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Abstract--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 medium size 150 tons per hour fumace transformer are considered for realizing the mathematical model for design. All the optimal solutions involve determining the design parameters satisfying performance constraints for minimum active material cost or weight or volume or a multi-objective combining the three objectives. The results of a 3-phase, core type 64.5 MVA, 33kV | 384 712 volts, star-delta connected fumace transformer show the potential for implementation of GA as an efficient search technique for design optimization of transformers. Key Words.'Fumace transformers; Genetiq Algorithm; Optimal Design; Multi-obj ective Optimi zation. In a direct-arc furnace, heat is generated by a powerfi,rl electric arc struck betwee