Multi-objective free-form shape optimization of a synchronous reluctance machine

Peter Gangl*, Stefan Köthe, Christiane Mellak, Alessio Cesarano, Annette Mütze

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Purpose: This paper aims to deal with the design optimization of a synchronous reluctance machine to be used in an X-ray tube, where the goal is to maximize the torque while keeping low the amount of material used, by means of gradient-based free-form shape optimization. Design/methodology/approach: The presented approach is based on the mathematical concept of shape derivatives and allows to obtain new motor designs without the need to introduce a geometric parametrization. This paper presents an extension of a standard gradient-based free-form shape optimization algorithm to the case of multiple objective functions by determining updates, which represent a descent of all involved criteria. Moreover, this paper illustrates a way to obtain an approximate Pareto front. Findings: The presented method allows to obtain optimal designs of arbitrary, non-parametric shape with very low computational cost. This paper validates the results by comparing them to a parametric geometry optimization in JMAG by means of a stochastic optimization algorithm. While the obtained designs are of similar shape, the computational time used by the gradient-based algorithm is in the order of minutes, compared to several hours taken by the stochastic optimization algorithm. Originality/value: This paper applies the presented gradient-based multi-objective optimization algorithm in the context of free-form shape optimization using the mathematical concept of shape derivatives. The authors obtain a set of Pareto-optimal designs, each of which is a shape that is not represented by a fixed set of parameters. To the best of the authors’ knowledge, this approach to multi-objective free-form shape optimization is novel in the context of electric machines.

Original languageEnglish
Pages (from-to)1849-1864
Number of pages16
JournalCOMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering
Issue number5
Publication statusPublished - 26 Aug 2022


  • Electrical machine
  • Multi-objective optimization
  • Shape optimization
  • Synchronous reluctance machine

ASJC Scopus subject areas

  • Computer Science Applications
  • Computational Theory and Mathematics
  • Electrical and Electronic Engineering
  • Applied Mathematics


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