This article presents a methodology for optimizing the geometric parameters of air-core coils using the Particle Swarm Optimization (PSO) algorithm. The design problem is formulated as a bi-objective task, aiming to maximize the magnetic flux density along the coil axis while simultaneously minimizing the conductor mass. An analytical model based on the Biot-Savart law was developed to drive the optimization process, allowing for the generation of Pareto fronts that illustrate the trade-off between magnetic performance and material consumption. To validate the proposed approach, five distinct design cases with varying geometric constraints were analyzed. The results obtained from the analytical model were verified against numerical simulations performed using the Finite Element Method (FEM) in Agros2D software. The comparative analysis demonstrated high convergence between the analytical and numerical methods, with relative deviations remaining below 2.5\%. The study confirms that the proposed hybrid methodology constitutes a robust tool for designing electromagnetic actuators, enabling the selection of optimal coil geometries that balance high magnetic force capabilities with lightweight construction.