Development of algorithms for solving routing problems in the people and parcel transportation = nghiên cứu và phát triển các thuật toán giải quyết các bài toán tối ưu trong giao thông vận tải người và hàng hóa

MINISTRY OF EDUCATION AND TRAINING

HANOI UNIVERSITY OF SCIENCE AND TECHNOLOGY

NGUYEN VAN SON

DEVELOPMENT OF ALGORITHMS
FOR SOLVING ROUTING PROBLEMS
IN THE PEOPLE AND PARCEL TRANSPORTATION

DOCTORAL DISSERTATION OF
COMPUTER SCIENCE

Hanoi−2023


MINISTRY OF EDUCATION AND TRAINING

HANOI UNIVERSITY OF SCIENCE AND TECHNOLOGY

NGUYEN VAN SON

DEVELOPMENT OF ALGORITHMS
FOR SOLVING ROUTING PROBLEMS
IN THE PEOPLE AND PARCEL TRANSPORTATION
Major: Computer Science
Code: 9480101

DOCTORAL DISSERTATION OF
COMPUTER SCIENCE
SUPERVISORS:

1. Ph.D. Pham Quang Dung
2. Assoc. Prof. Nguyen Xuan Hoai

Hanoi−2023


DECLARATION OF AUTHORSHIP
I declare that my thesis titled "Development of algorithms for solving routing problems in the people and parcel transportation" has been entirely composed by myself,
supervised by my cosupervisors, Ph.D. Pham Quang Dung and Assoc. Prof. Nguyen
Xuan Hoai. I assure some statements as follows:
ˆ This work was done as a part of requirements for the degree of PhD at Hanoi
University of Science and Technology.
ˆ This thesis has not previously been submitted for any degree.
ˆ The results in my thesis is my own independent work, except where works in the
collaboration have been included. Other appropriate acknowledgements are given
within this thesis by explicit references.
Hanoi, May, 2023
Ph.D. Student

NGUYEN VAN SON

SUPERVISORS

Ph.D. Pham Quang Dung

Assoc. Prof. Nguyen Xuan Hoai

i

ACKNOWLEDGEMENT
My thesis has been realized during my doctoral course at the School of Information
Communication and Technology (SoICT), Hanoi University of Science and Technology
(HUST). HUST is a really special place where I have accumulated immense knowledge
in my PhD process.
A PhD process is not a one-man process. Therefore, I am heartily thankful to my
supervisors, Ph.D. Pham Quang Dung and Assoc. Prof. Nguyen Xuan Hoai, whose
encouragement, guidance and support from start to end enabled me to develop my
research skills and understanding of the subject. I have learned the countless amount
of things from them. This thesis would not have been possible without their precious
support.
I would like to thank Prof. Luc De Raedt and all members of Faculty of Computer
Science, KU Leuven, Belgium for supporting me a lot in the research process. A special
thanks goes to Assoc. Prof. Mahito Sugiyama at National Institute of Informatics,
Japan for valuable guidance helps me obtain many scientic experiences during the
internship periods of the PhD. Many thanks go also to Ph.D Anton Dries, Ph.D Behrouz
Babaki, Ph.D Bui Quoc Trung, Msc. Nguyen Thanh Hoang, Msc. Phan Anh Tu for
a positive research-partnership during many months made this research signicant as
well as realistic.
I would like to thank Executive Board and all members of Computer Science Department, SoICT as well as HUST for the frequent support in my PhD course. I thank
my colleagues at Academy of Cryptography Techniques for their help.
Last but not the least, I would like to thank my family: my parents, my wife and
my friends, who support me spiritually throughout my life. They were always there
cheering me up and stood by me through the good and bad times.
Hanoi, May, 2023
Ph.D. Student

NGUYEN VAN SON

ii

CONTENTS
CONTENTS

vi

SYMBOLS

vi

LIST OF TABLES

viii

LIST OF FIGURES

ix

INTRODUCTION

1

1 BACKGROUND

10

1.1

Optimization Problem . . . . . . . . . . . . . . . . . . . . . . . . . . .

10

1.2

Vehicle Routing Problem and Extensions . . . . . . . . . . . . . . . . .

11

1.2.1

Capacitated Vehicle Routing Problem . . . . . . . . . . . . . . .

11

1.2.2

Pickup-and-Delivery Vehicle Routing Problem with Time Windows 12

1.2.3

People and Parcel Sharing Taxi Routing Problem . . . . . . . .

14

1.2.4

Rich Vehicle Routing Problem . . . . . . . . . . . . . . . . . . .

16

1.2.5

Static Routing Scenario . . . . . . . . . . . . . . . . . . . . . .

17

1.2.6

Dynamic Routing Scenario . . . . . . . . . . . . . . . . . . . . .

18

Solution Methodologies for VRP problems . . . . . . . . . . . . . . . .

18

1.3.1

Exact Methods . . . . . . . . . . . . . . . . . . . . . . . . . . .

19

1.3.2

Approximate Methods . . . . . . . . . . . . . . . . . . . . . . .

20

1.3.2.1

Classic Heuristics . . . . . . . . . . . . . . . . . . . . .

21

1.3.2.2

Metaheuristics . . . . . . . . . . . . . . . . . . . . . .

23

1.3

2 MODELLING AND SOLVING A NEW VARIANT OF STATIC VEHICLE ROUTING PROBLEM
28
2.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28

2.2

Problem description and formulation . . . . . . . . . . . . . . . . . . .

30

2.2.1

Problem description

. . . . . . . . . . . . . . . . . . . . . . . .

30

2.2.2

Notations and denitions . . . . . . . . . . . . . . . . . . . . . .

