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Clustering Heuristics for Robust Energy Capacitated Vehicle Routing Problem (ECVRP)

Mark Pustilnik, Francesco Borrelli

TL;DR

This work tackles Robust Energy Capacitated Vehicle Routing for electric fleets under stochastic edge times and energy consumption. It derives an exact Mixed Integer Program for RECVRP and introduces a simple clustering-based heuristic that partitions customers into groups, turning the problem into multiple smaller robust energy TSP (RECTSP) instances. The approach delivers high-quality tours quickly, achieving substantial speedups on large-scale problems while maintaining close alignment with benchmark solutions. The authors validate the method on standard EVRP benchmarks and random problem sets and provide public code to enable replication and reuse.

Abstract

The paper presents an approach to solving the Robust Energy Capacitated Vehicle Routing Problem (RECVRP), focusing on electric vehicles and their limited battery capacity. A finite number of customers, each with their own demand, have to be serviced by an electric vehicle fleet while ensuring that none of the vehicles run out of energy. The time and energy it takes to travel between any two points is modeled as a random variable with known distribution. We propose a Mixed Integer Program (MIP) for computing an exact solution and introduce clustering heuristics to enhance the solution speed. This enables efficient re-planning of routes in dynamic scenarios. The methodology transforms the RECVRP into smaller problems, yielding good quality solutions quickly compared to existing methods. We demonstrate the effectiveness of this approach using a well-known benchmark problem set as well as a set of randomly generated problems.

Clustering Heuristics for Robust Energy Capacitated Vehicle Routing Problem (ECVRP)

TL;DR

This work tackles Robust Energy Capacitated Vehicle Routing for electric fleets under stochastic edge times and energy consumption. It derives an exact Mixed Integer Program for RECVRP and introduces a simple clustering-based heuristic that partitions customers into groups, turning the problem into multiple smaller robust energy TSP (RECTSP) instances. The approach delivers high-quality tours quickly, achieving substantial speedups on large-scale problems while maintaining close alignment with benchmark solutions. The authors validate the method on standard EVRP benchmarks and random problem sets and provide public code to enable replication and reuse.

Abstract

The paper presents an approach to solving the Robust Energy Capacitated Vehicle Routing Problem (RECVRP), focusing on electric vehicles and their limited battery capacity. A finite number of customers, each with their own demand, have to be serviced by an electric vehicle fleet while ensuring that none of the vehicles run out of energy. The time and energy it takes to travel between any two points is modeled as a random variable with known distribution. We propose a Mixed Integer Program (MIP) for computing an exact solution and introduce clustering heuristics to enhance the solution speed. This enables efficient re-planning of routes in dynamic scenarios. The methodology transforms the RECVRP into smaller problems, yielding good quality solutions quickly compared to existing methods. We demonstrate the effectiveness of this approach using a well-known benchmark problem set as well as a set of randomly generated problems.
Paper Structure (12 sections, 20 equations, 1 figure, 3 tables, 3 algorithms)

This paper contains 12 sections, 20 equations, 1 figure, 3 tables, 3 algorithms.

Table of Contents

  1. ABSTRACT
  2. Introduction
  3. Problem Statement
  4. Mixed Integer Program Formulation of Robust ECVRP
  5. Clustering Heuristics
  6. Solving The Robust ECTSP
  7. Results
  8. Tuning of the cost function of the clustering algorithm
  9. Results For Set 1
  10. Results For Set 2
  11. Conclusions
  12. Data Availability Statement

Figures (1)

  • Figure 1: Tour Example