In the paper, a bi-objective optimization problem characterized by a multi-physics field analysis is investigated. The optimal design of a pancake inductor, related to the design of industrial devices for the controlled heating of a graphite disk is considered as the benchmark problem. The expected goal of the optimization process is to improve temperature uniformity in the disk as well as electrical efficiency of the inductor. The optimized device is designed using a multi-physics problem: magnetic problem for electrical efficiency computation and thermal problem for temperature uniformity computation. The solution of the relevant bi-objective optimization problem is based on a modified multi-objective genetic algorithm in the class of Non-dominated Sorting Genetic Algorithm. The proposed algorithm exploits the migration concept to vary the population genetic characteristics during optimization process in order to improve the Pareto front approximation
