Luận Án development Of Algorithms For Solving Routing Problems In The People And Parcel Transportation.pdf

MINISTRY OF EDUCATION AND TRAININGHANOI UNIVERSITY OF SCIENCE AND TECHNOLOGY NGUYEN VAN SON DEVELOPMENT OF ALGORITHMS FOR SOLVING ROUTING PROBLEMS IN THE PEOPLE AND PARCEL TRANSPORTATION

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 lems in the people and parcel transportation" has been entirely composed by myself,supervised by my cosupervisors, Ph.D Pham Quang Dung and Assoc Prof NguyenXuan Hoai I assure some statements as follows:

prob-• This work was done as a part of requirements for the degree of PhD at HanoiUniversity of Science and Technology

• This thesis has not previously been submitted for any degree

• The results in my thesis is my own independent work, except where works in thecollaboration have been included Other appropriate acknowledgements are givenwithin this thesis by explicit references

Hanoi, February, 2023 Ph.D Student

NGUYEN VAN SON

SUPERVISORS Ph.D Pham Quang Dung

Assoc Prof Nguyen Xuan Hoai

My thesis has been realized during my doctoral course at the School of InformationCommunication 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 mysupervisors, Ph.D Pham Quang Dung and Assoc Prof Nguyen Xuan Hoai, whoseencouragement, guidance and support from start to end enabled me to develop myresearch 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 precioussupport

I would like to thank Prof Luc De Raedt and all members of Faculty of ComputerScience, KU Leuven, Belgium for supporting me a lot in the research process A specialthanks goes to Assoc Prof Mahito Sugiyama at National Institute of Informatics,Japan for valuable guidance helps me obtain many scientific experiences during theinternship periods of the PhD Many thanks go also to Ph.D Anton Dries, Ph.D BehrouzBabaki, Ph.D Bui Quoc Trung, Msc Nguyen Thanh Hoang, Msc Phan Anh Tu for

a positive research-partnership during many months made this research significant aswell as realistic

I would like to thank Executive Board and all members of Computer Science partment, SoICT as well as HUST for the frequent support in my PhD course I thank

De-my colleagues at AcadeDe-my 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 therecheering me up and stood by me through the good and bad times

Hanoi, February, 2023 Ph.D Student

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

1.3 Solution Methodologies for VRP problems 18

1.3.1 Exact Methods 19

1.3.2 Incomplete Methods 21

1.3.2.1 Classic Heuristics 21

1.3.2.2 Metaheuristics 23

2 MODELLING AND SOLVING A NEW VARIANT OF STATIC VE-HICLE ROUTING PROBLEM 27 2.1 Introduction 27

2.2 Problem description and formulation 29

2.2.1 Problem description 29

2.2.2 Notations and definitions 31

2.2.3 Model formulation 33

2.3 The solution methods 36

2.3.1 Notations for heuristic algorithms and solution evaluation 36

2.3.2 Analysis of the challenges of the new capacity constraints in the MTDLC-VR problem 37

2.3.2.1 A review of construction heuristics 37

2.3.2.2 The challenges of the capacity constraints on construc-tion heuristics 39

2.3.2.3 Splitting procedure 40

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 49

2.3.4.3 Removal operators 50

2.3.4.4 Insertion operators 51

2.4 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 efficiency between construction heuristics 59

2.4.4 Experiment 3: The efficiency of the A-ALNS algorithm 62

2.4.4.1 Parameter tuning 62

2.4.4.2 The efficiency of removal and insertion operators 63

2.4.4.3 Robustness of the A-ALNS strategy 64

2.4.5 Experiment 4: Sensitivity analysis for the lower-bound capacity constraint 67

2.5 Chapter Summary 68

3 MODELLING AND SOLVING A NEW VARIANT OF DYNAMIC VEHICLE ROUTING PROBLEM 70 3.1 Introduction 70

3.2 Taxi-Share Routing Model 72

3.2.1 Problem Description 72

3.2.2 Problem Formulation 72

3.3 Online Taxi-Share Routing Problem Based on Predicted Information 75 3.3.1 Taxi Demand Prediction 75

3.3.1.1 Learning method with equal length subintervals 75

3.3.1.2 Learning framework with an adaptive binning method 76 3.3.2 Online Routing Algorithm 81

3.3.2.1 Route representation 81

3.3.2.2 Possible Positions for Insertion 82

3.3.2.3 Route Re-optimization 83

3.3.2.4 Route Establishment 83

3.3.2.5 Request Insertion 83

3.3.2.6 Improvement Operator 84

3.3.2.7 Prediction-Based Idle Taxi Direction 84

3.3.3 Experiments 85

3.3.3.1 Data Description 85

3.3.3.2 Simulation design 86

3.3.3.3 Experimental results 87

3.4 Chapter Summary 92

No Abbreviation Meaning

Window

30 PSO Particle Swarm Optimisation

LIST OF TABLES

2 A summary of the related papers 5

2.1 Sets and parameters 32

2.2 Modeling variables 33

2.3 Parameters of instance E21− 1 − 2 − 4 − 6 − 5 54

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 55 2.6 Travel time matrix of instances RG−1−2−2−2−6 and RG−2−2−2−2−6 56 2.7 The detail of the found optimal solutions 57

