Referring to difficulty as the time it takes to achieve optimal solutions, Solomon’s dataset does not seem to present a high-complexity in modern computation. On one hand, CPLEX 11.1 [139] finds optimal solutions for some Solomon’s instance in less than an hour. On the other hand, using state-of-the-art algorithms like MACS-VRPTW, optimal solutions are achieved in less than half an hour [104].
5.8
Conclusions
This chapter provides an analysis of the most important characteristics of the Solomon’s dataset. We have observed a number of unrealistic features regarding: 1) the position of customers and depot, 2) the travel distances, and 3) the travel times. The first assump- tion concerns the location of customers and depot. Customers are located in almost a perfect square in which the depot is always close to its centre. Assumptions two and three are related to the way travel distances and travel times are calculated. Solomon’s dataset does not provide a matrix for travel distances and travel times. Instead, the Euclidean distance measure is often used to calculate both using the customers’ posi- tions (geographical coordinates). This assumes that: 1) there is a way to go from one to another customer in straight line, and 2) travel distances and travel times between a pair of customers are equal regardless of the moving direction. These assumptions hardly occur in reality. Alternatives could be to: 1) create new instances with differ- ent geographic distributions of customers, and 2) create non-equal and non-symmetric travel distance and travel time matrices.
According to the characteristics observed in Solomon’s dataset and based on the study by Purshouse and Fleming [204], we think this dataset might not be suitable for the assessment of multi-objective algorithms. This hypothesis is based on 1) the lack of differences between travel distances and travel times from one to another customer, and 2) the assumption that travel distances and travel times between pairs of customers are symmetric.
The next chapter proposes a novel dataset for the assessment of Multi-Objective Ve- hicle Routing Problem with Time Windows (MOVRPTW). Unlike Solomon’s dataset, MOVRPTW has different travel distances and travel times, and they are non-symmetric. The next chapter analyses the characteristics of this dataset following a similar struc- ture to the one in this chapter.
A Dataset for the Multi-Objective
Vehicle Routing Problem with Time
Windows
Summary
This chapter introduces a new set of benchmark instances: MOVRPTW dataset. This project has two aims:
• It provides a public dataset for the assessment of multi-objective algorithms for the Vehicle Routing Problem with Time Windows (VRPTW).
• It presents a more challenging scenario in VRP(TW) benchmarks to motivate fur- ther improvement in the development of solving methods.
This dataset is based on real information provided by a distribution company. The structure of the test instances is similar to the one of Solomon’s but the MOVRPTW in- stances provide travel distance and travel time matrices. This chapter gives an overview of the main characteristics of the MOVRPTW dataset using the same organisation as the previous chapter.
6.1
Introduction
The previous chapter provides an overview of datasets proposed for the assessment of the Vehicle Routing Problem with Time Windows (VRPTW). In particular, we anal- ysed some important characteristics of the Solomon’s dataset. This dataset presents a number of unrealistic features due to:
• Travel distance and travel time matrices are not provided. The positions of the customers are used to calculate both. As a result, it is assumed that:
– There is a straight path that connects any pair of customers. – A unit of time is equal to a unit of distance.
– Travel distances and travel times are the same regardless of the moving di-
rection.
• Customers are place within the boundaries of a square, and the depot is very close to the centre.
This chapter presents a new set of problem instances which do not present the above- mentioned issues. This new dataset is based on data from a distribution company in Tenerife, Spain. The company delivers food products and serves more than 1000 cus- tomers overall, with around 150 customers being served each day. Realistic data for the travel distance and travel time between each pair of customers was obtained using Google Maps database. Travel distance and travel time matrices are distinct and non- symmetric, hence representing a realistic trade-off between travel distance and travel time. For example, for pairs of customers located within an urban area, travel time is high compared to the corresponding distance, reflecting the fact that travelling in urban areas is more time consuming than travelling in rural areas. Moreover, higher differences are found comparing travel times and travel distances due to difficult orog- raphy in the island. Time windows specifications were generated according to some information provided by the company. While demand specifications were established using a number of parameters in order to present different scenarios. We believe that
the features of this dataset make a better challenge for the assessment of multi-objective algorithms.
The remaining of this chapter contains the following sections. Section 6.2 explains the structure of the different files in each instance. Section 6.3 shows the details of cus- tomers’ locations layouts. Time windows characterisation are stated in Section 6.4. Section 6.5 explains the demands characterisations. The multi-objective suitability of this dataset is discussed in Section 6.7. Finally, a brief in-sight on the difficulty of this dataset is provided in 6.8.