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A two-dimensional analytical magnetic field model in cylindrical coordinates has been employed to quickly and accurately calculate the magnetic flux density distribution and electromagnetic force. The objectives of the optimization problem are to simultaneously minimize the power losses and machine volume and the constraints are to ensure to develop the required level of electromagnetic force and to avoid saturation in the back-iron. The optimization problem has been solved using two types of metaheuristic optimization techniques, i.e., particle swarm optimization (PSO), and fuzzy adaptive PSO (FAPSO). 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