Chaos-assisted multiobjective evolutionary algorithm to the design of transformer
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.
KeywordsMultiobjective 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.
This article does not contain any studies with human participants or animals performed by any of the authors.
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- Logistic Map (2001) Online document, available from http://en.wikipedia.org/wiki/Logistic_map
- 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
- 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
- Promotion Centre and European Copper InstituteGoogle Scholar
- Subramanian S, Padma S (2011a) Optimization of transformer design using bacterial foraging algorithm. Int J Comput Appl 19(3):52–57Google Scholar
- 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
- 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
- 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
- Williams SB, Abetti PA, Magnesson EF (1955) How digital computers aid transformer designer. Gen Electr Rev 58:24–25Google Scholar
- Wu CJ, Lee FC (1980) Minimum weight EI core and pot core inductor and transformer designs. IEEE Trans Magn 16(5):755–757Google Scholar
- 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
- 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
- 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