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We present a genetic algorithm based method to optimize the gain medium design of a passively mode-locked vertical external-cavity surface-emitting laser (VECSEL) for ultrashort pulse generation. Beginning with a given standard VECSEL design, we show that a simple modification to the DBR within the active mirror can significantly reduce both the duration and the chirp of the generated pulse. We demonstrate, using realistic numerical simulations, that the full-width at half-maximum of the pulse can be reduced by more than a factor of two. The required design changes come at the cost of increased sensitivity to perturbations in the active chip growth. Methods of counteracting this trend are presented.