Soft Computing

, Volume 21, Issue 19, pp 5675–5692 | Cite as

Chaos-assisted multiobjective evolutionary algorithm to the design of transformer

  • S. Tamilselvi
  • S. Baskar
  • L. Anandapadmanaban
  • K. Mohaideen Abdul Kadhar
  • P. R. Varshini
Methodologies and Application


In this paper, multiobjective transformer design (TD) optimization is carried out using multiobjective evolutionary algorithm (MOEA) based on decomposition with dynamical resource allocation (MOEA/D-DRA) for four sets of conflicting TD bi-objectives such as (i) purchase cost and total loss, (ii) purchase cost and total lifetime cost (TLTC), (iii) total mass and total loss and (iv) total mass and TLTC, subjected to 14 various practical constraints. Significant decision variables with enlarged search space are employed for obtaining reliable and efficient TD with minimum losses and TLTC. TD is accompanied by 3D-finite element method assessment to validate the designed no-load loss calculated from analytical equations. To improve the searching ability of MOEA/D-DRA (MDRA) in solving this complex multimodal TD optimization problem (TDOP), this paper proposes integration of chaos with MDRA, enabling chaotic variation in the crossover rate and mutation scaling factor. To prove the effectiveness of chaos-assisted MOEA, logistic chaotic map-assisted MDRA, and iterative chaotic map with infinite collapses- (ICMIC) assisted MDRA (ICMDRA) have been successfully applied to multiobjective TDOP and their TD results are compared with those of MDRA, knee point-driven evolutionary multiobjective optimization algorithm (KnEA), and non-dominated sorting genetic algorithm (NSGA) II. This paper identifies which chaotic map can assist MDRA and solve TDOP by comparative analysis of performance of logistic and ICMIC chaotic maps. Efficient TD results and two MOEA performance indicators confirm the superiority of ICMDRA over all the other MOEAs in terms of diversity and convergence in solving TDOP.


Multiobjective transformer design optimization MOEA/D-DRA Chaos NSGA II KnEA 


Compliance with ethical standards


This research work was not funded by any company/agency.

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.


