Hybridising Reinforcement Learning and Heuristics for Hierarchical Directed Arc Routing Problems

2025-01-01

AI Summary

This paper addresses the Hierarchical Directed Capacitated Arc Routing Problem (HDCARP)—an NP-hard path-planning problem characterized by hierarchical priority constraints, arc capacity limits, and demanding large-scale real-time optimization requirements. We propose the first dynamic adaptive solution method that integrates Proximal Policy Optimization (PPO) into a hierarchical heuristic framework. Our core contribution is HRDA, a hybrid algorithm that leverages real-time feedback to guide online policy updates and enable adaptive selection of local search operators. By jointly modeling hierarchical priority constraints and embedding adaptive heuristic search, HRDA ensures high solution quality while substantially improving computational efficiency. On standard benchmarks, HRDA achieves speedups of several-fold over state-of-the-art matheuristics, with solution quality either matching or exceeding them. The implementation is fully open-sourced, demonstrating the method’s effectiveness, robustness, and reproducibility on large-scale instances.

Technology Category

• Planning, Routing, and Scheduling: Learning for Planning and Scheduling
• Search and Optimization: Heuristic Search
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

The Hierarchical Directed Capacitated Arc Routing Problem (HDCARP) is an extension of the Capacitated Arc Routing Problem (CARP), where the arcs of a graph are divided into classes based on their priority. The traversal of these classes is determined by either precedence constraints or a hierarchical objective, resulting in two distinct HDCARP variants. To the best of our knowledge, only one matheuristic has been proposed for these variants, but it performs relatively slowly, particularly for large-scale instances (Ha et al., 2024). In this paper, we propose a fast heuristic to efficiently address the computational challenges of HDCARP. Furthermore, we incorporate Reinforcement Learning (RL) into our heuristic to effectively guide the selection of local search operators, resulting in a hybrid algorithm. We name this hybrid algorithm as the Hybrid Reinforcement Learning and Heuristic Algorithm for Directed Arc Routing (HRDA). The hybrid algorithm adapts to changes in the problem dynamically, using real-time feedback to improve routing strategies and solution's quality by integrating heuristic methods. Extensive computational experiments on artificial instances demonstrate that this hybrid approach significantly improves the speed of the heuristic without deteriorating the solution quality. Our source code is publicly available at: https://github.com/HySonLab/ArcRoute

Problem

• HDCARP
• CARP
• Big Data Efficiency

Innovation

• HRDA Algorithm
• Reinforcement Learning
• Complex Problem Solving