32

2.2.3

Model formulation . . . . . . . . . . . . . . . . . . . . . . . . .

34

The solution methods . . . . . . . . . . . . . . . . . . . . . . . . . . . .

37

2.3.1

Notations for heuristic algorithms and solution evaluation . . . .

37

2.3.2

Analysis of the challenges of the new capacity constraints in the

2.3

MTDLC-VR problem . . . . . . . . . . . . . . . . . . . . . . . .
iii

38


2.3.2.1

A review of construction heuristics . . . . . . . . . . .

2.3.2.2

The challenges of the capacity constraints on construction heuristics . . . . . . . . . . . . . . . . . . . . . . .

40

Splitting procedure . . . . . . . . . . . . . . . . . . . .

41

2.3.3

Adapted construction algorithms with splitting procedure . . . .

43

2.3.4

An adapted ALNS with splitting procedure . . . . . . . . . . . .

47

2.3.4.1

Outline of A-ALNS algorithm . . . . . . . . . . . . . .

48

2.3.4.2

Choosing the operators . . . . . . . . . . . . . . . . . .

50

2.3.4.3

Removal operators . . . . . . . . . . . . . . . . . . . .

50

2.3.4.4

Insertion operators . . . . . . . . . . . . . . . . . . . .

52

Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

53

2.4.1

Instances and setting . . . . . . . . . . . . . . . . . . . . . . . .

53

2.4.2

Experiment 1: Mathematical formulation validation . . . . . . .

56

2.4.3

Experiment 2: Comparison the eciency between construction

2.3.2.3

2.4

2.4.4

2.4.5
2.5

38

heuristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

61

Experiment 3: The eciency of the A-ALNS algorithm . . . . .

63

2.4.4.1

Parameter tuning . . . . . . . . . . . . . . . . . . . . .

63

2.4.4.2

The eciency of removal and insertion operators . . .

64

2.4.4.3

Robustness of the A-ALNS strategy

65

. . . . . . . . . .

Experiment 4: Sensitivity analysis for the lower-bound capacity
constraint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

68

Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

69

3 MODELLING AND SOLVING A NEW VARIANT OF DYNAMIC
VEHICLE ROUTING PROBLEM
71
3.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

71

3.2

Taxi-Share Routing Model . . . . . . . . . . . . . . . . . . . . . . . . .

73

3.2.1

Problem Description . . . . . . . . . . . . . . . . . . . . . . . .

73

3.2.2

Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . .

74

3.3

Online Taxi-Share Routing Problem Based on Predicted Information
3.3.1

3.3.2

.

76

Taxi Demand Prediction . . . . . . . . . . . . . . . . . . . . . .

76

3.3.1.1

Learning method with equal length subintervals . . . .

77

3.3.1.2

Learning framework with an adaptive binning method

78

Online Routing Algorithm . . . . . . . . . . . . . . . . . . . . .

79

3.3.2.1

Route representation . . . . . . . . . . . . . . . . . . .

81

3.3.2.2

Possible Positions for Insertion . . . . . . . . . . . . .

81

3.3.2.3

Route Re-optimization . . . . . . . . . . . . . . . . . .

82

3.3.2.4

Route Establishment . . . . . . . . . . . . . . . . . . .

82

3.3.2.5

Request Insertion . . . . . . . . . . . . . . . . . . . . .

82

iv


3.3.2.6

Improvement Operator . . . . . . . . . . . . . . . . . .

83

3.3.2.7

Prediction-Based Idle Taxi Direction . . . . . . . . . .

84

Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

84

3.3.3.1

Data Description . . . . . . . . . . . . . . . . . . . . .

84

3.3.3.2

Simulation design . . . . . . . . . . . . . . . . . . . . .

85

3.3.3.3

Experimental results . . . . . . . . . . . . . . . . . . .

85

Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

91

3.3.3

3.4

CONCLUSIONS

92

PUBLICATIONS

94

Bibliography

95

v


ABBREVIATIONS
No. Abbreviation Meaning
1

ACS

2

ALNS

3

BnB

4

BnC

5

BnP

6

CDF

7

CF-RS

8

CP

9

CVRP

10

DARP

11

DP

12

DVRP

13

EDF

14

ERM

15

GA

16

GRASP

17

ICTP

18

KS

19

LP

20

LS

21

MDVRP

22

MMCVRP

23

MMVRP

24

MILP

25

MTVRP

26

NHPP

27

NP

28

OP

29

PDVRPTW

Ant Colony System
Adaptive Large Neighborhood Search
Branch-and-Bound
Branch-and-Cut
Branch-and-Price
Cumulative Distribution Function
Cluster-First Route-Second
Constraint Programming
Capacitated Vehicle Routing Problem
Dial-A-Ride Problem
Dynamic Programming
Dynamic Vehicle Routing Problem
Empirical Distribution Function
Empirical Risk Minimization
Genetic Algorithm
Greedy Randomised Adaptive Search Procedure
Inland Container Transportation Problem
Kolmogorov-Smirnov
Linear Programming
Local Search
Multi-Depot Vehicle Routing Problem
Min-Max Capacitate Vehicle Routing Problem
MinMax Vehicle Routing Problem
Mixed-Integer Linear Programming
Multi-Trip Vehicle Routing Problem
NonHomogeneous Poisson Process
Non-deterministic Polynomial-time

Optimization Problem
Pickup-and-Delivery Vehicle Routing Problem with Time
Window
vi


30

PSO

31

RF-CS

32

RVRP

33

SA

34

SARP

35

SRM

36

SW

37

TSP

38

VRP

39

VRPB

40

VRPTW

Particle Swarm Optimisation
Route-First Cluster-Second
Rich Vehicle Routing Problem
Saving Algorithm
Shared-A-Ride Problem
Structural Risk Minimization
Sweep Algorithm
Travelling Salesman Problem
Vehicle Routing Problem
Vehicle Routing Problem with Backhauls

Vehicle Routing Problem with Time Windows

vii


LIST OF TABLES
2

A summary of the related papers. . . . . . . . . . . . . . . . . . . . . .

