The role of crossover operator in the genetic optimization of magnetic models

The Ising model, introduced almost 100 years ago by Wilhelm Lenz and Ernst Ising, is the formalism still popular as a tool to describe magnetic properties of a wide class of materials. Among many issues which arise when using this model there exist problems related to the process of finding minimum...

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Bibliographic Details
Published in:Applied mathematics and computation Vol. 217; no. 22; pp. 9368 - 9379
Main Author: GWIZDALLA, Tomasz M
Format: Journal Article
Language:English
Published: Amsterdam Elsevier Inc 15.07.2011
Elsevier
Subjects:
Approximation
Calculus of variations and optimal control
Crossover operators
Crossovers
Energy use
Exact sciences and technology
Global optimization
Ising model
Mathematical analysis
Mathematical models
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in mathematical programming, optimization and calculus of variations
Numerical methods in optimization and calculus of variations
Operators
Optimization
Sciences and techniques of general use
Crossover operators
Ising model
Global optimization
Numerical analysis
Genetic algorithm
Applied mathematics
Optimization method
NP hard problem
Variational calculus
Mathematical programming
ISSN:0096-3003, 1873-5649
Online Access:Get full text
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Summary:The Ising model, introduced almost 100 years ago by Wilhelm Lenz and Ernst Ising, is the formalism still popular as a tool to describe magnetic properties of a wide class of materials. Among many issues which arise when using this model there exist problems related to the process of finding minimum energy of the system. Since these problems are NP-hard, optimizations can either be performed for some approximated cases or be the subject of global optimization techniques. In this paper we present an analysis of the effect of different crossover operators on the efficiency of genetic algorithm used to minimize energy in the Ising model. Although it is not a benchmark tool, we hope it may be interesting as a testing tool.
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ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2011.04.025