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A Short Introduction to Stochastic Optimization

Ombach J.

Schedae Informaticae

2014

Vol. 23

9--20

We present some typical algorithms used for finding global minimum/ maximum of a function defined on a compact finite dimensional set, discuss commonly observed procedures for assessing and comparing the algorithms’ performance and quote theoretical results on convergence of a broad class of stochastic algorithms.

On Updating Finite Element Models of Real Structures Using Genetic Algorithm

Touat N., Pyrz M., Rechak S.

Machine Dynamics Problems

2008

Vol. 32, No. 2

74-87

An efficient method of updating numerical models for dynamics problems is presented. The objective is to minimize the difference between measured and simulated vibration data. The corresponding optimization problem is formulated in the modal domain and solved using the genetic algorithm (GA) stochastic algorithm. Original modifications of a standard GA are proposed to improve the updating process efficacy. New versions of GA exploit the speeding up procedures developed in the novel accelerated random search (ARS) algorithm. A finite element model of a lumped mass structure is analyzed to validate the approach. A real beam-like structure model is updated, making use of experimental modal data. The enhanced GA enables us to obtain results well correlated with experiments.

Lévy flights as an underlying mechanism for global optimization algorithms

Gutowski M.

Prace Naukowe Politechniki Warszawskiej. Elektronika

2002

z. 139

175--184

In this chapter we propose and advocate the use of the so called Lévy flights as a driving mechanism for a class of stochastic optimization computations. This proposal, for some reason overlooked until now, is - in the author's opinion - very relevant to our need for an algorithm which is capable of generating trial steps of very different length in the search space. The required balance between short and long steps can be easily and fully controlled. A simple example of the approximated Lévy distribution, implemented in FORTRAN 77, is given. We also discuss the physical grounds of presented methods.