Chaos-assisted multiobjective evolutionary algorithm to the design of transformer

Abstract

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.