Constraint Programming Approaches to the Discretizable Molecular Distance Geometry Problem

Integer Programming, Constraint Programming, and Hybrid Decomposition Approaches to Discretizable Distance Geometry Problems

Given an integer dimension K and a simple, undirected graph G with positive edge weights, the Distance Geometry Problem (DGP) aims to find a realization function mapping each vertex to a coordinate in K-dimensional space such that the distance between pairs of vertex coordinates is equal to the corresponding edge weights in G. The so-called discretization assumptions reduce the search space of the realization to a finite discrete one which can be explored via the branch-and-prune (BP) algorithm. Given a discretization vertex order in G, the BP algorithm constructs a binary tree where the nodes…

一种求解分子距离几何问题的组合-连续混合策略

A hybrid combinatorial-continuous strategy for solving molecular distance geometry problems

提出一种组合-连续混合框架求解区间分子距离几何问题，结合离散枚举与连续优化，在宽距离界限下高效重建有效蛋白质构象。

Molecular Design Based on Integer Programming and Quadratic Descriptors in a Two-layered Model

A novel framework has recently been proposed for designing the molecular structure of chemical compounds with a desired chemical property, where design of novel drugs is an important topic in bioinformatics and chemo-informatics. The framework infers a desired chemical graph by solving a mixed integer linear program (MILP) that simulates the computation process of a feature function defined by a two-layered model on chemical graphs and a prediction function constructed by a machine learning method. A set of graph theoretical descriptors in the feature function plays a key role to derive a comp…

面向计算机辅助分子设计的图神经网络混合整数优化

Mixed-Integer Optimisation of Graph Neural Networks for Computer-Aided Molecular Design

本文针对计算机辅助分子设计，提出将ReLU图卷积网络和GraphSAGE模型形式化为混合整数线性规划，实现嵌入已训练GNN的全局最优优化，并通过分子沸点设计案例验证其有效性。

BoGrape: 图上贝叶斯优化的最短路径编码

BoGrape: Bayesian optimization over graphs with shortest-path encoded

本文提出BoGrape，通过最短路径图核和混合整数规划方法，系统地将结构约束纳入贝叶斯优化，实现对未见图结构和节点属性的全局探索。

Dynamic Bounds on Stochastic Chemical Kinetic Systems Using Semidefinite Programming

Applying the method of moments to the chemical master equation (CME) appearing in stochastic chemical kinetics often leads to the so-called closure problem. Recently, several authors showed that this problem can be partially overcome using moment-based semidefinite programs (SDPs). In particular, they showed that moment-based SDPs can be used to calculate rigorous bounds on various descriptions of the stochastic chemical kinetic system's stationary distribution(s) -- for example, mean molecular counts, variances in these counts, and so on. In this paper, we show that these ideas can be extende…