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Enhancing CVRP Solver through LLM-driven Automatic Heuristic Design

Zhuoliang Xie, Fei Liu, Zhenkun Wang, Qingfu Zhang

TL;DR

This study presents AILS-AHD (Adaptive Iterated Local Search with Automatic Heuristic Design), a novel approach that leverages Large Language Models (LLMs) to revolutionize CVRP solving and establishes new best-known solutions for 8 out of 10 instances in the CVRPLib large-scale benchmark.

Abstract

The Capacitated Vehicle Routing Problem (CVRP), a fundamental combinatorial optimization challenge, focuses on optimizing fleet operations under vehicle capacity constraints. While extensively studied in operational research, the NP-hard nature of CVRP continues to pose significant computational challenges, particularly for large-scale instances. This study presents AILS-AHD (Adaptive Iterated Local Search with Automatic Heuristic Design), a novel approach that leverages Large Language Models (LLMs) to revolutionize CVRP solving. Our methodology integrates an evolutionary search framework with LLMs to dynamically generate and optimize ruin heuristics within the AILS method. Additionally, we introduce an LLM-based acceleration mechanism to enhance computational efficiency. Comprehensive experimental evaluations against state-of-the-art solvers, including AILS-II and HGS, demonstrate the superior performance of AILS-AHD across both moderate and large-scale instances. Notably, our approach establishes new best-known solutions for 8 out of 10 instances in the CVRPLib large-scale benchmark, underscoring the potential of LLM-driven heuristic design in advancing the field of vehicle routing optimization.

Enhancing CVRP Solver through LLM-driven Automatic Heuristic Design

TL;DR

This study presents AILS-AHD (Adaptive Iterated Local Search with Automatic Heuristic Design), a novel approach that leverages Large Language Models (LLMs) to revolutionize CVRP solving and establishes new best-known solutions for 8 out of 10 instances in the CVRPLib large-scale benchmark.

Abstract

The Capacitated Vehicle Routing Problem (CVRP), a fundamental combinatorial optimization challenge, focuses on optimizing fleet operations under vehicle capacity constraints. While extensively studied in operational research, the NP-hard nature of CVRP continues to pose significant computational challenges, particularly for large-scale instances. This study presents AILS-AHD (Adaptive Iterated Local Search with Automatic Heuristic Design), a novel approach that leverages Large Language Models (LLMs) to revolutionize CVRP solving. Our methodology integrates an evolutionary search framework with LLMs to dynamically generate and optimize ruin heuristics within the AILS method. Additionally, we introduce an LLM-based acceleration mechanism to enhance computational efficiency. Comprehensive experimental evaluations against state-of-the-art solvers, including AILS-II and HGS, demonstrate the superior performance of AILS-AHD across both moderate and large-scale instances. Notably, our approach establishes new best-known solutions for 8 out of 10 instances in the CVRPLib large-scale benchmark, underscoring the potential of LLM-driven heuristic design in advancing the field of vehicle routing optimization.
Paper Structure (49 sections, 7 equations, 17 figures, 7 tables)

This paper contains 49 sections, 7 equations, 17 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Problem Description
  3. AILS-AHD
  4. AILS
  5. Initialization
  6. Iterated Local Search
  7. Updating
  8. LLM-driven AHD
  9. Prompt Construction
  10. Heuristic Generation
  11. Evaluation
  12. Population Update
  13. Feature Construction for Heuristic Design
  14. Acceleration Manicheism
  15. Experiment
  16. ...and 34 more sections

Figures (17)

  • Figure 1: The AILS-AHD pipeline: (1) LLM-driven evolutionary computation generates ruin heuristics; (2) each candidate heuristic is evaluated via AILS, including initialization, iterated local search and updating; (3) the population is updated based on fitness of the heuristic.
  • Figure 2: Convergence curve of LLM designed heuristics.
  • Figure 3: Convergence curve on moderate-scale CVRP instances.
  • Figure 4: Result on large-scale CVRP instances.
  • Figure 5: Convergence curve and new best-known solution found for Antwerp1.
  • ...and 12 more figures