2.8 Comparison between MILP model and the A-ALNS algorithm 58

2.9 Comparison between MIP model and construction algorithms 59

2.10 The efficiency comparison between construction algorithms 61

2.11 Results of parameter tuning 63

2.12 The results of the A-ALNS algorithm 66

3.1 Parameter Setting 86

3.2 Taxi fare rate for calculating the profit introduced in [14] 87

3.3 The number of taxi requests need to be served in two scenarios 87

3.4 The routing results of four algorithms in the first scenario 88

3.5 The routing results of four algorithms in the second scenario 89

3.6 The efficiency of the algorithm based on the predicted information 90 3.7 The profit of scheduling algorithm using our proposed learning method 92

LIST OF FIGURES

1.1 An example of the CVRP problem 12

1.2 Rich vehicle routing problem 17

1.3 A classification 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 28

2.2 An example of vehicle itineraries in the MTDLC-VR problem 30

2.3 Results of solving the MIP model on random generated instances 58

2.4 Results of solving the MIP model on real small instances 58

2.5 Solution visualization of instance E21-1-2-4-6-5 59

2.6 The efficiency of operators 64

2.7 The number of requests removed from the solution for violating the lower-bound capacity constraints 68

3.1 An example of candidate taxi routes from the last drop-off point to the parking locations 73

3.2 Overfitting in piecewise-polynomial regression on the San Francisco taxi request data 79

3.3 The proposed learning framework 79

3.4 The exchange operator 85

3.5 The accumulated profit of four scheduling algorithms 90

3.6 The percentage of failure requests 91

As an important component of the economy, the transportation sector plays animportant role in economic development and connectivity between regions The con-nectivity is even more so in a global economy where the intensification of economiccooperation is related to the movement of people and freight Many models of trans-port of people and goods have been built in practice, such as public transportationservices with fixed routes (bus, rail, ferry, airline services), taxi services to transportpeople on call requests, container transportation, freight transportation service fromcenter depots to customers, etc In Vietnam, according to the preliminary report ofthe General Statistics Office [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 allthe energy consumption of an economy [2] Authors in [2] also specified that transportcosts account for 20 percent of the total cost of a product Cities have now become big-ger and bigger in terms of surface and population This phenomenon has caused someconsequences: severe traffic 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 efficient transport routing for people and parcels A good transport routingaims to save costs, thus bringing better profits to companies while meeting people’sdemands, significantly increasing the efficiency of transportation systems and possiblyreducing the above pointed out issues

The routing problem that finds the optimal solution for vehicle routes is called aVehicle Routing Problem (VRP) The pure VRP problems such as Capacitated Ve-hicle Routing Problem (CVRP), Min-Max Vehicle Routing Problem without capacityconstraint (MMVRP) and Pickup-and-Delivery Vehicle Routing Problem with TimeWindow (PDVRPTW) are simple models in the sense that it is usually far from thereality of the people and parcel transportation [3] In contrast, many different factorsand 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, portation of different kinds of products such as oil [4], milk [5], and frozen food [6, 7],

trans-or delivery of e-commerce packages [8] is an example of freight transptrans-ortation servicefrom 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 plications The VRP problem is a well-known NP-hard problem [13] Solving these

ap-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 tend the existing VRPs more flexibly and realistically It is crucial that new variantsare formulated and solution algorithms are developed to solve them as efficiently aspossible According to surveys from the literature as well as actual operations fromtransport companies, the routing operation is usually classified into two scenarios:static and dynamic Hence, this thesis focuses on real-life problems typical for thesetypes of VRP problems For the static VRP problem, the authors in [3] declared thatone of the most important objectives of routing problems is to balance the workloadallocation in order to ensure acceptance of operational plans, maintain employee satis-faction and morale, reduce overtime, and to reduce bottlenecks in resource utilization.Due to the limited capacity, the fixed fleet size, and time window constraints, vehiclesmust deliver product units from multiple distribution centers to customers and operatemultiple trips However, some trips of vehicles are scheduled to carry too little cargo

ex-in real-world situations due to tight time wex-indows Therefore, this thesis proposes anew variant of the static VRP problem taking into account most of the well-studiedfeatures Specifically, it is a new constraint on the lower bound of the capacity of vehi-cles that has not been investigated in the literature This dissertation formulates theconsidered problem as a mixed-integer linear programming (MILP) problem, analyzesthe challenges of the lower-bound capacity constraints and proposes an adaptive largeneighborhood search (ALNS) framework for solving it For the dynamic VRP prob-lem, a new people transport model is studied that is an extension of the share-a-rideproblem proposed by [14] In the considered model, people and parcels can share aride and information about future requests is predicted A new mathematical modeland a new anticipatory algorithm for scheduling taxis exploiting the predicted futurerequests are proposed in this dissertation

new variants of the VRP) has grown rapidly over the past decades [7, 17, 18] Moreover,the performance of current computers has increased significantly Therefore, we cansolve larger instances of the VRP, which promotes the progression in the research fieldand the development of efficient algorithms for the VRP.

