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Generative machine learning offers a shortcut: learn an evolvable latent space with implicit biases towards better solutions. We present SOLVE: Search space Optimization with Latent Variable Evolution, which creates a dataset of solutions that satisfy extra problem criteria or heuristics, generates a new latent search space, and uses a genetic algorithm to search within this new space to find solutions that meet the overall objective. We investigate SOLVE on five sets of criteria designed to detrimentally affect the search space and explain how this approach can be easily extended as the problems become more complex. We show that, compared to an identical GA using a standard representation, SOLVE with its learned latent representation can meet extra criteria and find solutions with distance to optimal up to two orders of magnitude closer. 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