Tackling the rich vehicle routing problem with nature-inspired algorithms

Veronika Lesch,Anthony Stein,Samuel Kounev,Christian Krupitzer,Maximilian König

doi:10.1007/s10489-021-03035-5

Veronika Lesch, Anthony Stein + Show 3 more

Open Access

https://doi.org/10.1007/s10489-021-03035-5

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Abstract

In the last decades, the classical Vehicle Routing Problem (VRP), i.e., assigning a set of orders to vehicles and planning their routes has been intensively researched. As only the assignment of order to vehicles and their routes is already an NP-complete problem, the application of these algorithms in practice often fails to take into account the constraints and restrictions that apply in real-world applications, the so called rich VRP (rVRP) and are limited to single aspects. In this work, we incorporate the main relevant real-world constraints and requirements. We propose a two-stage strategy and a Timeline algorithm for time windows and pause times, and apply a Genetic Algorithm (GA) and Ant Colony Optimization (ACO) individually to the problem to find optimal solutions. Our evaluation of eight different problem instances against four state-of-the-art algorithms shows that our approach handles all given constraints in a reasonable time.

Highlights

In the last two decades, the demand for road freight transport increased worldwide; for example, in Germany it increased by 150 billion ton kilometers to around 500 billion ton kilometers [1]
To sum up the evaluation results of all problem instances, we provide Table 4, which states whether time windows are met as well as mean and standard deviations of the tour length (S2 ) over 30 runs for probabilistic algorithms, that is, the Local Search, Genetic Algorithm (GA), and Ant Colony Optimization (ACO)
We focus on nature-inspired algorithms (ACO and GA) for tackling the rich VRP (rVRP) and compared them to a Brute-Force, two Blackbox algorithms implemented by our cooperation company, and local search

Summary

Introduction

In the last two decades, the demand for road freight transport increased worldwide; for example, in Germany it increased by 150 billion ton kilometers to around 500 billion ton kilometers [1]. Developments such as increased just-intime production and online shopping (especially during the Covid pandemic) will further increase those numbers in the years. The classical VRP specifies the assignment of customer orders to vehicles and the optimization of their tours [21], which refers to solving the underlying Traveling Salesman Problem (TSP). Tim Pigden stated that the original model of the VRP does not match real-world applications since it does not include concepts of order, separate resources corresponding to the driver, the tractor unit, and the trailer [31]

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