VRPTW is a well-known simple extension of VRP that extends the CVRP by addingtime windows to a depot and customers General and state-of-the-art surveys on thisproblem class are provided in [19] In [20], the authors implemented the Priority-basedHeuristic Algorithm for solving perishable food products delivery problems to maximizecustomer satisfaction In their model, customer satisfaction includes the freshness ofdelivered food Thus, the time window constraint of each customer demand is relativelytight Especially, the works in [21] investigated VRP with multiple prioritized timewindows for distributing confectionery and chocolate products in Iran Due to thecomplexity of their problem, a binary artificial bee colony algorithm tuned via theTaguchi method is developed to solve it Then, [22] reviewed VRPTW applicationsrelated to freight transportation that most logistics and distribution companies face intheir daily operations

The MDVRP arises as a generalization of VRP, where vehicles depart from andreturn to multiple depot locations [23] surveyed several studies on the MDVRP based

on either complete or incomplete methods In terms of complete algorithms, [24] sented a branch-and-cut-and-price algorithm to find the optimal solution of a variation

pre-of VRP in which vehicles have different capacities and fixed costs, located at differentdepots An exact method-based heuristic is proposed by [25] to solve the MDVRPproblem in which each subproblem becomes a single depot VRP and evolves indepen-dently in its domain space In [26], four fuzzy simulation-based heuristic algorithmsare also designed to search the exact solution of the MDVRP for hazardous materi-als transportation Regarding incomplete algorithms, [27] and [28] proposed variants

of the Variable Neighborhood Search algorithm for solving the MDVRP problem In[28], the authors considered a multi-depot multi-compartment vehicle routing problem,where the cargo space of each vehicle has multiple separate compartments to transportdifferent products simultaneously In the context of our problem, these compartments

of vehicles are adjustable Therefore, we only consider constraints on the total availablecargo space on each vehicle Recently, many heuristic methods have been developed inthe context of the MDVRP, including the genetic algorithm [29], the local search algo-rithm [30], and a variable tabu neighborhood search [31] In [31], their algorithms can

be implemented to solve the Multi-Depot Open Vehicle Routing Problem (MDOVRP),which is a generalization of the MDVRP [32] also considered the MDOVRP and de-veloped a general multiple variable neighborhood search hybridized with a tabu searchstrategy for solving it However, the complex objectives and constraints often lead tovarious solution spaces These challenges lead to considerable research efforts in em-

bedding learning mechanisms for more efficient neighborhood search through adaptiveneighborhood selection In [33], the authors proposed a hybrid ALNS algorithm that iscompetitive compared with the algorithm in [32] Their algorithm combines the ALNSstrategy with three insertion, five removal heuristics, and four post-optimization localsearch procedures In the MDOVRP model, vehicles do not return to their startingpoint after serving the last customer In our model, although a vehicle can also visitdifferent depots on different trips, it must return to a parking area after serving thelast customer The ALNS algorithm is also adapted for dealing with large probleminstances Furthermore, the advanced extension of the problem by combining MDVRPwith MTVRP is studied in this thesis.

The MTVRP was first proposed by [34], where a vehicle makes several journeysduring a day [35] proposed a mathematical programming model based on a set coveringformulation for MTVRP Recently, a branch-and-price algorithm in [36], and the firstexact solution framework based on a novel structure-based formulation in [37] werepresented to solve the MTVRP For incomplete algorithms, it is common to solve theMTVRP by combining VRP and packing procedure [38, 39, 40] The authors in [38]studied the one vehicle version with multi-trip in a route (a trip is called leg by theauthors) and considered the capacity of the vehicle as an output (i.e., the vehiclecapacity is not fixed) That is, their model proposed an approach to select the bestcapacity and the best route, in order to minimize the acquisition cost function andthe distance traveled In [39], the authors proposed an adapted ALNS algorithm thatiteratively modifies a CVRP solution and applies bin packing techniques to assign thecreated routes to available vehicles Their model assumed that the serving time at thedepot was fixed In contrast, the loading time-dependent at the depot is considered

in works of [41] which designs routes to replenish stocks for a cafe company aroundSingapore They also developed a hybrid ALNS algorithm that employs two-variableneighborhood descend operators However, both of those papers considered only onesingle depot A survey on the MTVRP can be found in [42]

A combination of the above problems has more practical applications Recently,more attention has been focused on the multi-trip multi-depot VRP with specific combi-nations of real-life constraints They also apply their model to transportation problemsfor different kinds of commodities For example, [43] proposed three metaheuristics tosolve the multi-trip multi-depot heterogeneous Dial-a-Ride problem Two-hybrid beealgorithms and an ALNS are presented These methods are highly effective and ef-ficient [44] also considered a multi-trip multi-depot VRP problem in which vehiclesmust pick up meals from multiple suppliers and deliver them to customers Their prob-lem under logistics resource sharing is solved by two popular algorithms: local searchand ALNS In the ALNS algorithm, the authors proposed a supplier-oriented removaloperator and three rules to choose a specific range of insertion for each insertion op-

erator Their results show that the sharing service has a significant advantage overthe exclusive service In addition, [8] first proposed a multi-trip multi-depot VRPTWwith release dates Their problem originates from the e-commerce package delivery inChina In their model, each trip starts and ends at the same depot The release dateintroduced in their paper is when the package requested by a customer in the distri-bution center can be delivered by a vehicle Therefore, they considered the practicesthat 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 Asummary of the assumptions of related papers is presented in Table 2

Table 2: A summary of the related papers.