5

2.1

Sets and parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . .

33

2.2

Modeling variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

34

2.3

Parameters of instance E21 − 1 − 2 − 4 − 6 − 5 . . . . . . . . . . . . . .

55

2.4

Travel time matrix of instance E21 − 1 − 2 − 4 − 6 − 5 . . . . . . . . .

55

2.5

Parameters of instances RG − 1 − 2 − 2 − 2 − 6 and RG − 2 − 2 − 2 − 2 − 6 56

2.6

Travel time matrix of instances RG−1−2−2−2−6 and RG−2−2−2−2−6 56

2.7

Comparison solutions of the MILP model with the found optimal solutions. 58

2.8

Comparison between MILP model and the A-ALNS algorithm. . . . . .

58

2.9

Comparison between MILP model and construction algorithms. . . . .

60

2.10 The eciency comparison between construction algorithms. . . . . . . .

62

2.11 Results of parameter tuning . . . . . . . . . . . . . . . . . . . . . . . .

64

2.12 The comparison of solution approaches . . . . . . . . . . . . . . . . . .

67

3.1

Parameter Setting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

86

3.2

Taxi fare rate for calculating the prot introduced in [14].

. . . . . . .

86

3.3

The number of taxi requests need to be served in two scenarios. . . . .

86

3.4

The routing results of four algorithms in the rst scenario. . . . . . . .

87

3.5

The routing results of four algorithms in the second scenario.

. . . . .

88

3.6

The eciency of the algorithm based on the predicted information . . .

89

3.7

The prot of scheduling algorithm using our proposed learning method.

91

viii

LIST OF FIGURES
1.1

An example of the CVRP problem. . . . . . . . . . . . . . . . . . . . .

12

1.2

Rich vehicle routing problem. . . . . . . . . . . . . . . . . . . . . . . .

17

1.3

A classication of the VRP methods. . . . . . . . . . . . . . . . . . . .

19

1.4

An illustration of search space for a minimization problem. . . . . . . .

22

1.5

Illustration of one-point move . . . . . . . . . . . . . . . . . . . . . . .

23

1.6

Illustration of two-point move . . . . . . . . . . . . . . . . . . . . . . .

24

1.7

Illustration of two-opt move . . . . . . . . . . . . . . . . . . . . . . . .

24

1.8

Illustration of or-opt move . . . . . . . . . . . . . . . . . . . . . . . . .

24

1.9

Illustration of three-opt move . . . . . . . . . . . . . . . . . . . . . . .

24

1.10 Illustration of three-point move . . . . . . . . . . . . . . . . . . . . . .

24

1.11 Illustration of cross-exchange move . . . . . . . . . . . . . . . . . . . .

24

2.1

An example of node transfers to satisfy the capacity constraints, where
the lower and the upper boundaries are 70 and 110, respectively. . . . .

29

2.2

An example of vehicle itineraries in the MTDLC-VR problem. . . . . .

32

2.3

Results of solving the MILP model on random generated instances. . .

59

2.4

Results of solving the MILP model on real small instances. . . . . . . .

59

2.5

Solution visualization of instance E21 -1-2-4-6-5. . . . . . . . . . . . . .

59

2.6

The eciency of operators . . . . . . . . . . . . . . . . . . . . . . . . .

65

2.7

The number of requests removed from the solution for violating the
lower-bound capacity constraints. . . . . . . . . . . . . . . . . . . . . .

3.1

69

An example of candidate taxi routes from the last drop-o point to the
parking locations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

74

3.2

The proposed learning framework. . . . . . . . . . . . . . . . . . . . . .

78

3.3

The exchange operator. . . . . . . . . . . . . . . . . . . . . . . . . . . .

84

3.4

The accumulated prot of four scheduling algorithms . . . . . . . . . .

89

3.5

The percentage of failure requests. . . . . . . . . . . . . . . . . . . . . .

90

ix


INTRODUCTION
As an important component of the economy, the transportation sector plays an
important role in economic development and connectivity between regions. The connectivity is even more so in a global economy where the intensication of economic
cooperation is related to the movement of people and freight. Many models of transport of people and goods have been built in practice, such as public transportation
services with xed routes (bus, rail, ferry, airline services), taxi services to transport
people on call requests, container transportation, freight transportation service from
center depots to customers, etc. In Vietnam, according to the preliminary report of
the General Statistics Oce [1], the number of vehicles has increased to approximately

