An Improved Integer Programming Formulation for Inferring Chemical Compounds with Prescribed Topological Structures

Abstract

AbstractVarious intelligent methods have recently been applied to the design of novel chemical graphs. As one of such approaches, a framework using both artificial neural networks (ANNs) and mixed integer linear programming (MILP) has been proposed. The method first constructs an ANN so that a specified chemical property is predicted from a feature vector f(G) of a chemical graph G. Next an MILP is formulated so that it simulates the construction of f(G) from G and the computation process in the ANN. Then a novel chemical graph with a given target chemical property is inferred by solving the MILP. Based on the framework, the class of graphs to which the above MILP can be formulated has been extended from the graphs with cycle index 0 to the graphs with cycle index 1 and 2. Recently an MILP has been designed to deal with a graph with any cycle index and the computational results on a system with the MILP showed that chemical graphs with around up to 50 non-hydrogen atoms can be inferred. However, this MILP is computationally costly for some instances, e.g., it takes about 10 h to solve some instances with 50 atoms. One of the main reasons for this is that the number of constraints and variables in the MILP is relatively large. In this paper, we improve the MILP by reducing the number of constraints and variables. For this purpose, we drive and utilize a characterization of a chemical acyclic graph in terms of the frequency of some configurations of atom-pairs, by which we can omit part of the construction of f(G) in the MILP. Our experimental results show that the improved MILP can be solved around 20 times faster than the previous MILP.