Multi- Multi- Trip No sta- Service- Time Lower- Com- trip depot limi- rt at depend- window bound plete plete

Incom-tation depot ent time capacity

of served customers and minimize the number of vehicles related to their availability

In our model, there are three types of points with different accessibility: points visitedone time in one-way direction (parking areas), points visited many times (distributioncenters), and points visited at most once (customers) Besides, the existence of servicesharing leads to the objective function of minimizing outsourcing costs The loadingtime at distribution centers and the unloading time at customers are depended on theproduct type and the product quantity Moreover, in the context of the MTDLC-VRproblem, dairy products are always available at distribution centers Managers areoften concerned with occupancy product rates in vehicles Thus, new lower-boundcapacity constraints are added to our model To the best of our knowledge, no workhas been conducted to address this problem

Most of the above studies deal with the VRP problem in the static scenario, where alldata 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 dynamicallyupdated while executing the current simulation [45] A neighborhood search heuristics

to optimize the routes of vehicles for dynamic PDVRPTW problems is proposed by

[46] The taxi routing problem can be seen as the specific practical application ofPDVRPTW problems in the dynamic scenario, firstly introduced by [13] as a Dial-A-Ride problem (DARP) Authors in [14] described a SARP problem and solved it in bothstatic and dynamic scenarios In that paper, the authors explained the conceptual andmathematical model of the DARP problem, where the same taxi network serves peopleand parcels There are new variants of this model and some heuristic algorithms thathave been proposed by [9, 10] to solve this problem As DARPs are NP-hard, theyare usually solved by heuristic approaches [47, 48, 49] Although the integration oflogistics and transportation into multiple modes of transportation with ridesharinghas received much attention, the number of studies remains limited [50, 51] Evenfewer studies have sought an efficient solution to the SARP of people and goods overrelatively short transportation distances [52, 53] A smart taxi-routing system based

on a histori- cal data analysis can improve the operational efficiency of drivers andoptimize the overall travel efficiency However, it appears that most researches haveopti- mized only the total route distance of all current events on the schedules [9, 54]

In the dynamic scenario, one of the novel components is the dispatch system withunknown requests, which aims to suggest more efficient routes for drivers as well as toserve more than requests by using the learned arrival rate of taxi requests Applyingthe learned information to the routing problem, this thesis attempts to maximize theoverall travel efficiency while minimizing the idle time of a driver

Motivation

The optimization of transportation has become a great issue in recent years Therouting problem is a new challenge for the transportation sector: improve productivityand reduce costs by increasing the number of served clients, reducing the time and cost

of transportation to achieve good human resources planning and efficient operation.The research on the VRP is beneficial not only to transportation companies but also

to society

With economic development, parcel distribution is one of the most significant staticVRP models Complete models and appropriate algorithms need to be developedfor the product distribution problem of the company in Vietnam as well as similarproblems around the world This motivated us to fill a gap in the literature on someVRP problems by combining real-world factors to extend these problems more flexiblyand realistically

For people transportation models, one of the most preferred transportation modesfor people in urban areas is taxi services due to its convenience, flexibility, and inno-vative operation strategies, e.g., integration of passenger and parcel transportation oneach taxi aims to discount the passenger Smart ridesharing services can be realizedthrough the convergence of location-based devices, geographic information systems,

global positioning systems, and wireless communication In addition, they enable thedeployment of intelligent routing services The motivation is to consider the share-a-ride taxi routing problem based on predictive information in online scenarios A smartrouting system based on historical data analysis can improve the operational efficiency

of drivers and optimize overall travel efficiency

Methodology

The methodology of this dissertation are as follows:

• Theoretical study of variants of the VRP problem as optimal problems

• Analyzing the related works to the considered problems

• Designing the practical and useful models of the VRP problem

• Proposing efficient metaheuristic algorithms to solve the investigated VRP models

Scope of Research

VRP problems are complex NP-hard problems that include many subproblems andvariants Therefore, the scope of my thesis is to investigate two practical transportationproblems 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 Theproblem considers specific combinations of real-life constraints to tackle real problems

in one of the biggest dairy companies in Vietnam In the class of dynamic VRP lems, 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]

prob-in which people and parcel requests are scheduled on the same taxi network The sidered problems are known as the NP -hard problems Moreover, the combination ofreal-life constraints makes the problem more challenging Therefore, the thesis mainlyfocuses on heuristic/metaheuristic algorithms for solving the proposed problems

con-Contributions

The three main contributions of the thesis are as follows:

• With the goal of developing parcel transportation models to cover real-life lems, the thesis has defined a novel product transportation problem for real-worldapplications taking into account most of the well-studied features, especially with

prob-a new constrprob-aint on the lower bound of the cprob-approb-acity of vehicles which hprob-as notbeen investigated in the literature The thesis formulates the considered problem

as a MILP model and proposes some efficient metaheuristic algorithms to solve

it Experiments are performed in various scenarios to examine the efficiency of

algorithms The quality of solutions and computation time are compared with isting methods and some insights are presented on each algorithm’s use in differentinstances.

ex-• For people transportation models, a new variant of the share-a-ride taxi portation routing model in the dynamic scenario is developed in this thesis Inthis model, people and parcels are served in the same taxi network in which therouting system needs to recommend the best route to the driver of a taxi withoutload so that the chance of receiving a new transportation demand is high whenthe taxi is still available We propose a new efficient algorithm for routing taxisand exploiting the predicted future requests Our model alleviates the deficiencies

trans-of the models in [9, 14] by considering the best route for the taxi driver withoutload The algorithm is experimented on real data sets in San Francisco city andcompared with the methods for DSARP in [14] under the same parameter settings

• This thesis proposed an adaptive and data-driven binning method for learning thenon-homogeneous Poison process (NHPP) to predict future transport requeststhat help minimize the vehicle’s idle distance The experimental results provethat applying improvement of traveling direction in routing based on the demandprediction leads to flexible movement and overall traveling efficiency This studylinked transportation problems with machine learning which is expected to copewith traditional traffic problems