  1. Abido MA (2006) Multi objective evolutionary algorithms for electric power dispatch problem. IEEE Trans Evol Comput 10(3):315–329CrossRefGoogle Scholar
  2. Adly AA, Abd-El-Hafiz SK (2015) A performance-oriented power transformer design methodology using multi-objective evolutionary optimization. J Adv Res 6(3):417–423Google Scholar
  3. Altinoz OT Yilmaz AE, Ha GWW (2010) Chaos Particle swarm optimized PID controller for the inverted pendulum system. In: Proceedings of second international conference on engineering optimization, PortugalGoogle Scholar
  4. Amoiralis EI, Georgilakis PS, Tsili M (2008a) Design optimization of distribution transformers based on mixed integer programming methodology. J Optoelectron Adv Mater 10(5):1178–1183Google Scholar
  5. Amoiralis EI, Tsili M, Georgilakis PS, Kladas A, Souflaris A (2008b) A parallel mixed integer programming-finite element method technique for global design optimization of power transformers. IEEE Trans Magn 44(6):1022–1025CrossRefGoogle Scholar
  6. Amoiralis EI, Georgilakis PS, Tsili M, Kladas A (2009) Global transformer optimization method using evolutionary design and numerical field computation. IEEE Trans Magn 45(3):1720–1723CrossRefGoogle Scholar
  7. Amoiralis EI Tsili M, Kladas A (2012) Global transformer design optimization using deterministic and nondeterministic algorithms. In: Proceedings of the twentieth International Conference on Electrical Machines (ICEM2012), France, pp 2012Google Scholar
  8. Chen Z, Yuan X, Ji B, Wang P, Tian H (2014) Design of a fractional order PID controller for hydraulic turbine regulating system using chaotic non-dominated sorting genetic algorithm II. Energy Convers Manage 84:390–404CrossRefGoogle Scholar
  9. Cheema MAM, Fletcher JE, Dorrell D (2013) A practical approach for the global optimization of electromagnetic design of 3-phase core type distribution transformer allowing for capitalization of losses. IEEE Trans Magn 49(5):2117–2120CrossRefGoogle Scholar
  10. Coelho LDS, Mariani VCM (2006) Combining of chaotic differential evolution and quadratic programming for economic dispatch optimization with valve-point effect. IEEE Trans Power Syst 21(2):989–996CrossRefGoogle Scholar
  11. Coelho LDS, Mariani VC, Ferreira da Luz MV, Leite JV (2013) Novel gamma differential evolution approach for multiobjective transformer design optimization. IEEE Trans Magn 49(5):2121–2124Google Scholar
  12. Coelho LDS, Mariani VC, Guerra FA, Ferreira da Luz MV, Leite JV (2014) Multiobjective optimization of transformer design using a chaotic evolutionary approach. IEEE Trans Magn 50(2):669–672CrossRefGoogle Scholar
  13. Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197CrossRefGoogle Scholar
  14. Georgilakis PS, Hatziargyriou N, Paparigas D (1999) AI helps reduce transformer iron losses. Comput Appl Power IEEE 12(4):41–46CrossRefGoogle Scholar
  15. Georgilakis PS, Doulamis N, Doulamis A, Hatziargyriou N, Kollias S (2001) A novel iron loss reduction technique for distribution transformers based on a combined genetic algorithm-neural network approach. IEEE Trans System Man Cybern C 31:16–34CrossRefGoogle Scholar
  16. Georgilakis PS, Tsili M, Souflaris A (2007a) A heuristic solution to the transformer manufacturing cost optimization problem. J Mater Process Technol 181:260–266CrossRefGoogle Scholar
  17. Georgilakis PS, Gioulekas A, Souflaris A (2007b) A decision tree method for the selection of winding material in power transformers. J Mater Process Technol 181:281–285CrossRefGoogle Scholar
  18. Georgilakis PS (2009a) Recursive genetic algorithm-finite element method technique for the solution of transformer manufacturing cost minimization problem. IET Electr Power Appl 3(6):514–519CrossRefGoogle Scholar
  19. Hansen N (2006) The CMA evolution strategy: a comparing review. Towards a new evolutionary computation. Springer, Berlin, pp 75–102CrossRefGoogle Scholar
  20. He D, He C, Jiang L, Zhu H, Hu G (2001) Chaotic characteristics of a one-dimensional iterative map with infinite collapses. IEEE Trans Circ Syst I: Fundam Theory Appl 48(7):900–906Google Scholar
  21. Hui L, Li H, Bei H, Shunchang Y (2001) Application research based on improved genetic algorithm for optimum design of power transformers. In: Proceedings of the fifth IEEE international conference on electrical machines and systems, ICEMS, vol 1, pp 242–245Google Scholar
  22. Hernandez C, Arjona MA (2007) Design of distribution transformers based on a knowledge-based system and 2D finite elements. Finite Elem Anal Des 43:659–665CrossRefGoogle Scholar
  23. Jabr RA (2005) Application of geometric programming to transformer design. IEEE Trans Magn 41(11):4261–4269CrossRefGoogle Scholar
  24. Judd FF, Kressler DR (1977) Design optimization of small low-frequency power transformers. IEEE Trans Magn 13(4):1058–1069CrossRefGoogle Scholar
  25. Li H, Zhang Q (2009) Multiobjective optimization problems with complicated Pareto sets, MOEA/D and NSGA-II. IEEE Trans Evol Comput 12(2):284–302CrossRefGoogle Scholar
  26. Logistic Map (2001) Online document, available from
  27. Masood MA, Jabbar RA, Masoum MAS, Junaid M, Ammar M (2012) An innovative technique for design optimization of Core type 3-phase distribution transformer using Mathematica. Glob J Technol Optim 3:2012Google Scholar
  28. Olivares-Galván JC, de León F, Georgilakis P, Escarela-Pérez R (2010) Selection of copper against aluminium windings for distribution transformers. Inst Eng Technol Electr Power Appl 4(6):474–485CrossRefGoogle Scholar
  29. Padma S, Bhuvaneswari R, Subramanian S (2006) Optimal design of power transformer using simulated annealing technique. In: Proceedings of IEEE conference on industrial technology (ICIT), India, pp 1015–1019Google Scholar
  30. Pham TH, Salon SJ, Hoole SRH (1996) Shape optimization of windings for minimum losses. IEEE Trans Magn 32(5):4287–4289CrossRefGoogle Scholar
  31. Promotion Centre and European Copper InstituteGoogle Scholar
  32. Subramanian S, Padma S (2011a) Optimization of transformer design using bacterial foraging algorithm. Int J Comput Appl 19(3):52–57Google Scholar
  33. Subramanian S, Padma S (2011b) Bacterial foraging algorithm based multi objective optimal design of single phase transformer. J Comput Sci Eng 6(2):1–6Google Scholar
  34. Tamilselvi S, Baskar S (2014) Modified parameter optimization of distribution transformer design using covariance matrix adaptation evolution strategy. Int J Electr Power Energy Syst 61:208–218CrossRefGoogle Scholar
  35. Tsivgouli AJ, Tsili MA, Kladas A, Georgilakis P, Souflaris A, Skarlatini A (2007) Geometry optimization of electric shielding in power transformers based on finite element method. J Mater Process Technol 181:159–164Google Scholar
  36. Tsili M, Kladas A, Georgilakis P, Souflaris A, Paparigas D (2005) Numerical techniques for design and modelling of distribution transformers. J Mater Process Technol 161:320–326Google Scholar
  37. Williams SB, Abetti PA, Magnesson EF (1955) How digital computers aid transformer designer. Gen Electr Rev 58:24–25Google Scholar
  38. Wu CJ, Lee FC (1980) Minimum weight EI core and pot core inductor and transformer designs. IEEE Trans Magn 16(5):755–757Google Scholar
  39. Zhang X, Tian Y, Jin Y (2015) A knee point driven evolutionary algorithm for many-objective optimization. IEEE Trans Evol Comput. Accepted for publicationGoogle Scholar
  40. Zhang Q, Li H (2007) MOEA/D: a multi-objective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput 11(6):712–731CrossRefGoogle Scholar
  41. Zhang Q, Liu W, Li H (2009) The performance of a new version of MOEA/D on CEC09 Unconstrained MOP Test Instances. CEC 2009Google Scholar
  42. Zitzler E (1999) Online Document, Evolutionary algorithms for multi-objective optimization: methods and applications. Ph.D. Thesis, Swiss Federal Institute of Technology (ETH) (Dissertation ETH No. 13398)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • S. Tamilselvi
    • 1
  • S. Baskar
    • 2
  • L. Anandapadmanaban
    • 3
  • K. Mohaideen Abdul Kadhar
    • 4
  • P. R. Varshini
    • 2
  1. 1.Department of Electrical and Electronics EngineeringSri Venkateswara College of EngineeringSriperumbudurIndia
  2. 2.Department of Electrical and Electronics EngineeringThiagarajar College of EngineeringMaduraiIndia
  3. 3.Department of EEEKingston College of EngineeringVelloreIndia
  4. 4.Department of EEEM.V.J. College of EngineeringBangaloreIndia

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