technology, Graz, Austria

    Ewald Schachinger

Authors
  1. Benjamin A. Stickler
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  2. Ewald Schachinger
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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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