Organization of the Dissertation

This dissertation is organized as follows

• Chapter 1 provides some background about VRP problems such as tion Problems, CVRP, PDVRPTW, SARP, RVRP problems and state-of-the-artapproaches for solving them

Optimiza-• Chapter 2 is the first of two chapters that detail the research on the RVRP lems carried out in this thesis The product distribution problem is discussed inthis chapter and an adapted ALNS algorithm is proposed for solving the prob-lem A strategy including generating initial solutions and subsequently applying

prob-an adaptive large neighborhood search (A-ALNS) to improve the quality of lutions is also proposed The performance of the proposed A-ALNS algorithm

so-is compared with that of other heurso-istics by conducting extensive numerical periments to evaluate the applicability of the proposed algorithm in real-worldapplications

ex-• Chapter 3 starts the investigation of the people and parcel share-a-ride taxi portation problem in the dynamic scenario, which is the more realistic variant of

trans-the dynamic VRP problem The considered problem is an extension of trans-the work

in Li et al 2014 and Nguyen et al 2015 A data-driven learning method is oped to predict the new transport requests and an efficient algorithm is proposedfor routing taxis and exploiting the predicted future requests

devel-• To conclude, Chapter Conclusion and Future works summaries the research thathas been undertaken in this thesis and outlines avenues for further research

Chapter 1 BACKGROUND

This Chapter will provide basic knowledge relevant to the VRP, the concepts of timal problems, and solution methodologies for solving the optimization problems Es-pecially, the basic concepts of heuristic/metaheuristic algorithms are described Theseconcepts will be used throughout the dissertation

mini-Definition 1 [55] 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, , nwhere x = {x1, x2, , xn} is the vector of decision variables, m is the total number ofconstraints, m∗ is the number of equal constrains and Di is the domain of variable xi

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

gj ≥ 0by multiplying the constraint equations by −1 Given a finite set Sf of feasiblesolutions x A globally optimal solution is the solution bx that minimizes objectivefunction value (i.e., f(bx) ≤ 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 morecomplex And then, OPs can be seen as problems that search the best solution in alarge set of candidate solutions in a reasonable time

OPs can be classified into two categories [56]:

• A discrete optimization problem is modelled including some or all of the variablesrequired to belong to a discrete set For example, an integer or a permutation or

a graph must be found from a countable set

• A problem with continuous variables is known as a continuous optimization lem, in which the variables are allowed to take any value within a range of valuesand the optimal value is found from a continuous function

prob-There are many applications of the OP problems in areas such as energy resourceplanning, construction management, jobs to machines allocation, portfolio selectionand vehicle routing Finding the optimum or best solution is one of the importantsteps to save costs and thus bring better profits 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 maintypes of methods for solving the OP problems: exact methods and incomplete methods

An exact method allows to find optimum solutions, and the other method, usually calledheuristic or metaheuristic, focuses on systematically finding an acceptable solutionwithin a limited number of iterations and does not guarantee to obtain an optimalsolution

1.2 Vehicle Routing Problem and Extensions

VRP is an optimization problem given to a whole class of problems involving thevisiting of customers by vehicles, also known as a NP-hard problem [57] We canget different types of VRP extensions by combining different extended criteria withthe classical VRP Several well-known extensions of the VRP closely related to theproblems 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 fixed fleet of homogeneous vehicles must scheduled to serve dertermined customerdemands for a single commodity from a specified depot at minimum shipping cost[13] In the CVRP, there is limitation to the loading capacity of each vehicle TheCVRP 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 vertexesand E = {(i, j) : i, j ∈ V } is a set of arcs Vertex 0 relates to a depot for a fleet

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) impliesthat S = {i} We define the lower bound on the number of vehicles required to visitall vertexes by r(S) = ⌈Pi∈S d i

Q ⌉ The integer variable xi,j denotes the number of timesarc (i, j) ∈ E is traversed in the solution The CVRP formulation proposed by [58] isthen:

(i,j)∈E

Figure 1.1: An example of the CVRP problem.

to the depot is equal to the number of vehicles In the constraints (1.4), both theconnectivity of the solution and the capacity constraints are stated The remainingconstraints (1.5) and (1.6) specify the definition domains of the variables 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 customerdemand of each customer is displayed in brackets

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 lem with Time Windows (PDVRPTW), which comes from real-life transport situations,

Prob-is much more complicated than the CVRP In the PDVRPTW, it Prob-is generally required

to find one or more minimum cost routes to serve a number of customer requests,where each request is defined by a pickup point, a corresponding delivery point, and

a demand (goods or passengers) to be transported between these locations within apredefined time window The PDVRPTW problems can be widely applied in areassuch as express package delivery from senders to receivers, food collection and delivery,and taxi operation

Following the notation introduced by [59], the PDVRPTW problem can be lated on a graph G = (V, E), where V is the set of points, consists of the set of pickuppoints O = {1, 2, , n}, the set of delivery points D = {n + 1, n + 2, , 2n} and thedepot points {0, 2n+1} The set of edges denoted by E represents feasible connectionsbetween points Each request consists of information about a pickup point i, deliverypoint n+i and demand di units need to be transported from point i to point n+i Let

formu-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 simustbegin 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 flow able xk

vari-i,j = 1 if and only if vehicle k travels on edge (i, j) ∈ E in the optimal solution,

