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Purpose – The purpose of this paper is to present the topology optimization method to design the rotor and the tooth base in the stator of the permanent magnet (PM) excited machine with the improved high-speed features. The topological and shape sensitivity through the multi-level set method (MLSM) have been used to attain an innovative design of both the rotor and stator made of different materials. Design/methodology/approach – This framework is based on the application of the topological and the shape derivative, obtained by incorporating the adjoint variable method into the MLSM for the magnetoquasistatic system. The representation of the shape and their evolution during the iterative optimization process are obtained by the MLSM. Findings – To find the optimal configuration of a PM machine, the stator and rotor poles were simultaneously optimized by redistributing the iron and the magnet material over the design domains. In this way, it was possible to obtain an innovative design which allows to reduce mechanical vibration and the acoustic noise caused by the cogging torque, while taking the back electromotive force into account. Originality/value – The novelty of the proposed method is to apply the modified multi-level set algorithm with the total variation to the magnetoquasistatic optimization problem. Given the eddy currents phenomenon in the model of a PM machine, it was possible not only to optimize the structure of a PM machine but also to analyze electromagnetic losses distribution. [ABSTRACT FROM AUTHOR]