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To improve the performance of a Thomson-coil actuator, a new global optimization algorithm is proposed with mixed integer-discrete-continuous variables. In the algorithm, an augmented objective function is constructed by introducing a penalty function and an extended function to treat the discrete quantities as continuous ones. For the discrete objective function, two kinds of continuous function approximation methods, step function and linear function approximations, are suggested. The coupling particles swarm optimization method is then applied to the augmented objective function to find all the global and local optimal points. Finally, the validity of the proposed method is proven by comparing obtained optimization results with those from the enumeration algorithm.