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GLOP: Learning Global Partition and Local Construction for Solving Large-scale Routing Problems in Real-time (2312.08224v2)

Published 13 Dec 2023 in cs.AI and cs.LG

Abstract: The recent end-to-end neural solvers have shown promise for small-scale routing problems but suffered from limited real-time scaling-up performance. This paper proposes GLOP (Global and Local Optimization Policies), a unified hierarchical framework that efficiently scales toward large-scale routing problems. GLOP partitions large routing problems into Travelling Salesman Problems (TSPs) and TSPs into Shortest Hamiltonian Path Problems. For the first time, we hybridize non-autoregressive neural heuristics for coarse-grained problem partitions and autoregressive neural heuristics for fine-grained route constructions, leveraging the scalability of the former and the meticulousness of the latter. Experimental results show that GLOP achieves competitive and state-of-the-art real-time performance on large-scale routing problems, including TSP, ATSP, CVRP, and PCTSP.

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Citations (20)
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Summary

  • The paper presents a hybrid framework that combines global partitioning with autoregressive local construction to efficiently address large-scale routing problems.
  • It achieves state-of-the-art real-time performance, notably solving a 100k-node TSP instance with a competitive optimality gap of 5.1%.
  • GLOP maintains consistent performance across varied distributions, offering promising practical applications in logistics, transportation, and robotics.

Overview: GLOP - A Framework for Large-Scale Routing Problem Solutions

The paper presents GLOP, a hierarchical framework aimed at efficiently addressing large-scale routing problems in real-time. Traditional methods such as mathematical programming or iterative heuristics often fail to meet the demands of such problems in modern logistics, transportation, and robotic systems, which require rapid dispatch and handling of multiple nodes. Neural Combinatorial Optimization (NCO) approaches have shown promise for tackling routing problems, but they struggle with scaling to instances comprising thousands or tens of thousands of nodes.

GLOP Framework

GLOP is designed to operate under both global partition and local construction paradigms. Here's how the framework is structured:

  • Global Partition: GLOP initially divides larger routing problems into smaller subproblems. These are often particular instances of the Travelling Salesman Problem (TSP) or even Shortest Hamiltonian Path Problems (SHPP).
  • Local Construction: GLOP harnesses the meticulousness of autoregressive (AR) neural heuristics to refine routes at finer granularities by solving SHPP instances.

This hybridization of non-autoregressive (NAR) and AR approaches allows GLOP to leverage the strengths of both paradigms in terms of scalability and solution precision.

Results and Comparisons

The paper provides extensive experimental evaluations demonstrating GLOP's efficacy:

  1. Performance: GLOP achieves state-of-the-art real-time results for TSP and its variants, including Asymmetric TSP (ATSP), Capacitated Vehicle Routing Problem (CVRP), and Prize Collecting TSP (PCTSP). It surpasses the previous methods with significant speedups in computation time, while maintaining competitive solution quality.
  2. Scaling: GLOP is capable of solving larger instances than traditional solvers. Notably, it solves a TSP instance with 100k nodes, performing significantly faster than LKH-3 with a reasonable optimality gap of 5.1%.
  3. Cross-Distribution Performance: Unlike many existing methods, GLOP maintains consistent performance across varying scales and distributions, using the same set of learned policies without the need for scale-specific or distribution-specific tuning.

Implications and Future Directions

The implications of this research are twofold:

  • Practical Implications: GLOP can be readily applied to modern logistics systems needing real-time solutions for large routing problems. It provides a potential pathway for integrating neural solvers into industry practices, where scalability and efficiency are crucial.
  • Theoretical Implications: From a theoretical standpoint, GLOP presents a successful hybridization of AR and NAR approaches, paving the way for future research on hybrid methods in combinatorial optimization.

Future developments may focus on incorporating dynamic graph clustering techniques or more nuanced node classification tasks to enhance hierarchical routing problem solutions. Investigating the unified perspectives of AR and NAR probabilistic construction graphs could yield further efficiencies and broaden applicability.

In conclusion, GLOP stands as a robust framework that enhances the capability of neural solvers in solving large-scale routing problems. Its scalability, speed, and cross-distribution consistency mark significant progress in the field of combinatorial optimization, with promising avenues for further research and practical application.

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