Global optimization and simulated annealing

A. Dekkers, E.H.L. Aarts

Research output: Book/ReportBookScientific

Abstract

In this paper we are concerned with global optimization, which can be defined as the problem of finding points on a bounded subset of Rn in which some real valued functionf assumes its optimal (i.e. maximal or minimal) value. We present a stochastic approach which is based on the simulated annealing algorithm. The approach closely follows the formulation of the simulated annealing algorithm as originally given for discrete optimization problems. The mathematic formulation is extended to continuous optimization problems and we prove asymptotic convergence to the set of global optima. Furthermore, we discuss an implementation of the algorithm and compare its performance with other well known algorithms. The performance evaluation is carried out for a standard set of test functions from the literature. Keywords: global optimization, continuous variables, simulated annealing.
Original languageEnglish
Place of PublicationEindhoven
PublisherTechnische Universiteit Eindhoven
Publication statusPublished - 1988
Externally publishedYes

Publication series

NameMemorandum COSOR

Fingerprint

Simulated Annealing Algorithm
Simulated Annealing
Global Optimization
Optimization Problem
Asymptotic Convergence
Continuous Optimization
Formulation
Discrete Optimization
Continuous Variables
Global Optimum
Test function
Performance Evaluation
Subset
Standards

Cite this

Dekkers, A., & Aarts, E. H. L. (1988). Global optimization and simulated annealing. (Memorandum COSOR). Eindhoven: Technische Universiteit Eindhoven.
Dekkers, A. ; Aarts, E.H.L. / Global optimization and simulated annealing. Eindhoven : Technische Universiteit Eindhoven, 1988. (Memorandum COSOR).
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Dekkers, A & Aarts, EHL 1988, Global optimization and simulated annealing. Memorandum COSOR, Technische Universiteit Eindhoven, Eindhoven.

Global optimization and simulated annealing. / Dekkers, A.; Aarts, E.H.L.

Eindhoven : Technische Universiteit Eindhoven, 1988. (Memorandum COSOR).

Research output: Book/ReportBookScientific

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T1 - Global optimization and simulated annealing

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AU - Aarts, E.H.L.

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N2 - In this paper we are concerned with global optimization, which can be defined as the problem of finding points on a bounded subset of Rn in which some real valued functionf assumes its optimal (i.e. maximal or minimal) value. We present a stochastic approach which is based on the simulated annealing algorithm. The approach closely follows the formulation of the simulated annealing algorithm as originally given for discrete optimization problems. The mathematic formulation is extended to continuous optimization problems and we prove asymptotic convergence to the set of global optima. Furthermore, we discuss an implementation of the algorithm and compare its performance with other well known algorithms. The performance evaluation is carried out for a standard set of test functions from the literature. Keywords: global optimization, continuous variables, simulated annealing.

AB - In this paper we are concerned with global optimization, which can be defined as the problem of finding points on a bounded subset of Rn in which some real valued functionf assumes its optimal (i.e. maximal or minimal) value. We present a stochastic approach which is based on the simulated annealing algorithm. The approach closely follows the formulation of the simulated annealing algorithm as originally given for discrete optimization problems. The mathematic formulation is extended to continuous optimization problems and we prove asymptotic convergence to the set of global optima. Furthermore, we discuss an implementation of the algorithm and compare its performance with other well known algorithms. The performance evaluation is carried out for a standard set of test functions from the literature. Keywords: global optimization, continuous variables, simulated annealing.

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Dekkers A, Aarts EHL. Global optimization and simulated annealing. Eindhoven: Technische Universiteit Eindhoven, 1988. (Memorandum COSOR).