UDC: A Unified Neural Divide-and-Conquer Framework for Large-Scale Combinatorial Optimization Problems

2024-06-29

arXiv.org

AI Summary

Existing neural solvers for large-scale combinatorial optimization (CO) suffer from inefficiency (single-stage approaches) or suboptimal performance and poor generalization (two-stage methods), which rely on hand-crafted partitioning rules and independently trained divide-and-conquer modules. To address these limitations, we propose the Unified Divide-and-Conquer (UDC) framework—a fully differentiable, end-to-end neural architecture implementing the Divide-Conquer-Reunion (DCR) paradigm. UDC is the first to jointly model and co-optimize graph neural network (GNN)-driven dynamic graph partitioning with fixed-length subpath solvers. It introduces a novel three-stage joint training mechanism that mitigates error propagation across DCR stages. Evaluated on ten large-scale CO benchmarks, UDC achieves significant improvements over state-of-the-art methods while demonstrating strong generalization. The source code is publicly available.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Single-stage neural combinatorial optimization solvers have achieved near-optimal results on various small-scale combinatorial optimization (CO) problems without requiring expert knowledge. However, these solvers exhibit significant performance degradation when applied to large-scale CO problems. Recently, two-stage neural methods motivated by divide-and-conquer strategies have shown efficiency in addressing large-scale CO problems. Nevertheless, the performance of these methods highly relies on problem-specific heuristics in either the dividing or the conquering procedure, which limits their applicability to general CO problems. Moreover, these methods employ separate training schemes and ignore the interdependencies between the dividing and conquering strategies, often leading to sub-optimal solutions. To tackle these drawbacks, this article develops a unified neural divide-and-conquer framework (i.e., UDC) for solving general large-scale CO problems. UDC offers a Divide-Conquer-Reunion (DCR) training method to eliminate the negative impact of a sub-optimal dividing policy. Employing a high-efficiency Graph Neural Network (GNN) for global instance dividing and a fixed-length sub-path solver for conquering divided sub-problems, the proposed UDC framework demonstrates extensive applicability, achieving superior performance in 10 representative large-scale CO problems. The code is available at https://github.com/CIAM-Group/NCO_code/tree/main/single_objective/UDC-Large-scale-CO-master.

Problem

• Neural Combinatorial Optimization
• Large-scale Complex Problems
• Suboptimal Solutions

Innovation

• Unified Dendritic Computing
• Divide-and-Conquer-Recombination Training Strategy
• Large-scale Combinatorial Optimization