Abstract Intelligent systems are applied in a wide range of areas, and computer-aided drug design is a highly important one. One major approach to drug design is the inverse QSAR/QSPR (quantitative structure-activity and structure-property relationship), for which a method that uses both artificial neural networks (ANN) and mixed integer linear programming (MILP) has been proposed recently. This method consists of two phases: a forward prediction phase, and an inverse, inference phase. In the prediction phase, a feature function f over chemical compounds is defined, whereby a chemical compound G is represented as a vector f(G) of descriptors. Following, for a given chemical property $$\pi$$ , using a dataset of chemical compounds with known values for property $$\pi$$ , a regressive prediction function $$\psi$$ is computed by an ANN. It is desired that $$\psi (f(G))$$ takes a value that is close to the true value of property $$\pi$$ for the compound G for many of the compounds in the dataset. In the inference phase, one starts with a target value $$y^*$$ of the chemical property $$\pi$$ , and then a chemical structure $$G^*$$ such that $$\psi (f(G^*))$$ is within a certain tolerance level of $$y^*$$ is constructed from the solution to a specially formulated MILP. This method has been used for the case of inferring acyclic chemical compounds. With this paper, we propose a new concept on acyclic chemical graphs, called a skeleton tree, and based on it develop a new MILP formulation for inferring acyclic chemical compounds. Our computational experiments indicate that our newly proposed method significantly outperforms the existing method when the diameter of graphs is up to 8. In a particular example where we inferred acyclic chemical compounds with 38 non-hydrogen atoms from the set {C, O, S} times faster.

Drug discovery is one of the major goals of computational biology and bioinformatics. A novel framework has recently been proposed for the design of chemical graphs using both artificial neural networks (ANNs) and mixed integer linear programming (MILP). This method consists of a prediction phase and an inverse prediction phase. In the first phase, an ANN is trained using data on existing chemical compounds. In the second phase, given a target chemical property, a feature vector is inferred by solving an MILP formulated from the trained ANN and then a set of chemical structures is enumerated by a graph enumeration algorithm. Although exact solutions are guaranteed by this framework, the types of chemical graphs have been restricted to such classes as trees, monocyclic graphs, and graphs with a specified polymer topology with cycle index up to 2. To overcome the limitation on the topological structure, we propose a new flexible modeling method to the framework so that we can specify a topological substructure of graphs and a partial assignment of chemical elements and bond-multiplicity to a target graph. The results of computational experiments suggest that the proposed system can infer chemical graphs with around up to 50 non-hydrogen atoms.

Enumerating chemical compounds with given structural properties plays an important role in structure elucidation, with applications such as drug design. We focus on the problem of enumerating tree-like chemical graphs specified by upper and lower bounds on feature vectors, where chemical graphs represent compounds, and a feature vector characterizes frequencies of finite paths in a graph. Building on the branch-and-bound algorithm proposed in earlier work, we propose a new bounding procedure, called Resource Cut, to speed up the enumeration process. Tree-like chemical graphs are modeled as vertex-colored trees, colors representing chemical elements. The algorithm is based on a scheme of generating each unique colored tree with a specified number n of vertices. A colored tree is constructed by repeatedly appending vertices. Given a set R of n colored vertices, we found that the algorithm often constructs trees that cannot be extended to a unique representation of a colored tree no matter how the remaining unused colored vertices in the set R are appended. We derive a mathematical condition to detect and discard such trees. Experimental results show that Resource Cut significantly reduces the search space. We have been able to obtain exact numbers of chemical graphs with up to 17 vertices excluding hydrogen atoms.