# A Novel Method for Inference of Acyclic Chemical Compounds with Bounded Branch-height Based on Artificial Neural Networks and Integer Programming

Analysis of chemical graphs is a major research topic in computational molecular biology due to its potential applications to drug design. One approach is inverse quantitative structure activity/property relationship (inverse QSAR/QSPR) analysis, which is to infer chemical structures from given chemical activities/properties. Recently, a framework has been proposed for inverse QSAR/QSPR using artificial neural networks (ANN) and mixed integer linear programming (MILP). This method consists of a prediction phase and an inverse prediction phase. In the first phase, a feature vector f(G) of a chemical graph G is introduced and a prediction function ψ on a chemical property π is constructed with an ANN. In the second phase, given a target value y^* of property π, a feature vector x^* is inferred by solving an MILP formulated from the trained ANN so that ψ(x^*) is close to y^* and then a set of chemical structures G^* such that f(G^*)= x^* is enumerated by a graph search algorithm. The framework has been applied to the case of chemical compounds with cycle index up to 2. The computational results conducted on instances with n non-hydrogen atoms show that a feature vector x^* can be inferred for up to around n=40 whereas graphs G^* can be enumerated for up to n=15. When applied to the case of chemical acyclic graphs, the maximum computable diameter of G^* was around up to around 8. We introduce a new characterization of graph structure, "branch-height," based on which an MILP formulation and a graph search algorithm are designed for chemical acyclic graphs. The results of computational experiments using properties such as octanol/water partition coefficient, boiling point and heat of combustion suggest that the proposed method can infer chemical acyclic graphs G^* with n=50 and diameter 30.

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