Optimal shape design of devices and systems for induction-heating: methodologies and applications P. Di Barba Department of Electrical Engineering, University of Pavia, Pavia, Italy F. Dughiero Department of Electrical Engineering, University of Padova, Padova, Italy S. Lupi Department of Electrical Engineering, University of Padova, Padova, Italy A. Savini Department of Electrical Engineering, University of Pavia, Pavia, Italy Keywords Design optimization, Electrical machines, Electromagnetics Abstract The paper reports recent experiences of the authors in the automated optimal design of devices and systems for induction heating. The results presented have been obtained in the frame of a long-lasting cooperation between Laboratory of Electroheat, University of Padova and Electromagnetic Devices CAD Laboratory, University of Pavia. In particular, two case studies are discussed; in both cases, the shape design of the inductor is carried out in a systematic way, by minimizing user-defined objective functions depending on design variables and subject to bounds and constraints. When the design problem is characterized by many objectives which are in mutual conflict, the non-dominated set of solutions is identified. Introduction To identify, in an automated way, the geometry of the device that is able to provide some prescribed performance is the essential goal of optimal shape design in electromagnetics. This is actually an inverse problem and implies the constrained minimization of user-defined objectives that depend on all the design variables defining the device. As a consequence, a fully automatic procedure is implemented, linking together the analysis and the optimization module. Formally, a single-objective design problem is cast as follows: x min f ðxÞ subject to gðxÞ , 0 and hðxÞ¼ 0 The Emerald Research Register for this journal is available at The current issue and full text archive of this journal is available at http://www.emeraldinsight.com/researchregister http://www.emeraldinsight.com/0332-1649.htm Optimal design of devices and systems 111 COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering Vol. 22 No. 1, 2003 pp. 111-122 q MCB UP Limited 0332-1649 DOI 10.1108/03321640310452213