Learning Branching Heuristics from Graph Neural Networks

TL;DR

This paper presents a novel approach using graph neural networks to learn effective branching heuristics that improve backtracking search efficiency in combinatorial optimization problems.

Contribution

It introduces a GNN-based method to learn probabilistic branching heuristics directly from graph data, enhancing classical backtracking algorithms.

Findings

Learned heuristics outperform traditional methods in the dominating-clique problem

GNN model effectively captures graph structure for heuristic learning

Approach demonstrates improved search efficiency in experiments

Abstract

Backtracking has been widely used for solving problems in artificial intelligence (AI), including constraint satisfaction problems and combinatorial optimization problems. Good branching heuristics can efficiently improve the performance of backtracking by helping prune the search space and leading the search to the most promising direction. In this paper, we first propose a new graph neural network (GNN) model designed using the probabilistic method. From the GNN model, we introduce an approach to learn a branching heuristic for combinatorial optimization problems. In particular, our GNN model learns appropriate probability distributions on vertices in given graphs from which the branching heuristic is extracted and used in a backtracking search. Our experimental results for the (minimum) dominating-clique problem show that this learned branching heuristic performs better than the minimum-remaining-values heuristic in terms of the number of branches of the whole search tree. Our approach introduces a new way of applying GNNs towards enhancing the classical backtracking algorithm used in AI.