It has been shown that mixed integer programming methods can effectively support minimal model, stable model and well-founded model semantics for ground deductive databases. Recently, a novel approach called partial instantiation has been developed which, when integrated with mixed integer programming methods, can handle non-ground logic programs. The goal of this paper is to explore how this integrated framework based on partial instantiation can be optimized. In particular, we develop an incremental algorithm that minimizes repetitive computations. We also develop several optimization techniques to further enhance the efficiency of our incremental algorithm. Experimental results indicate that our algorithm and optimization techniques can bring about very significant improvement in run-time performance.
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