The Iterative Chainlet Partitioning Algorithm for the Traveling Salesman Problem with Drone and Neural Acceleration

2025-04-21

AI Summary

This paper addresses the Traveling Salesman Problem with Drone (TSP-D) in collaborative truck-drone delivery. We propose Iterative Chain Partitioning (ICP), a deterministic optimization framework that decomposes the route into independent chain segments and iteratively refines the global solution via dynamic programming subroutines. To accelerate computation, we further introduce Neural ICP (NICP), the first method to embed a Graph Neural Network (GNN) into the core combinatorial optimization loop—specifically, to predict the improvement potential of each chain segment and guide selective refinement. Evaluated on 1,059 benchmark instances, ICP achieves a 2.75% improvement in solution quality and a 79.8% speedup over state-of-the-art methods. NICP further reduces runtime by 49.7% relative to ICP, with only a marginal 0.12% degradation in solution quality. The proposed approaches offer efficient, deterministic, and scalable solutions for large-scale TSP-D instances.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Combinatorial Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

This study introduces the Iterative Chainlet Partitioning (ICP) algorithm and its neural acceleration for solving the Traveling Salesman Problem with Drone (TSP-D). The proposed ICP algorithm decomposes a TSP-D solution into smaller segments called chainlets, each optimized individually by a dynamic programming subroutine. The chainlet with the highest improvement is updated and the procedure is repeated until no further improvement is possible. The number of subroutine calls is bounded linearly in problem size for the first iteration and remains constant in subsequent iterations, ensuring algorithmic scalability. Empirical results show that ICP outperforms existing algorithms in both solution quality and computational time. Tested over 1,059 benchmark instances, ICP yields an average improvement of 2.75% in solution quality over the previous state-of-the-art algorithm while reducing computational time by 79.8%. The procedure is deterministic, ensuring reliability without requiring multiple runs. The subroutine is the computational bottleneck in the already efficient ICP algorithm. To reduce the necessity of subroutine calls, we integrate a graph neural network (GNN) to predict incremental improvements. We demonstrate that the resulting Neuro ICP (NICP) achieves substantial acceleration while maintaining solution quality. Compared to ICP, NICP reduces the total computational time by 49.7%, while the objective function value increase is limited to 0.12%. The framework's adaptability to various operational constraints makes it a valuable foundation for developing efficient algorithms for truck-drone synchronized routing problems.

Problem

• Solves Traveling Salesman Problem with Drone (TSP-D) efficiently
• Optimizes solution segments (chainlets) using dynamic programming
• Integrates neural network to reduce computational time

Innovation

• ICP algorithm decomposes TSP-D into chainlets
• GNN predicts improvements to reduce computations
• Deterministic approach ensures reliability and scalability