43 million units, more than 3.3039 billion transported passengers and 1.2 billion tons
of transported freight in 2015. Transport typically accounts for about 25 percent of all
the energy consumption of an economy [2]. Authors in [2] also specied that transport
costs account for 20 percent of the total cost of a product. Cities have now become bigger and bigger in terms of surface and population. This phenomenon has caused some
consequences: severe trac congestion, noise, pollution, road accidents, etc. Hence,
transport systems face requirements to increase their capacity and reduce the costs
of movements. One of the major problems encountered in the urban environment is
to design ecient transport routing for people and parcels. A good transport routing
aims to save costs, thus bringing better prots to companies while meeting people's
demands, signicantly increasing the eciency of transportation systems and possibly
reducing the above pointed out issues.
The routing problem that nds the optimal solution for vehicle routes is called a
Vehicle Routing Problem (VRP). The pure VRP problems such as Capacitated Vehicle Routing Problem (CVRP), Min-Max Vehicle Routing Problem without capacity
constraint (MMVRP) and Pickup-and-Delivery Vehicle Routing Problem with Time
Window (PDVRPTW) are simple models in the sense that it is usually far from the
reality of the people and parcel transportation [3]. In contrast, many dierent factors
and constraints generally need to be added to capture real-world problems more fully,
leading to problems usually called Rich VRP (RVRP) problems. Therefore, thousands
of papers in world literature have been devoted to this problem. For example, transportation of dierent kinds of products such as oil [4], milk [5], and frozen food [6, 7],
or delivery of e-commerce packages [8] is an example of freight transportation service
from center depots to customers, Shared-a-Ride Problem (SARP) of taxis [9, 10, 11].
In [3, 12], the authors provided a concise review of existing problem features and applications. The VRP problem is a well-known NP-hard problem [13]. Solving these
1


problems is very hard and, then, still an active research topic that attracts the attention
of many computer scientists due to their impact on society and the economy.
Given the practical importance of VRPs, the main objective of this thesis is to
extend the existing VRPs more exibly and realistically. It is crucial that new variants
are formulated and solution algorithms are developed to solve them as eciently as

possible. According to surveys from the literature as well as actual operations from
transport companies, the routing operation is usually classied into two scenarios:

static and dynamic.

Hence, this thesis focuses on real-life problems typical for these

types of VRP problems.
For the static VRP problem, the authors in [3] declared that one of the most important objectives of routing problems is to balance the workload allocation in order
to ensure acceptance of operational plans, maintain employee satisfaction and morale,
reduce overtime, and to reduce bottlenecks in resource utilization. Due to the limited
capacity, the xed eet size, and time window constraints, vehicles must deliver product units from multiple distribution centers to customers and operate multiple trips.
However, some trips of vehicles are scheduled to carry too little cargo in real-world situations due to tight time windows. Therefore, this thesis proposes a new variant of the
static VRP problem taking into account most of the well-studied features. Specically,
there is a new constraint on the lower bound of the capacity of vehicles that has not
been considered in the literature. This dissertation formulates the considered problem
as a mixed-integer linear programming (MILP) problem, analyzes the challenges of the
lower-bound capacity constraints and proposes an adaptive large neighborhood search
(ALNS) framework for solving it.
For the dynamic VRP problem, a new people transport model is studied that extends
the share-a-ride problem proposed by [14]. In the considered model, people and parcels
can share a ride and information about future requests is predicted by learning a spatiotemporal Poisson point process. The thesis attempts to maximize the overall travel
eciency while minimizing the idle time of a driver by applying the learned information
to the routing problem. From this perspective, a new mathematical model and a new
anticipatory algorithm for scheduling taxis exploiting the predicted future requests are
proposed in this dissertation.

Related works
Authors in [15] were the rst scientists who introduced the Truck Dispatching Problem,
modelling how a eet of homogeneous trucks could serve the demand for oil of a number

of gas stations from a central hub and with a minimum travel distance. This problem
became known as the VRP problem, one of the most widely studied topics in the
eld of Operations Research [12, 16]. Since then, several variants of the problem have
been put forward, including CVRP [17], PDVRPTW [18], VRP with multiple depots
2


(MDVRP) [19] and VRP with multiple trips (MTVRP) [20]. The most classical VRP
is CVRP, where each customer has a given demand that has to be satised, and the
total demand of the customers served in the same route does not exceed the upperbound vehicle capacity. The number of solution methods introduced in the academic
literature (for old as well as new variants of the VRP) has grown rapidly over the past
decades [7, 21, 22]. Moreover, the performance of current computers has increased
signicantly. Therefore, we can solve larger instances of the VRP, which promotes the
progression in the research eld and the development of ecient algorithms for the
VRP.
Vehicle routing problem with time window (VRPTW) is a well-known simple extension of VRP that extends the CVRP by adding time windows to a depot and customers.
General and state-of-the-art surveys on this problem class are provided in [23]. In [24],
the authors implemented the Priority-based Heuristic Algorithm for solving perishable
food products delivery problems to maximize customer satisfaction. In their model,
customer satisfaction includes the freshness of delivered food. Thus, the time window
constraint of each customer demand is relatively tight. Especially, the works in [25]
investigated VRP with multiple prioritized time windows for distributing confectionery
and chocolate products in Iran. Due to the complexity of their problem, a binary articial bee colony algorithm tuned via the Taguchi method is developed to solve it.
Then, [26] reviewed VRPTW applications related to freight transportation that most
logistics and distribution companies face in their daily operations.
The MDVRP arises as a generalization of VRP, where vehicles depart from and
return to multiple depot locations. [27] surveyed several studies on the MDVRP based
on either exact or heuristics methods. In terms of complete algorithms, [28] presented a
branch-and-cut-and-price algorithm to nd the optimal solution of a variation of VRP
in which vehicles have dierent capacities and xed costs, located at dierent depots.