0 otherwise; the time variable STk

i represents the starting service time of vehicle k atpoint i ∈ V ; and variable Wk

i specifies the load of vehicle k after leaving point i ∈ V The problem can be formulated as the following MIP formulation:

xki,j, ∀i ∈ O ∪ D, ∀k ∈ K, (1.11)

X

i∈V

xki,2n+1 = 1, ∀k ∈ K, (1.12)(STki + si+ ti,j)xki,j ≤ STkj, ∀i ∈ V, ∀j ∈ V, ∀k ∈ K, (1.13)(Wik+ dj)xki,j ≤ Wjk, ∀i ∈ V, ∀j ∈ V, ∀k ∈ K, (1.14)

STki + si+ ti,n+i ≤ STkn+i, ∀i ∈ O, (1.15)

STk2n+1− STk0 ≤ Rk, ∀k ∈ K, (1.16)

ei≤ STki ≤ li, ∀i ∈ V, ∀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)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 exactlyonce and by the same vehicle Constraints (1.10)-(1.12) keep a multicommodity flowstructure and guarantee that all vehicles start at the starting depot and end at the re-turning 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 thepickup node before the delivery point Constraint (1.16) bounds the duration of eachroute Finally, Constraints (1.17) and (1.18) are related the time-window and capacityconstraints, respectively, while Constraint (1.19) specifies 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)[60] The DARP consists of designing vehicle routes and schedules for a number of userswho request pickup and drop-off points A routing system receives a large number ofrequests to transport people and goods during fixed 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 thefact that people and parcels share the same taxis It means that people and goods areserved by the same taxi network

We denote the number of requests by η = m + n, where m is the number of parcelrequests and n is the number of people requests The SARP is defined on a completeundirected graph G = (V, A), where V = Vp∪ Vf ∪ {0, 2η + 1} Subset Vp = Vp,o ∪

Vp,d(set of people pickup and delivery points) and Vf = Vf,o ∪ Vf,d (set of parcelpickup and delivery points) correspond to people and parcel stops, respectively, whilenodes 0 and 2η + 1 represent the starting and terminating depots There is a set oftaxis K, each taxi k ∈ K has a capacity Qk and the total duration of its route cannotexceed Tk Each point i is related to a load qi such that q0 = q2η+1 = 0, qi = −qi+η(i = 1, 2, , η) A time window [ei, li] is also related to point i ∈ V , where ei and liare the earliest and latest time, respectively The notations dij and tij are the traveldistance and time from point i to point j (∀(i, j) ∈ A) Let Xk

ij = 1, if vehicle ktravels from node i directly to node j (∀(i, j) ∈ A, ∀k ∈ K) The variable τk

i is thetime that vehicle k begins to serve node i, and wk

i is the load of vehicle k after visitingnode i (∀i ∈ V , ∀k ∈ K) For each people pickup point i (i ∈ Vp,o), rk

i denoteshis/her ride time on vehicle k, ωi represents the maximum ride time of i Let α and

β be the initial profit; σ1 and σ2 be the average profit per kilometer obtained from

a people and a parcel, respectively The fixed cost per kilometer is denoted by σ3

We denote the discount factor for exceeding the direct delivery time of people by σ4.Finally, the variable Pi∈ {1, 2, , 2(η + 1)} defines the serving sequence of taxis, and

ν represents the maximum number of requests that can be served between one people.The formulation of the SARP is as follows:

− σ3Xi∈V

Xjik, ∀i ∈ Vp∪ Vf, ∀k ∈ K (1.25)

τjk ≥ (τik+ tij)Xijk, ∀i, j ∈ V, ∀k ∈ K (1.26)

at its destination point The flow constrain is defined by Constraint (1.25) The traveltimes and loads of taxis are computed by Constraints (1.26) and (1.27), respectively.Constraint (1.28) defines the ride time of requests and Constraint (1.29) ensures theworking hours of taxi drivers The time window constraints are defined in (1.30).Constraint (1.31) guarantees that any people request must be served within a given timeperiod, and the people pickup point is visited before the delivery point Constraints(1.32) and (1.33) define the taxi capacities Constraints (1.34) and (1.35) represent theservice sequence of the requests Constraint (1.36) states that a people request has ahigher priority.

1.2.4 Rich Vehicle Routing Problem

The new tendency is mainly focused on applying the VRPs and their extensions toreal-life problems by combining multiple constraints That problem is called a RichVehicle Routing Problem (RVRP) While the standard VRP is the classical problemformulation, the RVRP covers additional requirements arising from practical scenariossuch as Multi-Depot Vehicle Routing Problem (MDVRP), Multi-Trip Vehicle Rout-ing Problem (MTVRP), Vehicle Routing Problem with Backhauls (VRPB), Min-MaxCVRP (MMCVRP) and so on

Figure 1.2: Rich vehicle routing problem.

