Meaning of the Rational Solution Obtained by Game Theory in a Multi-Objective Electromagnetic Apparatus Design Problem

The optimization method is often used for designing the configuration of electromagnetic apparatuses in order to enhance performance. Many optimal design methods have been developed and popularized. However, most of the optimal design methods can only take into account a single objective function. Therefore, when the problem has a few purposes, a weighted summed objective function is usually employed. Recently, we have proposed a new method, taking into account the multiple purposes simultaneously and individually. The proposed method can select one rational solution from among the Pareto optima, based on the game theory. However, the meaning of the selected rational solution is unclear. Therefore, the meaning is investigated by calculating the weight parameters of the weighted summed objective function so that the optimal solution of the weighted summed objective function is identical to the rational solution of the game theory. We can intuit the meaning of the rational solution by comparing the weight parameters.