Heuristic Optimization Based on Penalty Approach for Surface Permanent Magnet Synchronous Machines


This paper aims to provide a smart design to improve the efficiency of surface permanent magnet synchronous motor. An efficient design strategy involving penalty approaches are considered for extracting all the possible parameter combinations and the solutions in the infeasible region. We compare the performance of tree heuristic optimization algorithms and six penalty methods. The heuristic optimization algorithms are: particle swarm optimization, differential search algorithm, and tree seed algorithm. The penalty methods are: three of which are static penalty approaches, two of dynamic penalty approaches, and Deb’s rule. Besides, the optimized motor design is tested with finite element analysis. Two conclusions were drawn from the experiments. First, heuristic algorithms using penalty approaches had significantly better performance compared to standard and popular heuristic algorithms. This emphasizes the importance of using heuristic algorithms with penalty approaches in SPMSM design optimization. Second, the compatibility of design optimization and numerical analysis results are acceptable and highly satisfactory for surface permanent magnet synchronous motor design. According to the analytical design, a 4% improvement in efficiency was achieved with the proposed approach.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10


  1. 1.

    Hafner, M.; Finken, T.; Felden, M.; Hameyer, K.: Automated virtual prototyping of permanent magnet synchronous machines for HEVs. IEEE Trans. Magn. 47(5), 1018–1021 (2011)

    Article  Google Scholar 

  2. 2.

    Bianchi, N.; Bolognani, S.; Fomasiero, E.: A general approach to determine the rotor losses in three-phase fractional-slot PM machines. In: 2007 IEEE International Electric Machines & Drives Conference, pp. 634–641. IEEE (2007)

  3. 3.

    Cassimere, B.N.; Sudhoff, S.D.: Population-based design of surface-mounted permanent-magnet synchronous machines. IEEE Trans. Energy Convers. 24(2), 338–346 (2009)

    Article  Google Scholar 

  4. 4.

    Libert, F.; Soulard, J.: Design study of different direct-driven permanent-magnet motors for a low speed application. In: Proceedings of the Nordic Workshop on Power and Industrial Electronics (NORpie), Trondheim, Norway (2004)

  5. 5.

    Bramerdorfer, G.; Tapia, J.A.; Pyrhönen, J.J.; Cavagnino, A.: Modern electrical machine design optimization: techniques, trends, and best practices. IEEE Trans. Ind. Electron. 65(10), 7672–7684 (2018)

    Article  Google Scholar 

  6. 6.

    Rastogi, S.; Kumar, R.R.; Singh, S.K.: Design, analysis and optimization of permanent magnet synchronous generator. In: 2016 IEEE International Conference on Power Electronics, Drives and Energy Systems (PEDES), pp. 1–5. IEEE (2016)

  7. 7.

    Ion, I.G.; Bontinck, Z.; Loukrezis, D.; Römer, U.; Lass, O.; Ulbrich, S.; Schöps, S.; De Gersem, H.: Robust shape optimization of electric devices based on deterministic optimization methods and finite-element analysis with affine parametrization and design elements. Electr. Eng. 100(4), 2635–2647 (2018)

    Article  Google Scholar 

  8. 8.

    Hruska, K.; Kindl, V.; Pechanek, R.: Design of a high-speed permanent magnet synchronous motor for electric kart. Electr. Eng. 99(4), 1141–1150 (2017)

    Article  Google Scholar 

  9. 9.

    Luxin, Z.; Jinji, S.; Xin, M.; Weitao, H.; Xiaosan, L.: Thermal–structure coupling analysis and multi-objective optimization of motor rotor in MSPMSM. Chin. J. Aeronaut. 32(7), 1733–1747 (2019)

    Article  Google Scholar 

  10. 10.

    Ponomarev, P.; Petrov, I.; Bianchi, N.; Pyrhönen, J.: Selection of geometric design variables for fine numerical optimizations of electrical machines. IEEE Trans. Magn. 51(12), 1–8 (2015)

    Article  Google Scholar 

  11. 11.

    Jeong, C.-L.; Hur, J.: Optimization design of PMSM with hybrid-type permanent magnet considering irreversible demagnetization. IEEE Trans. Magn. 53(11), 1–4 (2017)

    Google Scholar 

  12. 12.

