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Multi-objective design of a power inductor: a benchmark problem of inverse induction heating

Paolo Di Barba (Department of Industrial and Information Engineering, University of Pavia, Pavia, Italy)
Michele Forzan (Department of Industrial Engineering, University of Padova, Padova, Italy)
Elisabetta Sieni (Department of Industrial Engineering, University of Padova, Padova, Italy)



The purpose of this paper is to investigate a bi-objective optimization problem characterized by coupled field analysis. The optimal design of a pancake inductor for the controlled heating of a graphite disk is considered as the benchmark problem. The case study is related to the design of industrial applications of the induction heating of graphite disk.


The expected goal of the optimization process is twofold: to improve temperature uniformity in the disk and also electrical efficiency of the inductor. The solution of the relevant bi-objective optimization problem is based on multiphysics field analysis. Specifically, the direct problem is solved as a magnetic and thermal coupled problem by means of finite elements; a mesh-inspired definition of thermal uniformity is proposed. In turn, the Pareto front trading off electrical efficiency and thermal uniformity is identified exploiting evolutionary computing.


By varying the problem targets, different Pareto fronts are identified trading off thermal uniformity and electrical efficiency of the induction-heating device.

Practical implications

These results suggest how to improve the design of this kind of device for the epitaxial growth of silicon wafer; the advantage of using a magnetic concentrator placed close to the inductor axis is pointed out.


The coupling of a multiphysics direct problem with a multiobjective inverse problem is presented as a benchmark problem and accordingly solved. The benchmark provides a simple analysis problem that allows testing various optimization algorithms in a comparative way.



Di Barba, P., Forzan, M. and Sieni, E. (2014), "Multi-objective design of a power inductor: a benchmark problem of inverse induction heating", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 33 No. 6, pp. 1990-2005.



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