The permanent magnet eddy current coupler (PMEC) solves the problem of flexible connection and speed regulation between the motor and the load and is widely used in electrical transmission systems. It provides torque to the load and generates heat and losses, reducing its energy transfer efficiency. This issue has become an obstacle for PMEC to develop toward a higher power. This paper aims to improve the overall performance of PMEC through multi-objective optimization methods. Firstly, a PMEC modeling method based on the Levenberg-Marquardt back propagation (LMBP) neural network is proposed, aiming at the characteristics of the complex input-output relationship and the strong nonlinearity of PMEC. Then, a novel competition mechanism-based multi-objective particle swarm optimization algorithm (NCMOPSO) is proposed to find the optimal structural parameters of PMEC. Chaotic search and mutation strategies are used to improve the original algorithm, which improves the shortcomings of multi-objective particle swarm optimization (MOPSO), which is too fast to converge into a global optimum, and balances the convergence and diversity of the algorithm. In order to verify the superiority and applicability of the proposed algorithm, it is compared with several popular multi-objective optimization algorithms. Applying them to the optimization model of PMEC, the results show that the proposed algorithm has better comprehensive performance. Finally, a finite element simulation model is established using the optimal structural parameters obtained by the proposed algorithm to verify the optimization results. Compared with the prototype, the optimized PMEC has reduced eddy current losses by 1.7812 kW, increased output torque by 658.5 N•m, and decreased costs by 13%, improving energy transfer efficiency.