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Designing a gradient coil for magnetic resonance imaging (MRI) is an electromagnetic inverse problem often formulated as a constrained optimization, which has been successfully solved by inverse boundary element methods. The constant search for new coil features and improved performance has highlighted the need of employing more versatile optimization techniques capable of dealing with the new requirements. In this paper, the solution of linear and nonlinear optimization problems using particle-swarm optimization (PSO) algorithms is presented. Examples of coil designed using this heuristic method are shown, including a comparison to solutions provided by conventional optimization approaches. Numerical experiments reveal that the application of PSO for the solution of inverse boundary element problems for coil design is a computationally efficient algorithm that is capable of handling nonlinear problems and that offers fast convergence, especially for those symmetric coil geometries where the computational effort can be drastically reduced by using suitable dimensionality-reduction techniques.