ARS: Automatic Routing Solver with Large Language Models

TL;DR

This paper introduces ARS, an LLM-based automatic routing solver that generates constraint-aware heuristics, significantly improving the efficiency and effectiveness of solving complex real-world vehicle routing problems.

Contribution

The paper presents RoutBench, a comprehensive VRP benchmark, and ARS, an LLM-powered solver that automatically creates heuristics for complex VRPs, addressing a wide range of real-world constraints.

Findings

ARS solves 91.67% of VRPs in benchmarks

ARS outperforms existing LLM-based methods and traditional solvers

Achieves at least 30% improvement across benchmarks

Abstract

Real-world Vehicle Routing Problems (VRPs) are characterized by a variety of practical constraints, making manual solver design both knowledge-intensive and time-consuming. Although there is increasing interest in automating the design of routing algorithms, existing research has explored only a limited array of VRP variants and fails to adequately address the complex and prevalent constraints encountered in real-world situations. To fill this gap, this paper introduces RoutBench, a benchmark of 1,000 VRP variants derived from 24 attributes, for evaluating the effectiveness of automatic routing solvers in addressing complex constraints. Along with RoutBench, we present the Automatic Routing Solver (ARS), which employs Large Language Model (LLM) agents to enhance a backbone algorithm framework by automatically generating constraint-aware heuristic code, based on problem descriptions and several representative constraints selected from a database. Our experiments show that ARS outperforms state-of-the-art LLM-based methods and commonly used solvers, automatically solving 91.67% of common VRPs and achieving at least a 30% improvement across all benchmarks.