In the MDVRP problem, there are several depots where vehicles can pick up goods

to transport to customers or deliver goods taken from customers Therefore, someroutes will have different starting or ending points Besides, the MTVRP problemallows a vehicle to serve multiple routes in a working day As in the PDVRP, theVRPB problem is an extension of the standard VRP problem where there are twotypes of customers The first one is the inflow customers who need to receive a certainamount of goods The second is the outflow customers who need to return a certainamount of goods to the depot Hence, the outflow customers must be served after all theinflow customers have been served in a route In real-life problems, there exists a specialVRP problem, called a MMCVRP problem, whose objective is not to minimize the totaltravel distance or the total transit cost of the routing solution but to minimize the traveldistance or the travel time of the longest route in the routing solution Moreover, thereexists also VRP problems where the existence of the input fields is known in advance,but specific values of them are not available at the scheduling time point or revealedduring execution, for example, real-time data such as current vehicle locations [61],new customer requests [62], and periodic estimates of road travel times [63] Theseelements are considered in the Dynamic Vehicle Routing Problem (DVRP) Severalhybrid variants have been created in the literature from these variants, all inspired

by real-life scenarios such as share-a-ride or multi-trip multi-depot or undeterminedquantity of demand or undetermined quantity of travel time and so on Figure 1.2presents several extensions of the standard VRP Many VRP acronyms referred to as

a variant of VRP problems have been developed to consider combinations of real-lifeconstraints All these new combinations can be encompassed in the larger family ofRVRP Several problems are investigated and explained in Chapters 2, ?? and 3

1.2.5 Static Routing Scenario

In static scenario of a VRP problem, inputs of the problem do not change eitherduring the execution of the algorithm that solves it or during the eventual execution

of the route [64, 65] More precisely, VRP problems in the static scenario (so-called

static VRP problems) only focus on the generation of the best tour solution beforethe transportation process is executed and the information as input data revealedduring execution time is not considered The objective of the static VRP problemsoften addresses the minimization of transit costs (or the revenue maximization) such

as transit distances, transit times, and the number of utilized vehicles [66]

1.2.6 Dynamic Routing Scenario

The processing of real-time data is more and more feasible and diverse due to thedevelopment of communication technologies Therefore, real-time routing scenarios, inwhich the problem information (such as new requests, status and location of vehicles,actual customer demand) is dynamically revealed to the dispatcher, are becoming moreand more important A dynamic VRP problem considers the problem information may

be changed during the execution of the algorithm that solves it or the eventual execution

of the route It means that the problem information is time-dependent In this case,queuing considerations may become necessary By using the queue theory, the dynamicproblem is considered as a sequence of static problems (subproblems) consisting ofthe currently pending requests Therefore, most approaches use fast approximationmethods that give a good solution in a relatively low computational time Differenceswith static VRP problems are pointed out by [67, 68]

The most common source of dynamism in VRP problems is the online arrival ofcustomer requests during the operation The author in [69] states that the unexpectedoccurrence of new requests may lead to situations in which it becomes very difficult

or impossible to service all pending requests However, some information availableabout future events is known with uncertainty (forecasted) The utilization of goodforecasted stochastic information can lead to a superior system performance compared

to applying a deterministic real-time control approach that only considers informationknown with certainty [70] In VRP problems, the quality of services greatly depends onthe performance of the routing techniques, for example, a smart taxi routing system canimprove the operational efficiency of drivers and optimize the overall travel efficiency

by using historical data

1.3 Solution Methodologies for VRP problems

Different methods to solve the VRP have been explored The current VRP ologies can be divided into two categories: exact methods and incomplete methods.While the exact methods find the optimal solution for small to medium-sized prob-lems (up to about 50–100 customers) with relatively simple constraints, the incompletemethods explore near-optimal solutions for medium and large-sized problems with morecomplex constraints Even though the VRP has been studied for decades, and a largeset of efficient exact and incomplete methods have been developed for more realistic or

method-Figure 1.3: A classification of the VRP methods.

RVRP problems Following the survey of [71], Figure 1.3 presents a tree that classifiesthe family of VRP methodologies

1.3.1 Exact Methods

An exact method can provide the optimal solution to the problem if there is sufficientexecution time The method is often applied to small-sized instances of VRPs Ingeneral, the most efficient exact algorithms often try to slim the searching space andthen reduce the number of different alternatives that need to be exploited in order

to obtain the optimum solution Some widely-used exact algorithms that have beenapplied to solving optimization problems are the following [67]:

• Dynamic Programming: The Dynamic programming (DP) approach is similar

to divide and conquer in breaking the origin problem down into simpler problems in a recursive manner and using the fact that there is a relation betweenthe optimal solution of the larger problem and the optimal solution of the sub-problems The main idea is to store the found solution of subproblems so that

sub-we do not have to re-compute them when needed later DP is used when thesubproblems are not independent Therefore, the optimal solution of the originalproblem depends on the optimal solution of subproblems DP offers two methods

to solve a problem The first method is top-down with a memorization approach.This approach tries to solve the bigger problem by recursively finding the solution

to smaller sub-problems Whenever a sub-problem is solved, its result is cached

so that it does not end up repeatedly solving (if it is called again) The otherapproach is bottom-up with tabulation, where tabulation is the opposite of thetop-down approach and avoids recursion This approach solves all the relatedsub-problems first, combines the solution of smaller subproblems to solve largersubproblems and eventually arrives at a solution to complete the problem

• Branch-and-bound/cut/price: The Branch-and-Bound (BnB) algorithm

con-sists of a systematic enumeration of candidate solutions The complete set of ble solutions is partitioned into smaller subsets of solutions, representing branches

feasi-of a rooted tree The BnB is based on the principle that each branch is checkedagainst upper and lower estimated bounds on the optimal solution and is removed

if it cannot provide a better solution than the best one found so far by the rithm The Branch-and-Cut (BnC) algorithm involves running a BnB algorithmand using cutting planes to tighten the linear programming (LP) relaxations Thelatter principle is to add new constraints (so-called cutting planes) to obtain wholesolutions The cutting-planes are generated throughout the BnB tree Many VRPsinvolve variables that are not continuous but instead have integer values, and theycan be solved by BnC method The Branch-and-Price (BnP) algorithm is a hybrid

algo-of BnB and column generation methods The philosophy algo-of BnP is different fromthat of BnC in that columns generation is being added instead of cut planes beingadded in BnC In BnP, sets of columns are excluded from the LP relaxation in or-der to reduce the computational and memory requirements because most of themwill have their associated variable equal to zero in an optimal solution anyway.The pricing part refers to the iteratively solved pricing subproblem in the columngeneration process These columns are generated iteratively by solving subprob-lems or pricing problems and applied throughout the branching and bound treeprior to branching

