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This paper presents a new analysis method for air core permanent-magnet synchronous linear motor design optimization problems with a large search space. The aim is to reduce the total computational time by replacing most of the finite-element analysis (FEA) steps with an analytical model of the motor consisting of nonlinear equivalent magnetic circuit and flux density distribution models. A small number of FEA steps are used to determine some parameters of the analytical model. The result of the proposed method is compared with results of both a pure FEA design and experiments on a real motor. The proposed method has similar performance to FEA, although computationally it is at least two orders of magnitude faster.