[Paper Review] Learn to Design the Heuristics for Vehicle Routing Problem

Lei Gao, Mingxiang Chen+4 more|arXiv (Cornell University)|Feb 20, 2020

Vehicle Routing Optimization Methods20 references41 citations

TL;DR

The paper presents a neural network that learns large-neighborhood search heuristics for VRP, outperforming handcrafted and neural baselines on medium-scale data and solving 400-node VRP effectively.

ABSTRACT

This paper presents an approach to learn the local-search heuristics that iteratively improves the solution of Vehicle Routing Problem (VRP). A local-search heuristics is composed of a destroy operator that destructs a candidate solution, and a following repair operator that rebuilds the destructed one into a new one. The proposed neural network, as trained through actor-critic framework, consists of an encoder in form of a modified version of Graph Attention Network where node embeddings and edge embeddings are integrated, and a GRU-based decoder rendering a pair of destroy and repair operators. Experiment results show that it outperforms both the traditional heuristics algorithms and the existing neural combinatorial optimization for VRP on medium-scale data set, and is able to tackle the large-scale data set (e.g., over 400 nodes) which is a considerable challenge in this area. Moreover, the need for expertise and handcrafted heuristics design is eliminated due to the fact that the proposed network learns to design the heuristics with a better performance. Our implementation is available online.

Motivation & Objective

• Automate the design of generic destroy/repair heuristics for VRP without supervised expert data.
• Integrate node and edge information in a graph-based encoder to handle non-Euclidean VRP instances.
• Demonstrate scalability to medium- and large-scale VRP (e.g., >400 nodes) with competitive performance.

Proposed method

• Use an encoder–decoder architecture where the encoder is an EGATE (Element-wise Graph Attention Network with Edge Embedding) that combines node and edge information.
• Represent the destroy/repair heuristics as a stochastic sequential policy π([η1,...,ηM]), trained via actor–critic reinforcement learning with PPO.
• Decode by a GRU-based Pointer Network to output an ordered list of removal nodes, guiding the insertion order.
• Train with an actor–critic setup where the reward equals the reduction in VRP cost (distance plus vehicle cost), using a value network to estimate state value.
• Apply a simulated-annealing-based acceptance criterion to update solutions, enabling SA-guided exploration during learning.

Experimental results

Research questions

• RQ1 Can a neural network learn generic, high-level destroy/repair heuristics for VRP instead of a single handcrafted heuristic?
• RQ2 Does integrating node and edge information via an EGATE encoder improve VRP performance over standard GAT-based encoders?
• RQ3 Can the learned heuristics scale to large VRP instances (e.g., 400 nodes) and outperform traditional heuristics and other neural methods?
• RQ4 How does the learned approach compare to handcrafted heuristics and existing neural methods under CVRP and CVRPTW settings?

Key findings

• The learned heuristics approach nearly matches the benchmark for CVRP with 1000 iterations, achieving a 0.58% gap.
• For CVRPTW, the method yields the best result among tested solvers with 1000 iterations, outperforming the SISR baseline even at 1 million iterations.
• The method outperforms handcrafted ALNS and SISR baselines on medium-scale CVRP/CVRPTW within the same iteration budget.
• The model demonstrates the ability to tackle VRP with 400 nodes, achieving competitive results and a 4.4% gap to the benchmark in that scale.
• The encoder–decoder design (EGATE + GRU-based Pointer Network) enables learning generic large-neighborhood search heuristics, reducing reliance on expert-crafted heuristics.