Learning to Solve Combinatorial Optimization under Positive Linear Constraints via Non-Autoregressive Neural Networks

Abstract

Combinatorial optimization (CO) is the fundamental problem at the intersection of computer science, applied mathematics, etc. The inherent hardness in CO problems brings up challenge for solving CO exactly, making deep-neural-network-based solvers a research frontier. In this paper, we design a family of non-autoregressive neural networks to solve CO problems under positive linear constraints with the following merits. First, the positive linear constraint covers a wide range of CO problems, indicating that our approach breaks the generality bottleneck of existing non-autoregressive networks. Second, compared to existing autoregressive neural network solvers, our non-autoregressive networks have the advantages of higher efficiency and preserving permutation invariance. Third, our offline unsupervised learning has lower demand on high-quality labels, getting rid of the demand of optimal labels in supervised learning. Fourth, our online differentiable search method significantly improves the generalizability of our neural network solver to unseen problems. We validate the effectiveness of this framework in solving representative CO problems including facility location, max-set covering, and traveling salesman problem. Our non-autoregressive neural solvers are competitive to and can be even superior to state-of-the-art solvers such as SCIP and Gurobi, especially when both efficiency and efficacy are considered. Code is available at https://github.com/Thinklab-SJTU/NAR-CO-Solver

English version of the same paper published on Scientia Sinica Informationis

References in corpus (14)

• Learning Combinatorial Optimization Algorithms over Graphs
• Exact Combinatorial Optimization with Graph Convolutional Neural Networks
• Learning to Dispatch for Job Shop Scheduling via Deep Reinforcement Learning
• Learning Latent Permutations with Gumbel-Sinkhorn Networks
• Deep Declarative Networks: A New Hope
• Solving Mixed Integer Programs Using Neural Networks
• A Multi-task Selected Learning Approach for Solving 3D Flexible Bin Packing Problem
• Stochastic Optimization of Sorting Networks via Continuous Relaxations
• Simulation-guided Beam Search for Neural Combinatorial Optimization
• A Bi-Level Framework for Learning to Solve Combinatorial Optimization on Graphs
• On Representing Linear Programs by Graph Neural Networks
• On Representing Mixed-Integer Linear Programs by Graph Neural Networks
• Revocable Deep Reinforcement Learning with Affinity Regularization for Outlier-Robust Graph Matching
• LinSATNet: The Positive Linear Satisfiability Neural Networks