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Most researches regarding structural design of electromagnetic systems have been focused on a single physical phenomenon such as magnetic, electric or thermal effect. However, analysis and design of the multi-physics phenomenon is coming to the fore related with the actuator system targeting on the small size and high performance. Two or more physics phenomena are taken into account in a multi-physics system and the multi-physics analysis is performed using the governing equation in the formulation of a partial differential equation. Accordingly, in actuator design, it is generally hard to predict an optimal shape accurately considering both the magnetic and the thermal effect simultaneously. The objective of this research is set to establish a simultaneous/parallel design process for a multi-physics problem combining magnetic and thermal effects by employing the adoptive weighting factor while the previous work mostly suggests a sequential design process. The proposed method has been applied to yoke shape design of a C-core type magnetic actuator for minimizing the heat transfer effect as well as maximizing the actuating force. The topology optimization scheme based on the density approach is employed to obtain the optimal shape.