    Jeong, C.-L.; Kim, Y.-K.; Hur, J.: Optimized design of PMSM with hybrid type permanent magnet for improving performance and reliability. IEEE Trans. Ind. Appl. 55(5), 4692–4701 (2019)

    Article  Google Scholar 

  13. 13.

    Chen, Q-h; Wang, Q-f; Wang, T.: Optimization design of an interior permanent-magnet synchronous machine for a hybrid hydraulic excavator. Front. Inf. Technol. Electron. Eng. 16(11), 957–968 (2015)

    Article  Google Scholar 

  14. 14.

    El-Refaie, A.M.: Fractional-slot concentrated-windings synchronous permanent magnet machines: opportunities and challenges. IEEE Trans. Ind. Electron. 57(1), 107–121 (2009)

    Article  Google Scholar 

  15. 15.

    Bianchi, N.; Bolognani, S.: Design optimisation of electric motors by genetic algorithms. IEE Proc. Electr. Power Appl. 145(5), 475–483 (1998)

    Article  Google Scholar 

  16. 16.

    Mutluer, M.; Bilgin, O.: Comparison of stochastic optimization methods for design optimization of permanent magnet synchronous motor. Neural Comput. Appl. 21(8), 2049–2056 (2012)

    Article  Google Scholar 

  17. 17.

    Knypiński, Ł.; Jedryczka, C.; Demenko, A.: Influence of the shape of squirrel-cage bars on the dimensions of permanent magnets in an optimized line-start permanent magnet synchronous motor. COMPEL Int. J. Comput. Math. Electr. Electron. Eng. 36(1), 298–308 (2017)

    Article  Google Scholar 

  18. 18.

    Hwang, C.-C.; Lyu, L.-Y.; Liu, C.-T.; Li, P.-L.: Optimal design of an SPM motor using genetic algorithms and Taguchi method. IEEE Trans. Magn. 44(11), 4325–4328 (2008)

    Article  Google Scholar 

  19. 19.

    Lee, J.H.; Song, J.; Kim, D.; Kim, J.; Kim, Y.; Jung, S.: Particle swarm optimization algorithm with intelligent particle number control for optimal design of electric machines. IEEE Trans. Ind. Electron. 65(2), 1791–1798 (2018)

    Article  Google Scholar 

  20. 20.

    Hahn, I.: Heuristic structural optimization of the permanent magnets used in a surface mounted permanent-magnet synchronous machine. IEEE Trans. Magn. 48(1), 118–127 (2011)

    Article  Google Scholar 

  21. 21.

    Knypiński, Ł.; Pawełoszek, K.; Le Menach, Y.: Optimization of low-power line-start PM motor using gray wolf metaheuristic algorithm. Energies 13(5), 1186 (2020)

    Article  Google Scholar 

  22. 22.

    Fodorean, D.; Idoumghar, L.; Brévilliers, M.; Minciunescu, P.; Irimia, C.: Hybrid differential evolution algorithm employed for the optimum design of a high-speed PMSM used for EV propulsion. IEEE Trans. Ind. Electron. 64(12), 9824–9833 (2017)

    Article  Google Scholar 

  23. 23.

    Mohamed, M.R.; Ishak, D.: Optimization of surface-mounted permanent magnet brushless AC motor using analytical model and differential evolution algorithm. J. Electr. Eng. 70(3), 208–217 (2019)

    Google Scholar 

  24. 24.

    Alsawalhi, J.Y.; Sudhoff, S.D.: Design optimization of asymmetric salient permanent magnet synchronous machines. IEEE Trans. Energy Convers. 31(4), 1315–1324 (2016)

    Article  Google Scholar 

  25. 25.

    Liu, X.; Lin, Q.; Fu, W.: Optimal design of permanent magnet arrangement in synchronous motors. Energies 10(11), 1700 (2017)

    Article  Google Scholar 

  26. 26.

    Hanselman, D.C.: Brushless permanent magnet motor design: The Writers’ Collective (2003)

  27. 27.

    Khan, M.N.; Cowley, W.G.; Nguyen, K.D.: Puncturing optimization algorithm and its applications in free space communications. In: 2013 Australian Communications Theory Workshop (AusCTW), 29 Jan–1 Feb 2013, pp. 152–157 (2013)

  28. 28.

