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An Overview and Experimental Study of Learning-based Optimization Algorithms for Vehicle Routing Problem

arXiv 2107.07076 ↗First posted 15 Jul 2021cs.LGcited by 22

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Abstract (arXiv)

Vehicle routing problem (VRP) is a typical discrete combinatorial optimization problem, and many models and algorithms have been proposed to solve the VRP and its variants. Although existing approaches have contributed a lot to the development of this field, these approaches either are limited in problem size or need manual intervening in choosing parameters. To solve these difficulties, many studies have considered the learning-based optimization (LBO) algorithms to solve the VRP. This paper reviews recent advances in this field and divides relevant approaches into end-to-end approaches and step-by-step approaches. We performed a statistical analysis of the reviewed articles from various aspects and designed three experiments to evaluate the performance of four representative LBO algorithms. Finally, we conclude the applicable types of problems for different LBO algorithms and suggest directions in which researchers can improve LBO algorithms.

Key facts. Cited by 22 papers in the map (data through 7 Oct 2026). Builds on 56 of its 203 references that are in the map. First posted on arXiv 15 Jul 2021.

Builds on

56 of 203 references.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 2; 2023: 2; 2024: 5; 2025: 6; 2026: 7.

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  1. 2023Neural Combinatorial Optimization with Heavy Decoder: Toward Large Scale Generalizationcited by 140
  2. 2022Backpropagation through Combinatorial Algorithms: Identity with Projection Workscited by 29
  3. 2024Neural Combinatorial Optimization Algorithms for Solving Vehicle Routing Problems: A Comprehensive Survey with Perspectivescited by 23
  4. 2025Learning to Reduce Search Space for Generalizable Neural Routing Solvercited by 14
  5. 2024Instance-Conditioned Adaptation for Large-scale Generalization of Neural Routing Solvercited by 9
  6. 2022A Survey on Learnable Evolutionary Algorithms for Scalable Multiobjective Optimizationcited by 7
  7. 2025URS: A Unified Neural Routing Solver for Cross-Problem Zero-Shot Generalizationcited by 7
  8. 2024Prompt Learning for Generalized Vehicle Routingcited by 6
  9. 2025Learning for routing: A guided review of recent developments and future directionscited by 6
  10. 2023A Scalable Test Problem Generator for Sequential Transfer Optimizationcited by 5
  11. 2026Survey on Neural Routing Solverscited by 4
  12. 2024From Inverse Optimization to Feasibility to ERMcited by 3
10 more
  1. 2026Vision-Assisted Foundation Model for Solving Multi-Task Vehicle Routing Problemscited by 1
  2. 2024Multi-Agent Environments for Vehicle Routing Problemscited by 0
  3. 2025REMS: a unified solution representation, problem modeling and metaheuristic algorithm design for general combinatorial optimization problemscited by 0
  4. 2025Test-Time Search in Neural Graph Coarsening Procedures for the Capacitated Vehicle Routing Problemcited by 0
  5. 2025A Unified Deep Reinforcement Learning Approach for Close Enough Traveling Salesman Problemcited by 0
  6. 2026Hybrid Quantum Reinforcement Learning with QAOA for Improved Vehicle Routing Optimizationcited by 0
  7. 2026Teacher-Aware Evolution of Heuristic Programs from Learned Optimization Policiescited by 0
  8. 2026RACL: Reasoning-Agent Control Layers for Continuous Metaheuristic Learningcited by 0
  9. 2026Adaptive Cluster-First Route-Second Decomposition for Industrial-Scale Vehicle Routingcited by 0
  10. 2026Robust Feasible Route Construction through Collaborative Partition Optimizationcited by 0