An exact method-based heuristic is proposed by [29] to solve the MDVRP problem
in which each subproblem becomes a single depot VRP and evolves independently in
its domain space. In [30], four fuzzy simulation-based heuristic algorithms are also
designed to search the exact solution of the MDVRP for hazardous materials transportation. Regarding incomplete algorithms, [31] and [32] proposed variants of the
Variable Neighborhood Search algorithm for solving the MDVRP problem. In [32], the
authors considered a multi-depot multi-compartment vehicle routing problem, where
the cargo space of each vehicle has multiple separate compartments to transport different products simultaneously. In the context of our problem, these compartments of
vehicles are adjustable. Therefore, we only consider constraints on the total available
cargo space on each vehicle. Recently, many heuristic methods have been developed in
the context of the MDVRP, including the genetic algorithm [33], the local search algorithm [34], and a variable tabu neighborhood search [35]. In [35], their algorithms can
3


be implemented to solve the Multi-Depot Open Vehicle Routing Problem (MDOVRP),
which is a generalization of the MDVRP. [36] also considered the MDOVRP and developed a general multiple variable neighborhood search hybridized with a tabu search
strategy for solving it. However, the complex objectives and constraints often lead to
various solution spaces. These challenges lead to considerable research eorts in embedding learning mechanisms for more ecient neighborhood search through adaptive
neighborhood selection. In [37], the authors proposed a hybrid ALNS algorithm that is
competitive compared with the algorithm in [36]. Their algorithm combines the ALNS
strategy with three insertion, ve removal heuristics, and four post-optimization local
search procedures. In the MDOVRP model, vehicles do not return to their starting
point after serving the last customer. In our model, although a vehicle can also visit
dierent depots on dierent trips, it must return to a parking area after serving the
last customer. The ALNS algorithm is also adapted for dealing with large problem
instances. Furthermore, the advanced extension of the problem by combining MDVRP
with MTVRP is studied in this thesis.
The MTVRP was rst proposed by [38], where a vehicle makes several journeys
during a day. [39] proposed a mathematical programming model based on a set covering
formulation for MTVRP. Recently, a branch-and-price algorithm in [40], and the rst
exact solution framework based on a novel structure-based formulation in [41] were

presented to solve the MTVRP. For incomplete algorithms, it is common to solve the
MTVRP by combining VRP and packing procedure [42, 43, 44]. The authors in [42]
studied the one vehicle version with multi-trip in a route (a trip is called

leg by the

authors) and considered the capacity of the vehicle as an output (i.e., the vehicle

capacity is not xed). That is, their model proposed an approach to select the best
capacity and the best route, in order to minimize the acquisition cost function and
the distance traveled. In [43], the authors proposed an adapted ALNS algorithm that
iteratively modies a CVRP solution and applies bin packing techniques to assign the
created routes to available vehicles. Their model assumed that the serving time at the
depot was xed. In contrast, the loading time-dependent at the depot is considered
in works of [45] which designs routes to replenish stocks for a cafe company around
Singapore. They also developed a hybrid ALNS algorithm that employs two-variable
neighborhood descend operators. However, both of those papers considered only one
single depot. A survey on the MTVRP can be found in [46].
A combination of the above problems has more practical applications. Recently,
more attention has been focused on the multi-trip multi-depot VRP with specic combinations of real-life constraints. They also apply their model to transportation problems
for dierent kinds of commodities. For example, [47] proposed three metaheuristics to
solve the multi-trip multi-depot heterogeneous Dial-a-Ride problem. Two-hybrid bee
algorithms and an ALNS are presented. These methods are highly eective and ef4


cient. [48] also considered a multi-trip multi-depot VRP problem in which vehicles
must pick up meals from multiple suppliers and deliver them to customers. Their problem under logistics resource sharing is solved by two popular algorithms: local search
and ALNS. In the ALNS algorithm, the authors proposed a supplier-oriented removal
operator and three rules to choose a specic range of insertion for each insertion operator. Their results show that the sharing service has a signicant advantage over
the exclusive service. In addition, [8] rst proposed a multi-trip multi-depot VRPTW

with release dates. Their problem originates from the e-commerce package delivery in
China. In their model, each trip starts and ends at the same depot. The release date
introduced in their paper is when the package requested by a customer in the distribution center can be delivered by a vehicle. Therefore, they considered the practices
that vehicles can only deliver available packages that have been released. It is solved
by a hybrid particle swarm optimization algorithm and a hybrid genetic algorithm. A
summary of the assumptions of related papers is presented in Table 2.
Table 2: A summary of the related papers.
Ref.

[47]
[32]
[48]
[41]
[8]
[45]
This work

Multitrip

Multidepot

√

√
√
√

√
√
√

√
√

Trip
limitation
√

Constraints
No sta- Servicert at
dependdepot ent time
√
√

√

√
√

√
√

√
√

√

Time
window
√
√

√
√
√
√
√

Lowerbound
capacity

Solution methods
Com- Incomplete
plete
√

√
√
√

√

√

√
√
√

The dierence of our study is exploring logistics services and combining real-world
constraints in product delivery, where product companies want to maximize the number
of served customers and minimize the number of vehicles related to their availability.
In our model, there are three types of points with dierent accessibility: points visited

one time in one-way direction (parking areas), points visited many times (distribution
centers), and points visited at most once (customers). Besides, the existence of service
sharing leads to the objective function of minimizing outsourcing costs. The loading
time at distribution centers and the unloading time at customers are depended on the
product type and the product quantity. Moreover, in the context of the considered
problem, dairy products are always available at distribution centers. Managers are
often concerned with occupancy product rates in vehicles. Thus, new lower-bound
capacity constraints are added to our model. We call this problem as multi-trip multidepot VRP with lower bound constraints (MTDLC-VR). To the best of our knowledge,
5


