Improving Primal Heuristics for Mixed Integer Programming Problems based on Problem Reduction: A Learning-based Approach

TL;DR

This paper introduces a learning-based bi-layer framework using graph convolutional networks to reduce problem size and improve primal heuristics in mixed integer programming, leading to faster solution times and higher-quality feasible solutions.

Contribution

The paper presents a novel bi-layer prediction-based reduction framework that integrates GCNs for problem reduction and variable prediction in MIP, enhancing primal heuristic efficiency.

Findings

Speeds up primal heuristic process.

Finds high-quality feasible solutions faster.

Reduces variable and constraint sizes significantly.

Abstract

In this paper, we propose a Bi-layer Predictionbased Reduction Branch (BP-RB) framework to speed up the process of finding a high-quality feasible solution for Mixed Integer Programming (MIP) problems. A graph convolutional network (GCN) is employed to predict binary variables' values. After that, a subset of binary variables is fixed to the predicted value by a greedy method conditioned on the predicted probabilities. By exploring the logical consequences, a learning-based problem reduction method is proposed, significantly reducing the variable and constraint sizes. With the reductive sub-MIP problem, the second layer GCN framework is employed to update the prediction for the remaining binary variables' values and to determine the selection of variables which are then used for branching to generate the Branch and Bound (B&B) tree. Numerical examples show that our BP-RB framework speeds up the primal heuristic and finds the feasible solution with high quality.