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An Efficient Learning-based Solver Comparable to Metaheuristics for the Capacitated Arc Routing Problem

Runze Guo, Feng Xue, Anlong Ming, Nicu Sebe

TL;DR

This paper proposes the direction-aware attention model (DaAM) to incorporate directionality into the embedding process, facilitating more effective one-stage decision-making and designs a supervised reinforcement learning scheme that involves supervised pre-training to establish a robust initial policy for subsequent reinforcement fine-tuning.

Abstract

Recently, neural networks (NN) have made great strides in combinatorial optimization. However, they face challenges when solving the capacitated arc routing problem (CARP) which is to find the minimum-cost tour covering all required edges on a graph, while within capacity constraints. In tackling CARP, NN-based approaches tend to lag behind advanced metaheuristics, since they lack directed arc modeling and efficient learning methods tailored for complex CARP. In this paper, we introduce an NN-based solver to significantly narrow the gap with advanced metaheuristics while exhibiting superior efficiency. First, we propose the direction-aware attention model (DaAM) to incorporate directionality into the embedding process, facilitating more effective one-stage decision-making. Second, we design a supervised reinforcement learning scheme that involves supervised pre-training to establish a robust initial policy for subsequent reinforcement fine-tuning. It proves particularly valuable for solving CARP that has a higher complexity than the node routing problems (NRPs). Finally, a path optimization method is proposed to adjust the depot return positions within the path generated by DaAM. Experiments illustrate that our approach surpasses heuristics and achieves decision quality comparable to state-of-the-art metaheuristics for the first time while maintaining superior efficiency.

An Efficient Learning-based Solver Comparable to Metaheuristics for the Capacitated Arc Routing Problem

TL;DR

This paper proposes the direction-aware attention model (DaAM) to incorporate directionality into the embedding process, facilitating more effective one-stage decision-making and designs a supervised reinforcement learning scheme that involves supervised pre-training to establish a robust initial policy for subsequent reinforcement fine-tuning.

Abstract

Recently, neural networks (NN) have made great strides in combinatorial optimization. However, they face challenges when solving the capacitated arc routing problem (CARP) which is to find the minimum-cost tour covering all required edges on a graph, while within capacity constraints. In tackling CARP, NN-based approaches tend to lag behind advanced metaheuristics, since they lack directed arc modeling and efficient learning methods tailored for complex CARP. In this paper, we introduce an NN-based solver to significantly narrow the gap with advanced metaheuristics while exhibiting superior efficiency. First, we propose the direction-aware attention model (DaAM) to incorporate directionality into the embedding process, facilitating more effective one-stage decision-making. Second, we design a supervised reinforcement learning scheme that involves supervised pre-training to establish a robust initial policy for subsequent reinforcement fine-tuning. It proves particularly valuable for solving CARP that has a higher complexity than the node routing problems (NRPs). Finally, a path optimization method is proposed to adjust the depot return positions within the path generated by DaAM. Experiments illustrate that our approach surpasses heuristics and achieves decision quality comparable to state-of-the-art metaheuristics for the first time while maintaining superior efficiency.
Paper Structure (25 sections, 10 equations, 4 figures, 4 tables, 1 algorithm)

This paper contains 25 sections, 10 equations, 4 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Graph Embedding Learning
  4. Learning for Routing Problems
  5. Background
  6. Method
  7. Direction-aware Attention Model
  8. Arc Feature Formulation via Graph Transformation
  9. Arc Relation Encoding via Graph Attention Network
  10. Arc Selection via Attention Model
  11. Supervised Reinforcement Learning for CARP
  12. Supervised Pre-training via Multi-class Classification
  13. Reinforcement Fine-tuning via PPO with self-critical
  14. Path Optimization via Dynamic Programming
  15. Experiments
  16. ...and 10 more sections

Figures (4)

  • Figure 1: Pipeline of our DaAM consists of two parts. The first part transforms the input graph $\mathbf{G}$ by treating the arcs on $\mathbf{G}$ as nodes of a new directed graph $G$, which only executes once in the entire pipeline. The second part leverages the GAT and AM to update arc embeddings and select arcs, which executes at each time step.
  • Figure 2: Comparison of run time. For each dataset, the mean time of each method on 100 CARP instances is shown.
  • Figure 3: Convergence trends of different embedding learning methods in reinforcement learning training.
  • Figure 4: Qualitative comparison in four real street scenes. The paths are marked in different colors, with gray indicating roads that do not require service and red points indicating depots.