no work has been conducted to address this problem.
Most of the above studies deal with the VRP problem in the static scenario, where all
data is known in advance. In the dynamic scenario of VRP problems, new requests can
be revealed online during the plan execution. Therefore, routes must be dynamically
updated while executing the current simulation [49]. A neighborhood search heuristics
to optimize the routes of vehicles for dynamic PDVRPTW problems is proposed by
[50]. The taxi routing problem can be seen as the specic practical application of
PDVRPTW problems in the dynamic scenario, rstly introduced by [13] as a Dial-ARide problem (DARP). Authors in [14] described a SARP problem and solved it in both
static and dynamic scenarios. In that paper, the authors explained the conceptual and
mathematical model of the DARP problem, where the same taxi network serves people
and parcels. There are new variants of this model and some heuristic algorithms that
have been proposed by [9, 10] to solve this problem. As DARPs are NP-hard, they
are usually solved by heuristic approaches [51, 52, 53]. Although the integration of
logistics and transportation into multiple modes of transportation with ridesharing
has received much attention, the number of studies remains limited [54, 55]. Even
fewer studies have sought an ecient solution to the SARP of people and goods over
relatively short transportation distances [56, 57]. A smart taxi-routing system based on
a historical data analysis can improve the operational eciency of drivers and optimize
the overall travel eciency. However, it appears that most researches have optimized

only the total route distance of all current events on the schedules [9, 58]. In the
dynamic scenario, one of the novel components is the dispatch system with unknown
requests, which aims to suggest more ecient routes for drivers as well as to serve more
than requests by using the learned arrival rate of taxi requests. Applying the learned
information to the routing problem, this thesis attempts to maximize the overall travel
eciency while minimizing the idle time of a driver.

Motivation
The optimization of transportation has become a great issue in recent years. The
routing problem is a new challenge for the transportation sector: improve productivity
and reduce costs by increasing the number of served clients, reducing the time and cost
of transportation to achieve good human resources planning and ecient operation.
The research on the VRP is benecial not only to transportation companies but also
to society.
With economic development, parcel distribution is one of the most signicant static
VRP models. Complete models and appropriate algorithms need to be developed
for the product distribution problem of the company in Vietnam as well as similar
problems around the world. This motivated us to ll a gap in the literature on some
VRP problems by combining real-world factors to extend these problems more exibly
6


and realistically.
For people transportation models, one of the most preferred transportation modes
for people in urban areas is taxi services due to its convenience, exibility, and innovative operation strategies, e.g., integration of passenger and parcel transportation on
each taxi aims to discount the passenger. Smart ridesharing services can be realized
through the convergence of location-based devices, geographic information systems,
global positioning systems, and wireless communication. In addition, they enable the
deployment of intelligent routing services. The motivation is to consider the share-aride taxi routing problem based on predictive information in online scenarios. A smart
routing system based on historical data analysis can improve the operational eciency

of drivers and optimize overall travel eciency.

Methodology
The methodology of this dissertation are as follows:
ˆ Theoretical study of variants of the VRP problem as optimization problems.
ˆ Analyzing the related works to the considered problems.
ˆ Designing the practical and useful models of the VRP problem.
ˆ Proposing ecient metaheuristic algorithms to solve the investigated VRP models.

Scope of Research
VRP problems are complex NP-hard problems that include many subproblems and
variants. Therefore, the scope of my thesis is to investigate two practical transportation
problems typical for two types of VRP problems,

static and dynamic VRP problems.

In the class of static VRP problems, the parcel distribution problem is studied. The
problem considers specic combinations of real-life constraints to tackle real problems
in one of the biggest dairy companies in Vietnam. In the class of dynamic VRP problems, the dynamic taxi scheduling problem with predictive information is investigated.
This problem is extended from the novel share-a-ride VRP problem proposed by [9, 14]
in which people and parcel requests are scheduled on the same taxi network. The considered problems are known as the N P -hard problems. Moreover, the combination of
real-life constraints makes the problem more challenging. Therefore, the thesis mainly
focuses on heuristic/metaheuristic algorithms for solving the proposed problems.

Contributions
The three main contributions of the thesis are as follows:

7

ˆ With the goal of developing parcel transportation models to cover real-life problems, the thesis has dened a novel product transportation problem for real-world
applications taking into account most of the well-studied features, especially with
a new constraint on the lower bound of the capacity of vehicles which has not
been investigated in the literature. The thesis formulates the considered problem
as a MILP model and proposes some ecient metaheuristic algorithms to solve
it. Experiments are performed in various scenarios to examine the eciency of
algorithms. The quality of solutions and computation time are compared with existing methods and some insights are presented on each algorithm's use in dierent
instances.
ˆ For people transportation models, a new variant of the share-a-ride taxi transportation routing model in the dynamic scenario is developed in this thesis. In
this model, people and parcels are served in the same taxi network in which the
routing system needs to recommend the best route to the driver of a taxi without
load so that the chance of receiving a new transportation demand is high when
the taxi is still available. We propose a new ecient algorithm for routing taxis
and exploiting the predicted future requests. Our model alleviates the deciencies
of the models in [9, 14] by considering the best route for the taxi driver without
load. The algorithm is experimented on real data sets in San Francisco city and
compared with the methods for DSARP in [14] under the same parameter settings.
ˆ This thesis proposed an adaptive and data-driven binning method for learning the
non-homogeneous Poison process (NHPP) to predict future transport requests
that help minimize the vehicle's idle distance. The experimental results prove
that applying improvement of traveling direction in routing based on the demand
prediction leads to exible movement and overall traveling eciency. This study
linked transportation problems with machine learning which is expected to cope
with traditional trac problems.

