Adapted Branch-and-Bound Algorithm Using SVM With Model Selection

Branch-and-Bound algorithm is the basis for the majority of solving methods in mixed integer linear programming. It has been proving its efficiency in different fields. In fact, it creates little by little a tree of nodes by adopting two strategies. These strategies are variable selection strategy and node selection strategy. In our previous work, we experienced a methodology of learning branch-and-bound strategies using regression-based support vector machine twice. That methodology allowed firstly to exploit information from previous executions of Branch-and-Bound algorithm on other instances. Secondly, it created information channel between node selection strategy and variable branching strategy. And thirdly, it gave good results in term of running time comparing to standard Branch-and-Bound algorithm. In this work, we will focus on increasing SVM performance by using cross validation coupled with model selection.

Exact Combinatorial Optimization with Graph Convolutional Neural Networks

Combinatorial optimization problems are typically tackled by the branch-and-bound paradigm. We propose a new graph convolutional neural network model for learning branch-and-bound variable selection policies, which leverages the natural variable-constraint bipartite graph representation of mixed-integer linear programs. We train our model via imitation learning from the strong branching expert rule, and demonstrate on a series of hard problems that our approach produces policies that improve upon state-of-the-art machine-learning methods for branching and generalize to instances significantly larger than seen during training. Moreover, we improve for the first time over expert-designed branching rules implemented in a state-of-the-art solver on large problems. Code for reproducing all the experiments can be found at https://github.com/ds4dm/learn2branch.Comment: Accepted paper at the NeurIPS 2019 conferenc