Abstract

The Vehicle Routing Problem with Time Windows (VRPTW) is an important logistics problem which in the real-world appears to be multi-objective. Most research in this area has been carried out using classic datasets designed for the single-objective case, like the well-known Solomon's problem instances. Some unrealistic assumptions are usually made when using these datasets in the multi-objective case (e.g. assuming that one unit of travel time corresponds to one unit of travel distance). Additionally, there is no common VRPTW multi-objective oriented framework to compare the performance of algorithms because different implementations in the literature tackle different sets of objectives. In this work, we investigate the conflicting (or not) nature of various objectives in the VRPTW and show that some of the classic test instances are not suitable for conducting a proper multi-objective study. The insights of this study have led us to generate some problem instances using data from a real-world distribution company. Experiments in these new dataset using a standard evolutionary algorithm (NSGA-II) show stronger evidence of multi-objective features. Our contribution focuses on achieving a better understanding about the multi-objective nature of the VRPTW, in particular the conflicting relationships between 5 objectives: number of vehicles, total travel distance, makespan, total waiting time, and total delay time.

Highlights

  • The Vehicle Routing Problem with Time Windows (VRPTW) consists of creating the set of routes to serve a number of customers with a fleet of vehicles that depart from a central depot

  • The VRPTW consists of creating the set of routes to serve a number of customers with a fleet of vehicles that depart from a central depot

  • We have chosen to minimise five objectives commonly used across different datasets in the literature: number of vehicles (Z1), total travel distance (Z2), makespan (Z3), total waiting time (Z4), and total delay time (Z5)

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Summary

INTRODUCTION

The VRPTW consists of creating the set of routes to serve a number of customers with a fleet of vehicles that depart from a central depot (with unlimited capacity). We conduct experiments to show that the Solomon’s problem instances are perhaps not entirely adequate to investigate the multi-objective VRPTW. This is because the correlation between different objectives is weak which means that there is little interaction (conflict and harmony) between objectives when searching for solutions. The analysis conducted in this paper to compare the multiobjective nature of Solomon’s and our dataset is based on the work by Purshouse and Fleming [10] They indicate that three main relationships may occur between pairs of objectives: conflict, harmony or independence.

BACKGROUND
Characterisation of Time Windows
Characterisation of Demands
Dataset Settings
EXPERIMENTAL DESIGN
Correlation Between Objectives
Solomon’s Dataset
Proposed MOVRPTW Dataset
CONCLUSIONS
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