Exact Combinatorial Optimization with Graph Convolutional Neural Networks

Combinatorial optimization problems are typically tackled by the branch-and-bound paradigm. We propose to learn a variable selection policy for branch-and-bound in mixed-integer linear programming, by imitation learning on a diversified variant of the strong branching expert rule. We encode states as bipartite graphs and parameterize the policy as a graph convolutional neural network. Experiments on a series of synthetic problems demonstrate that our approach produces policies that can improve upon expert-designed branching rules on large problems, and generalize to instances significantly larger than seen during training

Learning Models for Discrete Optimization

We consider a class of optimization approaches that incorporate machine learning models into the algorithm structure. Our focus is on the algorithms that can learn the patterns in the search space in order to boost computational performance. The idea is to design optimization techniques that allow for computationally efficient tuning a priori. The final objective of this work is to provide efficient solvers that can be tuned for optimal performance in serial and parallel environments.This dissertation provides a novel machine learning model based on logistic regression and describes an implementation for scheduling problems. We incorporate the proposed learning model into a well-known optimization algorithm, tabu search, and demonstrate the potential of the underlying ideas. The dissertation also establishes a new framework for comparing optimization algorithms. This framework provides a comparison of algorithms that is statistically meaningful and intuitive. Using this framework, we demonstrate that the inclusion of the logistic regression model into the tabu search method provides significant boost of its performance. Finally, we study the parallel implementation of the algorithm and evaluate the algorithm performance when more connections between threads exist