Generation of Near-Optimal Solutions Using ILP-Guided Sampling

Our interest in this paper is in optimisation problems that are intractable to solve by direct numerical optimisation, but nevertheless have significant amounts of relevant domain-specific knowledge. The category of heuristic search techniques known as estimation of distribution algorithms (EDAs) seek to incrementally sample from probability distributions in which optimal (or near-optimal) solutions have increasingly higher probabilities. Can we use domain knowledge to assist the estimation of these distributions? To answer this in the affirmative, we need: (a) a general-purpose technique for the incorporation of domain knowledge when constructing models for optimal values; and (b) a way of using these models to generate new data samples. Here we investigate a combination of the use of Inductive Logic Programming (ILP) for (a), and standard logic-programming machinery to generate new samples for (b). Specifically, on each iteration of distribution estimation, an ILP engine is used to construct a model for good solutions. The resulting theory is then used to guide the generation of new data instances, which are now restricted to those derivable using the ILP model in conjunction with the background knowledge). We demonstrate the approach on two optimisation problems (predicting optimal depth-of-win for the KRK endgame, and job-shop scheduling). Our results are promising: (a) On each iteration of distribution estimation, samples obtained with an ILP theory have a substantially greater proportion of good solutions than samples without a theory; and (b) On termination of distribution estimation, samples obtained with an ILP theory contain more near-optimal samples than samples without a theory. Taken together, these results suggest that the use of ILP-constructed theories could be a useful technique for incorporating complex domain-knowledge into estimation distribution procedures.