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This paper introduces a multi‐objective optimal design for an axial magnetic gear (AMG). In this study, the condition for high torque density and low cogging torque was deduced while the cost of the active materials was also reduced. The number and direction of permanent magnets and their arrangement were unchanged in the optimisation process, and the considered AMG's main dimensions were optimised using the particle swarm optimisation method. The optimised AMG was compared with the latest and similar structures with a relatively high torque density. To extract the produced torque density and cogging torque, three‐dimensional (3D) finite element analyses were conducted. The results showed that while torque density increased and cogging torque decreased, the total volume and magnetic materials used decreased significantly. [ABSTRACT FROM AUTHOR]