Hypothetical reasoning is an important framework for knowledge-based systems, however, its inference time grows exponentially with respect to problem size. In this paper, we present an understandable efficient method called slide-down and lift-up (SL) method which uses a linear programming technique for determining an initial search point and a non-linear programming technique for efficiently finding a near-optimal 0-1 solution. To escape from trapping into local optima, we have developed a new local handler, which systematically fixes a variable to a locally consistent value. Since the behavior of the SL method is illustrated visually, the simple inference mechanism of the method can be easily understood.
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