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

arXiv: https://arxiv.org/abs/2009.09646 · HTML: https://mlsanity.com/paper/2009.09646/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Sep 2020.

## Built on by (most cited first, 9 of 9)

- [Molecular Design Based on Artificial Neural Networks, Integer Programming and Grid Neighbor Search](https://mlsanity.com/paper/2108.10266/) (2021)
- [A Method for Inferring Polymers Based on Linear Regression and Integer Programming](https://mlsanity.com/paper/2109.02628/) (2021)
- [An Inverse QSAR Method Based on Linear Regression and Integer Programming](https://mlsanity.com/paper/2107.02381/) (2021)
- [Molecular Design Based on Integer Programming and Quadratic Descriptors in a Two-layered Model](https://mlsanity.com/paper/2209.13527/) (2022)
- [Molecular Design Based on Integer Programming and Splitting Data Sets by Hyperplanes](https://mlsanity.com/paper/2305.00801/) (2023)
- [Combining Graph Neural Networks and Mixed Integer Linear Programming for Molecular Inference under the Two-Layered Model](https://mlsanity.com/paper/2507.03920/) (2025)
- [Cycle-Configuration: A Novel Graph-theoretic Descriptor Set for Molecular Inference](https://mlsanity.com/paper/2408.05136/) (2024)
- [A Unified Approach to Inferring Chemical Compounds with the Desired Aqueous Solubility](https://mlsanity.com/paper/2409.04301/) (2024)
- [Mixing Vector Model for Copolymer Inference via Mixed Integer Linear Programming](https://mlsanity.com/paper/2605.29329/) (2026)

## Abstract (arXiv)

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 psi 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 psi(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.