A Bi-Level Framework for Learning to Solve Combinatorial Optimization on Graphs

Abstract

Combinatorial Optimization (CO) has been a long-standing challenging research topic featured by its NP-hard nature. Traditionally such problems are approximately solved with heuristic algorithms which are usually fast but may sacrifice the solution quality. Currently, machine learning for combinatorial optimization (MLCO) has become a trending research topic, but most existing MLCO methods treat CO as a single-level optimization by directly learning the end-to-end solutions, which are hard to scale up and mostly limited by the capacity of ML models given the high complexity of CO. In this paper, we propose a hybrid approach to combine the best of the two worlds, in which a bi-level framework is developed with an upper-level learning method to optimize the graph (e.g. add, delete or modify edges in a graph), fused with a lower-level heuristic algorithm solving on the optimized graph. Such a bi-level approach simplifies the learning on the original hard CO and can effectively mitigate the demand for model capacity. The experiments and results on several popular CO problems like Directed Acyclic Graph scheduling, Graph Edit Distance and Hamiltonian Cycle Problem show its effectiveness over manually designed heuristics and single-level learning methods.

arXiv commentNeurIPS 2021. Code at https://github.com/Thinklab-SJTU/PPO-BiHyb

References in corpus (12)

• Semi-Supervised Classification with Graph Convolutional Networks
• Playing Atari with Deep Reinforcement Learning
• Trust Region Policy Optimization
• Fast Graph Representation Learning with PyTorch Geometric
• Learning Combinatorial Optimization Algorithms over Graphs
• Discriminative Embeddings of Latent Variable Models for Structured Data
• Graph Matching Networks for Learning the Similarity of Graph Structured Objects
• An Efficient Graph Convolutional Network Technique for the Travelling Salesman Problem
• Attention, Learn to Solve Routing Problems!
• TAP-Net: Transport-and-Pack using Reinforcement Learning
• A Multi-task Selected Learning Approach for Solving 3D Flexible Bin Packing Problem
• A Survey on Reinforcement Learning for Combinatorial Optimization

Cited by in corpus (2)

• A hybrid deep-learning-metaheuristic framework for bi-level network design problems
• Learning to Solve Combinatorial Optimization under Positive Linear Constraints via Non-Autoregressive Neural Networks