This paper presents design optimization of a class of special purpose transformers used in direct-arc melting furnace, adopting Genetic Algorithm (GA). The operation and performance characteristics of a furnace transformer connected to a large direct arc furnace formed the basis for realizing the rating of the transformer. The nonlinear mathematical model of the transformer is based on the core geometry available from manufacturer's published data. In order to verify the effectiveness of GA method, an example is considered. The results show the potential for implementation of GA as an efficient search technique for design optimization of transformers. A discussion on the variation of GA parameters while minimizing the single and multi-objective functions satisfying the performance constraints concludes the paper. © 2006 IEEE.