Journal of Magnetism and Magnetic Materials 272–276 (2004) 690–692 Field computation in non-linear magnetic media using particle swarm optimization A.A. Adly a, *, S.K. Abd-El-Hafiz b a Electrical Power and Machines Department, Faculty of Engineering, Cairo University, Giza 12211, Egypt b Department of Engineering Mathematics, Faculty of Engineering, Cairo University, Giza 12211, Egypt Abstract This paper presents an automated particle swarm optimization approach using which field computations may be carried out in devices involving non-linear magnetic media. Among the advantages of the proposed approach are its ability to handle complex geometries and its computational efficiency. The proposed approach has been implemented and computations were carried out for an electromagnet subject to different DC excitation conditions. These computations showed good agreement with the results obtained by the finite-element approach. r 2004 Elsevier B.V. All rights reserved. PACS: 02.90.+p; 02.60.Pn; 41.20.Gz Keywords: Magnetostatics; Non-linear magnetic medium; Particle swarm optimization 1. Introduction Itiswellknownthatthecomputationofmagneticfields in non-linear magnetic media may be carried out using differentanalyticalandnumericalapproaches.Inthecase of problems involving complex geometries, both numer- icalandartificialintelligencetechniquesbecomeespecially moreappealing(referforinstancetoRef. [1]).Irrespective oftheadoptedapproach,geometricaldomainsubdivision is usually performed and local magnetic quantities are considered. One way to obtain an electromagnetic field solution is through the minimization of the problem’s energy functional, which may take non-quadratic forms. 2. The proposed approach The purpose of this paper is to present an automated particle swarm optimization (PSO) approach [2] using which field computations may be carried out in devices involving non-linear magnetic media. More specifically, the energy functional is first formulated in terms of the unknown vector magnetic potentials corresponding to the discretization scheme. A swarm of particles, each designated by a position vector whose length is equal to thenumberofunknownpotentials,isinitiallyrandomly generated. These position vectors may be regarded as potential solutions to the energy minimization problem. The swarm is repeatedly moved (i.e., modified) by the optimization algorithm in the direction of the particle with the best fitness in a more or less stochastic way. Upon convergence, the unknown vector magnetic potentials are found and, consequently, the field distribution is computed everywhere. Among the advantages of the proposed approach are its ability to handle complex magnetic media and computational efficiency, which stems from its search nature without the involvement of matrix manipulation operations. Although the approach is presented in this paper for magnetostatic field computations, it may be easily extended to solve time harmonic problems. 3. Numerical implementation and conclusions The proposed approach has been implemented and computations were carried out for the particular ARTICLE IN PRESS *Corresponding author. Tel.: +02-5163364; fax: +1-775- 248-4429. E-mail address: amradlya@intouch.com (A.A. Adly). 0304-8853/$-see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2003.12.1130