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This paper introduces a meta-optimization algorithm called NeuroEvolutionary Meta-Optimization (NEMO) that evolves an algorithm targeted at optimizing only within a specific problem class. More specifically, a form of neural network is evolved that acts as the controller of a kind of optimization algorithm that can potentially exploit problem class-specific structure. NEMO is demonstrated on several benchmark problems that confirm its ability to succeed on problems within the class on which it is trained. The key implication is that it is indeed possible to evolve this kind of meta-optimizer with a neural network-like structure, opening up a promising research direction in automatically evolving such class-specific optimizers.