[論文レビュー] Searching Large Neighborhoods for Integer Linear Programs with Contrastive Learning

Taoan Huang, Aaron Ferber+3 more|arXiv (Cornell University)|Feb 3, 2023

Vehicle Routing Optimization Methods被引用数 9

ひとこと要約

tldr: CL-LNS uses contrastive learning to train a destroy heuristic for Large Neighborhood Search in ILPs, achieving state-of-the-art anytime performance across multiple benchmarks and generalizing to larger instances.

ABSTRACT

Integer Linear Programs (ILPs) are powerful tools for modeling and solving a large number of combinatorial optimization problems. Recently, it has been shown that Large Neighborhood Search (LNS), as a heuristic algorithm, can find high quality solutions to ILPs faster than Branch and Bound. However, how to find the right heuristics to maximize the performance of LNS remains an open problem. In this paper, we propose a novel approach, CL-LNS, that delivers state-of-the-art anytime performance on several ILP benchmarks measured by metrics including the primal gap, the primal integral, survival rates and the best performing rate. Specifically, CL-LNS collects positive and negative solution samples from an expert heuristic that is slow to compute and learns a new one with a contrastive loss. We use graph attention networks and a richer set of features to further improve its performance.

研究の動機と目的

• Motivate improved ILP solving via learning-based destroy heuristics within Large Neighborhood Search (LNS).
• Develop a contrastive-learning framework to imitate an expert LB heuristic while leveraging positive/negative samples for better discrimination.
• Enhance feature richness with graph attention networks to boost destroy-subset selection quality.
• Demonstrate strong generalization to larger, unseen instances and favorable anytime performance across benchmarks.

提案手法

• Formulate LNS for binary ILPs with a destroy subset 〜 to reoptimize.
• Use Local Branching (LB) as the expert to generate positive/negative samples by solving LB ILPs.
• Train a policy network (Graph Attention Network) on a bipartite ILP graph with a contrastive (InfoNCE) loss to distinguish good vs. bad destroy subsets.
• Represent ILP state via a bipartite graph of variables and constraints with rich node/edge features and windowed incumbent values.
• Apply the trained policy greedily (or via sampling when needed) to select the destroy set 〜 in each LNS iteration, and solve the corresponding sub-ILP with SCIP.
• Evaluate performance on MVC, MIS, CA, SC benchmarks, comparing primal gap, primal integral, survival rate, and best-performing rate against baselines.

実験結果

リサーチクエスチョン

• RQ1 Does CL-LNS with contrastive learning outperform existing ML-guided and non-ML LNS baselines for ILPs across multiple problem types?
• RQ2 Can the approach generalize from small training instances to larger, unseen instances while maintaining strong anytime performance?
• RQ3 What is the impact of using a richer feature set and Graph Attention Networks (GAT) versus prior GCN-based setups?
• RQ4 How does the learned policy compare to the expert LB in terms of per-iteration efficiency and eventual solution quality?

主な発見

• CL-LNS achieves state-of-the-art anytime performance across several ILP benchmarks, measured by primal gap, primal integral, survival rate, and best-performing rate.
• CL-LNS attains strong generalization, performing well on test instances up to twice as large as those seen during training.
• In ablations, the combination of contrastive loss, richer features, and GAT yields the best performance, surpassing IL-LNS and other baselines in several settings.
• Greedy action selection by the learned policy often matches or surpasses LB-derived policies in efficiency and solution quality across small test instances.