Purpose: This paper aims to investigate different multi-objective optimization (MOO) approaches for design and control of electromagnetic devices. The main goal of MOO is to find the set of design variables or control parameters which will provide the best possible values of typical conflicting objective functions. Design/methodology/approach: In the research studies, standard genetic algorithm (GA), non-dominated sorting GA (NSGA-II), migration NSGA algorithm and alternance method of optimal control theory are discussed and compared. Findings: The test practical problems of multi-criteria optimization of induction heating processes with respect to chosen quality criteria confirm the effectiveness of application of considered MOO approaches...