Organization of the Dissertation
This dissertation is organized as follows.
ˆ Chapter 1 provides some background about VRP problems such as Optimization Problems, CVRP, PDVRPTW, SARP, RVRP problems and state-of-the-art
approaches for solving them.
ˆ Chapter 2 is the rst of two chapters that detail the research on the VRP problems

carried out in this thesis. The product distribution problem is discussed in this
chapter and an adapted ALNS algorithm is proposed for solving the problem.
A strategy including generating initial solutions and subsequently applying an
8


adaptive large neighborhood search (A-ALNS) to improve the quality of solutions
is also proposed. The performance of the proposed A-ALNS algorithm is compared
with that of other heuristics by conducting extensive numerical experiments to
evaluate the applicability of the proposed algorithm in real-world applications.
ˆ Chapter 3 starts the investigation of the people and parcel share-a-ride taxi transportation problem in the dynamic scenario, which is the more realistic variant of
the dynamic VRP problem. The considered problem is an extension of the work
in [14] and [9]. A data-driven learning method is developed to predict the new
transport requests and an ecient algorithm is proposed for routing taxis and
exploiting the predicted future requests.
ˆ To conclude, Chapter Conclusion and Future works summaries the research that
has been undertaken in this thesis and outlines avenues for further research.

9


Chapter 1
BACKGROUND
This Chapter will provide basic knowledge relevant to the concepts of optimal problems including the vehicle routing problem, extensions and solution methodologies for
solving the problems. Especially, the basic concepts of heuristic/metaheuristic algorithms are described. These concepts will be used throughout the dissertation.

1.1 Optimization Problem
Optimization problems (OPs) are those in which a set of unknown decision variables {x}n1 is required to be determined such that an objective function f is minimized/maximized and a number of constraints is satised [59] (from now on we will
only consider minimization).

Denition 1.

[59] The standard form of an optimization problem is:
Minimize f (x)
subject to gj (x) = 0, j = 1, . . . , m∗ ,

gj (x) ≤ 0, j = m∗ + 1, . . . , m,
xi ∈ Di , ∀i = 1, . . . , n

where x = {x , x , . . . , x } is the vector of decision variables, m is the total number of
constraints, m is the number of equal constrains and D is the domain of variable x .
1

2

n

∗

i

i

We note that each inequality constraint is of the form gj ≤ 0 can be converted to

gj ≥ 0 by multiplying the constraint equations by −1. Given a nite set Sf of feasible
solutions x. A globally optimal solution is the solution x
b that minimizes objective

function value (i.e., f (x

b) ≤ f (x), ∀x ∈ Sf ). The set Sf is usually called search space.

The presence of constraints on solutions can make the structure of search space more
complex. And then, OPs can be seen as problems that search the best solution in a
large set of candidate solutions in a reasonable time.
OPs can be classied into two categories [60]:
ˆ A

discrete optimization problem is modelled including some or all of the variables

required to belong to a discrete set. For example, an integer or a permutation or
a graph must be found from a countable set.
ˆ A problem with continuous variables is known as a

continuous optimization prob-

lem, in which the variables are allowed to take any value within a range of values
and the optimal value is found from a continuous function.
10


There are many applications of the OP problems in areas such as energy resource
planning, construction management, jobs to machines allocation, portfolio selection
and vehicle routing. Finding the optimum or best solution is one of the important
steps to save costs and thus bring better prots and clients' satisfaction. However,
most of problems are the

NP-hard problem. Therefore, solving OP problems has been

a challenge that attracts the attention of many computer scientists. There are two

main types of methods for solving the OP problems:

exact methods and approximate

methods. An exact method allows to nd optimum solutions, and the other method,
usually called

heuristic or metaheuristic, focuses on systematically nding an accept-

able solution within a limited number of iterations and does not guarantee to obtain
an optimal solution.

1.2 Vehicle Routing Problem and Extensions
VRP is an optimization problem given to a whole class of problems involving the
visiting of customers by vehicles, also known as a

NP-hard problem [61].

We can

get dierent types of VRP extensions by combining dierent extended criteria with
the classical VRP. Several well-known extensions of the VRP closely related to the
problems investigated in this dissertation are discussed below.

1.2.1 Capacitated Vehicle Routing Problem
The standard VRP is the Capacitated Vehicle Routing Problem (CVRP), in which
a xed eet of homogeneous vehicles must scheduled to serve dertermined customer
demands for a single commodity from a specied depot at minimum shipping cost [13].
In the CVRP, there is limitation to the loading capacity of each vehicle. An example
of a solution of CVRP is shown in Figure 1.1 in which there are 12 customers (n = 12)

served by four vehicles (m = 4) with the same capacity Q = 100. The customer
demand of each customer is displayed in brackets.
The CVRP can be formulated as an integer linear programming model as follows.
Let G = (V, E) be a complete directed graph where V = {0, 1, . . . , n} is a set of vertexes
and E = {(i, j) : i, j ∈ V } is a set of arcs. Vertex 0 relates to a depot for a eet of

m homogeneous vehicles with capacity Q, while vertex i ∈ {1, . . . , n} corresponds to
a customer having a non-negative demand di . Vehicles must serve all customers at
minimum total cost, with ci,j ≥ 0 denoting the travel cost from vertex i to vertex

j , ∀i, j ∈ V . The cost structure is assumed symmetric, i.e., ci,j = cj,i and ci,i = 0,
∀i, j ∈ V . For S ⊂ V , let σ(S) = {(i, j) : i ∈ S, j ∈
/ S or i ∈
/ S, j ∈ S}. σ(i) implies
that S = {i}. We denePthe lower bound on the number of vehicles required to visit
all vertexes by r(S) = ⌈

i∈S

Q

di

⌉. The integer variable xi,j denotes the number of times

arc (i, j) ∈ E is traversed in the solution. The CVRP formulation proposed by [62] is
11


Figure 1.1: An example of the CVRP problem.

then:

X

Minimize

(1.1)

ci,j xi,j

(i,j)∈E

subject to

X

xi,j = 2, ∀i ∈ V \ {0},

(1.2)

