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An algorithm that learns from a set of examples should ideally be able to exploit the available resources of (a) abundant computing power and (b) domain-specific knowledge to improve its ability to generalize. Connectionist theory-refinement systems, which use background knowledge to select a neural network's topology and initial weights, have proven to be effective at exploiting domain-specific knowledge; however, most do not exploit available computing power. This weakness occurs because they lack the ability to refine the topology of the neural networks they produce, thereby limiting generalization, especially when given impoverished domain theories. We present the REGENT algorithm which uses (a) domain-specific knowledge to help create an initial population of knowledge-based neural networks and (b) genetic operators of crossover and mutation (specifically designed for knowledge-based networks) to continually search for better network topologies. Experiments on three real-world domains indicate that our new algorithm is able to significantly increase generalization compared to a standard connectionist theory-refinement system, as well as our previous algorithm for growing knowledge-based networks.