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

• 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
• DOI: 10.1016/j.amc.2011.04.025

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.