The study focuses on developing an objective function for optimizing a synchronous generator design, specifically by replacing rare-earth magnets with ferrite magnets. Rare-earth magnets, though offering high magnetic performance, are costly and reliant on scarce materials. To address this, the proposed approach considers key performance factors: power losses, magnet cost, and rotor weight, combined into a weighted objective function. Each parameter is normalized against a reference generator using NdFeB magnets. Three generator variants were analyzed: the baseline with rare-earth magnets, a non-optimized ferrite version, and an optimized ferrite design. The optimization process led to a significant improvement in efficiency, lowering power losses and reducing magnet costs, while maintaining acceptable rotor mass. As a result, the optimized ferrite generator achieved an objective function value 19% better than the baseline. The findings demonstrate that through proper optimization, ferrite magnets can be a viable alternative, offering a balance between performance and cost.