An improved red deer algorithm for addressing a direct current brushless motor design problem

Document Type : Article


1 Department of Industrial Engineering and Management Systems, Amirkabir University of Technology, Tehran, Iran

2 Department of Electrical Engineering, University of Science and Technology of Mazandaran, Behshahr, Iran

3 Department of Industrial Engineering, University of Science and Technology of Mazandaran, Behshahr, Iran


The Red Deer Algorithm (RDA) is one of recent metaheuristic algorithms inspired by the behavior of red deers during a breading season. The RDA revealed its performance for a variety of combinatorial optimization problems in different real-world applications. In this paper, the parameters and operators of RDA using some adaptive strategies have been modified to improve the performance of this optimizer. To prove the efficiency of Improved RDA (IRDA), not only some benchmarked functions are utilized but also a Direct Current (DC) brushless motor design as one of real-world engineering design issues. The results of developed IRDA have been compared with its general idea and existing algorithms from the literature. This comparative study confirms that the offered IRDA outperforms the other algorithms and provide very competitive results.


Main Subjects

References  1. Fathollahi-Fard, A.M., Hajiaghaei-Keshteli, M., and  Tavakkoli-Moghaddam, R. A bi-objective green home  health care routing problem", Journal of Cleaner  Production, 200, pp. 423{443 (2018).  2. Fathollahi-Fard, A.M., Hajiaghaei-Keshteli, M., and  Tavakkoli-Moghaddam, R. The Social Engineering  Optimizer (SEO)", Engineering Applications of Arti-  _cial Intelligence, 72, pp. 267{293 (2018).  3. Mirjalili, S. Moth-ame optimization algorithm: A  novel nature-inspired heuristic paradigm", Knowledge-  Based Systems, 89, pp. 228{249 (2015).  4. Mirjalili, S. SCA: a sine cosine algorithm for solving  optimization problems", Knowledge-Based Systems,  96, pp. 120{133 (2016).  5. Ghorbani, N. and Babaei, E. Exchange market algorithm",  Applied Soft Computing, 19, pp. 177{187  (2014).  6. Fathollahi Fard, A.M. and Hajighaei-Keshteli, M.  Red deer algorithm (RDA); a new optimization algorithm  inspired by red deer's mating", International  Conference on Industrial Engineering, IEEE, 12, pp.  331{342 (2016).  7. Faris, H., Mafarja, M.M., and Heidari, A.A., et al. An  e_cient binary salp swarm algorithm with crossover  scheme for feature selection problems", Knowledge-  Based Systems, 154, pp. 43{67 (2018).  8. Duan, H. and Gan, L. Orthogonal multiobjective  chemical reaction optimization approach for the brushless  DC motor design", IEEE Transactions on Magnetics,  51(1), pp. 1{7 (2015).  9. Lee, T.-Y., Trung, P.X., Kim, J.-W., Kim, Y.-J., and  Jung, S.-Y. Search region management method for local  search algorithm employing design optimization of  brushless dc motor", IEEE Transactions on Magnetics,  52(3), pp. 1{6 (2016).  10. Wolpert, D.H. and Macready, W.G. No free lunch  theorems for optimization", IEEE Transaction on  Evolutionary Computation, 1(1), pp. 67{82 (1997).  11. Fathollahi Fard, A.M. and Hajiaghaei-Keshteli, M. A  bi-objective partial interdiction problem considering  di_erent defensive systems with capacity expansion  of facilities under imminent attacks", Applied Soft  Computing, 68, pp. 343{359 (2018).  12. Ayala, H.V., Segundo, E.H., Mariani, V.C., and  Coelho, L.D.S. Multiobjective krill herd algorithm for  electromagnetic optimization", IEEE Transactions on  Magnetics, 52(3), pp. 31{48 (2016).  13. Ishikawa, T., Yonetake, K., and Kurita, N. An  optimal material distribution design of brushless DC  motor by genetic algorithm considering a cluster of  material", IEEE Transactions on Magnetics, 47(5),  pp. 1310{1313 (2011).  14. Son, B., Park, G.-J., Kim, J.-W., Kim, Y.-J., and  Jung, S.-Y. Interstellar search method with mesh  adaptive direct search for optimal design of brushless  DC motor", IEEE Transactions on Magnetics, 52(3),  pp. 1{4 (2011).  15. Yoon, K.-Y. and Kwon, B.-I. Optimal design of a new  interior permanent magnet motor using a ared-shape  arrangement of ferrite magnets", IEEE Transactions  on Magnetics, 52(7), pp. 11{24 (2016).  16. Kim, H.-S., You, Y.-M., and Kwon, B.-I. Rotor shape  optimization of interior permanent magnet BLDC  motor according to magnetization direction", IEEE  Transactions on Magnetics, 49(5), pp. 2193{2196  (2013).  