(i,j)∈σ(i)

X

xi,j = 2m,

(1.3)

xi,j ≥ 2r(S), ∀S ⊂ V \ {0}, S ̸= ∅,

(1.4)

xi,j ∈ {0, 1}, ∀(i, j) ∈
/ σ(0),

(1.5)

xi,j ∈ {0, 1, 2}, ∀(i, j) ∈ σ(0)

(1.6)

(i,j)∈σ(0)

X
(i,j)∈σ(S)

The objective function (1.1) minimizes the total travel cost. The degree constraints
(1.2) ensure that each customer is visited by exactly one. The depot degree constraints
(1.3) guarantee that the number of vehicles departing from the depot and returning
to the depot is equal to the number of vehicles. In the constraints (1.4), both the
connectivity of the solution and the capacity constraints are stated. The remaining
constraints (1.5) and (1.6) specify the denition domains of the variables.

1.2.2 Pickup-and-Delivery Vehicle Routing Problem with Time
Windows
One important variant of the VRP is the Pickup-and-Delivery Vehicle Routing Problem with Time Windows (PDVRPTW), which comes from real-life transport situations,
12

is much more complicated than the CVRP. In the PDVRPTW, it is generally required
to nd one or more minimum cost routes to serve a number of customer requests,
where each request is dened by a pickup point, a corresponding delivery point, and
a demand (goods or passengers) to be transported between these locations within a
predened time window. The PDVRPTW problems can be widely applied in areas
such as express package delivery from senders to receivers, food collection and delivery,
and taxi operation.
Following the notation introduced by [63], the PDVRPTW problem can be formulated on a graph G = (V, E), where V is the set of points, consists of the set of pickup
points O = {1, 2, . . . , n}, the set of delivery points D = {n + 1, n + 2, . . . , 2n} and the
depot points {0, 2n + 1}. The set of edges denoted by E represents feasible connections
between points. Each request consists of information about a pickup point i, delivery
point n + i and demand di units need to be transported from point i to point n + i. Let

K be the set of vehicles. Each vehicle k ∈ K has a capacity Ck , and the total duration
of its route cannot exceed Rk . If the vehicle visits point i ∈ V , the service time si must
begin within the time window [ei , li ]. We assume that dn+i = −di , d0 = d2n+1 = 0, and

s0 = s2n+1 = 0. The travel time and cost between distinct points i, j ∈ V are given by
ti,j and ci,j , respectively. The model uses three type of variables: the binary ow variable xki,j = 1 if and only if vehicle k travels on edge (i, j) ∈ E in the optimal solution,

0 otherwise; the time variable
point i ∈ V ; and variable

Wik

ST

k
i

represents the starting service time of vehicle k at

species the load of vehicle k after leaving point i ∈ V .

The problem can be formulated as the following MILP formulation:
Minimize

X X
k∈K (i,j)∈E

13

ci,j xki,j

(1.7)


subject to:

XX

xki,j = 1, ∀i ∈ O,

(1.8)

xkn+i,j , ∀i ∈ O, ∀k ∈ K,

(1.9)

k∈K j∈V

X

xki,j

j∈V

=

X
j∈V

X

xk0,j = 1, ∀k ∈ K,

(1.10)

∀i ∈ O ∪ D, ∀k ∈ K,

(1.11)

xki,2n+1 = 1, ∀k ∈ K,

(1.12)

j∈V

X

xkj,i

=

j∈V

X

xki,j ,

j∈V

X

ST

k
i

i∈V
k
k
+ si + ti,j )xi,j ≤
j , ∀i ∈ V, ∀j ∈ V,
(Wik + dj )xki,j ≤ Wjk , ∀i ∈ V, ∀j ∈ V,
k
k
i + si + ti,n+i ≤
n+i ,
k

k
2n+1 −
0 ≤ Rk ,
k
ei ≤
i ≤ li , ∀i ∈ V,

ST

∀k ∈ K,

(1.13)

∀k ∈ K,

(1.14)

∀i ∈ O,

(1.15)

∀k ∈ K,

(1.16)

∀k ∈ K,

(1.17)

max{0, di } ≤ Wik ≤ min{Ck , Ck + di }, ∀i ∈ V, ∀k ∈ K,

(1.18)

xki,j ∈ {0, 1}, ∀i ∈ V, ∀j ∈ V, ∀k ∈ K

(1.19)

(

ST

ST

ST

ST

ST

The objective function (1.7) is to minimize the total transit cost. Constraints (1.8)(1.9) impose that each request (i.e., the pickup and delivery points) is served exactly
once and by the same vehicle. Constraints (1.10)-(1.12) keep a multicommodity ow
structure and guarantee that all vehicles start at the starting depot and end at the returning depot. Consistency of the time and load variables is guaranteed by Constraints
(1.13) and (1.14). For each request, Constraint (1.15) forces the vehicle to visit the
pickup node before the delivery point. Constraint (1.16) bounds the duration of each
route. Finally, Constraints (1.17) and (1.18) are related the time-window and capacity
constraints, respectively, while Constraint (1.19) species the domains of variables.

1.2.3 People and Parcel Sharing Taxi Routing Problem
Most ride-sharing models are based on the well-known Dial-a-Ride Problem (DARP)
[64]. The DARP consists of designing vehicle routes and schedules for a number of users

who request pickup and drop-o points. A routing system receives a large number of
requests to transport people and goods during xed working hours. The description
of the dynamic Shared-A-Ride taxi routing Problem (SARP) was proposed recently
by [14]. The authors in [14] present MILP formulations for the SARP,referring to the
fact that people and parcels share the same taxis. It means that people and goods are
served by the same taxi network.
14