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2012 | OriginalPaper | Chapter

1. Stochastic Approach to Global Optimization at a Glance

Author : Stefan Schäffler

Published in: Global Optimization

Publisher: Springer New York

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Excerpt

Let
$$f : R(\subseteq {\mathbb{R}}^{n}) \rightarrow \mathbb{R}$$
be a given objective function of a global minimization problem and let P be a probability distribution defined on the feasible region R, then a random search algorithm is defined as follows:
1.
Compute m pseudorandom vectors x 1, , x m as realizations of m stochastically independent identically P-distributed random variables
$${\mathbf{X}}_{1},\ldots,{\mathbf{X}}_{m}.$$
 
2.
Choose j ∈ { 1, , m} such that
$$f({\mathbf{x}}_{j}) \leq f({\mathbf{x}}_{i})\quad \mbox{ for all}\quad i \in \{ 1,\ldots,m\}.$$
 
3.
Use x j as global minimum point or apply a local minimization procedure with starting point x j to minimize f.
 

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Metadata
Title
Stochastic Approach to Global Optimization at a Glance
Author
Stefan Schäffler
Copyright Year
2012
Publisher
Springer New York
DOI
https://doi.org/10.1007/978-1-4614-3927-1_1