A.M. Fathollahi-Fard et al./Scientia Iranica, Transactions E: Industrial Engineering 28 (2021) 1750{1764 1761  17. Liu, X., Hu, H., Zhao, J., Belahcen, A., Tang, L., and  Yang, L. Analytical solution of the magnetic _eld  and emf calculation in ironless BLDC motor", IEEE  Transactions on Magnetics, 52(2), pp. 1{10 (2016).  18. Lee, T.-Y., Seo, M.-K., Kim, Y.-J., and Jung, S.-  Y. Motor design and characteristics comparison of  outer-rotor-type BLDC motor and blac motor based  on numerical analysis", IEEE Transactions on Applied  Superconductivity, 26(4), pp. 1{6 (2016).  19. Azari, M.N., Samani, M., and Pahnekolaie, S.M.A.  Optimal design of a Brushless DC motor, by using  the Cuckoo Optimization", International Journal of  Engineering, Transaction B: Applications, 30(5), pp.  668{677 (2017).  20. Xu, X. and Deng, Y. UAV power component-DC  brushless motor design with merging adjacentdisturbances  and integrated-dispatching pigeoninspired  optimization", IEEE Transactions on  Magnetics, 56(5), pp. 1{7 (2018).  21. Golmohamadi, S., Tavakkoli-Moghaddam, R., and  Hajiaghaei-Keshteli, M. Solving a fuzzy _xed charge  solid transportation problem using batch transferring  by new approaches in meta-heuristic", Electronic  Notes in Discrete Mathematics, 58, pp. 143{150  (2017).  22. Samadi, A., Mehranfar, N., Fathollahi Fard, A.M.,  and Hajiaghaei-Keshteli, M. Heuristic-based metaheuristic  to address a sustainable supply chain network  design problem", Journal of Industrial and Production  Engineering, 35(2), pp. 102{117 (2018).  23. Hajiaghaei-Keshteli, M. and Fathollahi Fard, A.M.  Sustainable closed-loop supply chain network design  with discount supposition", Neural Computing and  Applications, 31(9), pp. 5543{5537 (2019).  24. Sahebjamnia, N., Fathollahi-Fard, A.M., and  Hajiaghaei-Keshteli, M. Sustainable tire closed-loop  supply chain network design: Hybrid metaheuristic  algorithms for large-scale networks", Journal of  Cleaner Production, 196, pp. 273{296 (2018).  25. Fathollahi-Fard, A.M., Hajiaghaei-Keshteli, M., and  Mirjalili S. Multi-objective stochastic closed-loop supply  chain network design with social considerations",  Applied Soft Computing, 71, pp. 505{525 (2018).  26. Mohammadzadeh, H., Sahebjamnia, N., Fathollahi-  Fard, A.M., and Hajiaghaei-Keshteli, M. New approaches  in Metaheuristics to solve the truck scheduling  problem in a cross docking center", International  Journal of Engineering, Transaction B: Applications,  31(8), pp. 1258{1266 (2018).  27. Rahideh, A., Korakianitis, T., Ruiz, P., Keeble, T.,  and Rothman, M. Optimal brushless DC motor  design using genetic algorithms", Journal of Magnetism  and Magnetic Materials, 322(22), pp. 3680{  3687 (2010).  28. Taguchi, G., Introduction to Quality Engineering: Designing  Quality Into Products and Processes, Springer,  No. 658.562 T3 (1986).  29. Tian, G., Ren, Y., Feng, Y., Zhou, M., Zhang,  H., and Tan, J. Modeling and planning for dualobjective  selective disassembly using AND/OR graph  and discrete arti_cial bee colony", IEEE Transactions  on Industrial Informatics, 15, pp. 2456{2468 (2019).  30. Esfandiyari, Z., Bashiri, M., and Tavakkoli-  Moghaddam, R. Resilient network design in a  location-allocation problem with multi-level facility  hardening", Scientia Iranica, 26(2), pp. 996{1008  (2019).  31. Tian, G., Zhou, M., and Li, P. Disassembly sequence  planning considering fuzzy component quality  and varying operational cost", IEEE Transactions on  Automation Science and Engineering, 15, pp. 748{760  (2018).  32. Safaeian, M., Fathollahi-Fard, A.M., Tian, G., et  al. A multi-objective supplier selection and order  allocation through incremental discount in a fuzzy  environment", Journal of Intelligent & Fuzzy Systems,  37(1), pp. 1435{1455 (2019).  33. Fu, Y., Tian, G., Fathollahi-Fard, A.M., et al.  Stochastic multi-objective modelling and optimization  of an energy-conscious distributed permutation  ow shop scheduling problem with the total tardiness  constraint", Journal of Cleaner Production, 226, pp.  515{525 (2019).  34. Abdi, A., Abdi, A., Fathollahi-Fard, A.M., et al. A  set of calibrated metaheuristics to address a closedloop  supply chain network design problem under uncertainty",  International Journal of Systems Science:  Operations & Logistics, 8(1), pp. 23{40 (2021).  35. Bahadori-Chinibelagh, S., Fathollahi-Fard, A.M., and  Hajiaghaei-Keshteli, M. Two constructive algorithms  to address a multi-depot home healthcare routing  problem", IETE Journal of Research, pp. 1{7 (2019).  DOI:  36. Fathollahi-Fard, A.M., Hajiaghaei-Keshteli, M., and  Mirjalili, S. A set of e_cient heuristics for a home  healthcare problem", Neural Computing and Applications,  32(10), pp. 6185{6205 (2020).