    Khan, M.N.; Rafay, A.; Gilani, S.O.; Jamil, M.: Link adaptation for maximizing MI of hybrid optical/RF communication system. Procedia Comput. Sci. 110, 282–289 (2017)

    Article  Google Scholar 

  29. 29.

    Liu, J.; Teo, K.L.; Wang, X.; Wu, C.: An exact penalty function-based differential search algorithm for constrained global optimization. Soft. Comput. 20(4), 1305–1313 (2016)

    Article  Google Scholar 

  30. 30.

    Kiran, M.S.: TSA: tree-seed algorithm for continuous optimization. Expert Syst. Appl. 42(19), 6686–6698 (2015)

    Article  Google Scholar 

  31. 31.

    Khan, M.N.; Jamil, M.: Adaptive hybrid free space optical/radio frequency communication system. Telecommun. Syst. 65(1), 117–126 (2017)

    Article  Google Scholar 

  32. 32.

    Khan, M.N.; Cowley, W.G.; Nguyen, K.D.: Link adaptation of FAHOR communication system. In: 2012 Australian Communications Theory Workshop (AusCTW), 30 Jan–2 Feb 2012, pp. 120–125 (2012)

  33. 33.

    Khan, M.N.; Gilani, S.O.; Jamil, M.; Rafay, A.; Awais, Q.; Khawaja, B.A.; Uzair, M.; Malik, A.W.: Maximizing throughput of hybrid FSO-RF communication system: an algorithm. IEEE Access 6, 30039–30048 (2018)

    Article  Google Scholar 

  34. 34.

    Ursem, R.K.; Vadstrup, P.: Parameter identification of induction motors using stochastic optimization algorithms. Appl. Soft Comput. 4(1), 49–64 (2004)

    Article  Google Scholar 

  35. 35.

    Kennedy, J.; Eberhart, R.: Particle swarm optimization (PSO). In: Proceedings of IEEE International Conference on Neural Networks, Perth, Australia, pp. 1942–1948 (1995)

  36. 36.

    Trianni, V.; Tuci, E.; Passino, K.M.; Marshall, J.A.: Swarm cognition: an interdisciplinary approach to the study of self-organising biological collectives. Swarm Intell. 5(1), 3–18 (2011)

    Article  Google Scholar 

  37. 37.

    Civicioglu, P.: Transforming geocentric cartesian coordinates to geodetic coordinates by using differential search algorithm. Comput. Geosci. 46, 229–247 (2012)

    Article  Google Scholar 

  38. 38.

    Sahman, M.A.; Altun, A.A.; Dündar, A.O.: The binary differential search algorithm approach for solving uncapacitated facility location problems. J. Comput. Theor. Nanosci. 14(1), 670–684 (2017)

    Article  Google Scholar 

  39. 39.

    Parsopoulos, K.E.; Vrahatis, M.N.: Particle swarm optimization method for constrained optimization problems. Intell. Technol. Theory Appl. New Trends Intell. Technol. 76(1), 214–220 (2002)

    MATH  Google Scholar 

  40. 40.

    Smith, A.E.; Coit, D.W.; Baeck, T.; Fogel, D.; Michalewicz, Z.: Penalty functions. Evol. Comput. 2, 41–48 (2000)

    Google Scholar 

  41. 41.

    Joines, J.A.; Houck, C.R.: On the use of non-stationary penalty functions to solve nonlinear constrained optimization problems with GA’s. In: Proceedings of the First IEEE Conference on Evolutionary Computation IEEE World Congress on Computational Intelligence, pp. 579–584. IEEE (1994)

  42. 42.

    Kuri-Morales, A.F.; Gutiérrez-García, J.: Penalty function methods for constrained optimization with genetic algorithms: a statistical analysis. In: Mexican International Conference on Artificial Intelligence, pp. 108–117. Springer (2002)

  43. 43.

    Deb, K.: An efficient constraint handling method for genetic algorithms. Comput. Methods Appl. Mech. Eng. 186(2), 311–338 (2000)

    Article  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Mehmet Çunkaş.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Mutluer, M., Şahman, M.A. & Çunkaş, M. Heuristic Optimization Based on Penalty Approach for Surface Permanent Magnet Synchronous Machines. Arab J Sci Eng (2020). https://doi.org/10.1007/s13369-020-04689-y

Download citation


  • Heuristic algorithms
  • Penalty function
  • Finite element analysis
  • Constrained optimization