• Constraint Programming: The basic idea in Constraint Programming (CP) isthat the user declares the constraints on the feasible solutions for a set of decisionvariables and then specifies a solver to solve these constraints When each feasiblesolution is found, the objective function value is evaluated and constraint prop-agation is performed Constraints are just relations and a constraint satisfactionproblem states which relations should hold among the given decision variables

CP is based on feasibility, i.e., it focuses on finding a feasible solution rather than

an optimal solution Constraint violation elimination and domain reduction ofvariables have higher priority than optimization of the objective function value.Thus, the general algorithms are usually concerned with reducing the search spaceand specific search methods The main mechanism for solving a problem using

CP is called constraint propagation and the algorithms using the one are calledconstraint propagation algorithms So these algorithms potentially reduce thesearch space and consequently attempt to limit the rapid increase in the number

of combinations

1.3.2 Incomplete Methods

1.3.2.1 Classic Heuristics

A heuristic is an incomplete algorithm that provides a good quality feasible solutionwithin reasonable computer time but it does not guarantee that the found solution isthe optimal solution or the same solution quality is found every time the algorithm isrun Heuristic algorithms are often used to solve NP-hard problems such as VRP prob-lems Classical heuristics for the VRP are naturally divided into constructive heuristicsand improvement heuristics A constructive algorithm builds a feasible solution fromscratch, while an improvement algorithm tries to find a better solution based on alreadyavailable solutions

In [72], authors classified classical heuristics for the VRP in three classes:

• Constructive heuristics: The heuristic is characterized by a constructive methodthat refers to the approach of generating feasible solutions that are used as astarting point for the improvement process, for example, Saving Algorithm [73],Sequential Insertion Heuristic [74]

• Two-step heuristics: A two-step method uses either Route-First Cluster-Second(RF-CS) strategy or Cluster-First Route-Second (CF-RS) strategy In the CF-

RS approach, customer points are first grouped into clusters, and each route isseparately defined by solving a Travelling Salesman Problem (TSP) within eachcluster The most widely used technique, the Sweep Algorithm (SW), has beenproposed by [75] for the clustering phase and referred to as the first example ofthis approach Another adaptation of these ideas can be found in [76, 77] Thesecond approach was firstly proposed by [78] In this approach, a giant TSP tour ofoverall customers is constructed in the first stage and later subdivided into feasibletrips In the last decade, the RF-CS approach has led to successful constructionheuristics and metaheuristics for CVRP and VRPTW problems The detail can

be found in [16, 65, 79]

• Local Search: Local Search (LS) is an alternative technique that aims at finding

a high-quality solution to an OP problem in polynomial time LS algorithms startfrom a feasible solution and then move to a neighbor solution (modifying some ofits components in an appropriately defined neighborhood of the current solution)

to try to improve it until some criteria are reached The notion of neighborhood

is essential to understand LS, is defined as follows:

Definition 2 [55] The neighborhood N (s) of a solution s is a function N : S →

2S that assigns to every s ∈ S a set of neighbors N (s) ⊆ S

Definition 3 [55] A local optimum of the minimization OP can be defined as acandidate solution s for which it holds that ∀s ∈ N (s), we have f (s) ≤ f (s)

Figure 1.4: An illustration of search space for a minimization problem.

The local optimums (s1 and s2) and the global optimum (s∗) in a search space of

an OP problem is illustrated by Figure 1.4 A general outline of the LS algorithm

is presented in Algorithm 1 which is based on [80] The algorithm starts from

an initial solution (line 1), iteratively considers one of its neighbors and decideswhether to accept this neighbor as the new current solution or not (lines 3-7).The function M identifies a set of legal solution (the definition of legality depends

on the given problem and LS algorithm), and then the function K selects one

of these legal solutions However, the LS approach searches on a single path of

Input: Input: an OP instance, functions f, N, M, K with

3 while stop-criterion not met do

4 if the solution s has no violation and f (s) < f (s∗) then

solutions, not a tree of solutions A number of moves on the solution are evaluated

at each solution, and the most appropriate move is applied to take the next step

on this path Therefore, the LS approach is a popular heuristic method for itsability to sacrifice optimality or accuracy of solutions against computation time

By spending more execution time, we will generally get better solutions If thenumber of neighbors is polynomial in the instance size and the objective function

(a) Current solution (b) A neighbor

Figure 1.5: Illustration of one-point move

is computable in polynomial time, then determining a candidate solution is a localoptimum or not can also be done in polynomial time We describe in this partthe seven popular neighborhoods proposed in the literature for solving VRPs.The neighborhoods we consider in our algorithm are described in [81] includ-ing one-point-move, two-point-move, two-opt-move, or-opt-move neighborhood,three-opt-move, three-point-move, cross-exchange neighborhoods All of theseneighborhoods will be considered in our proposed local search algorithm Figure1.5 illustrates one-point-move neighborhood in which point 3 will be removed fromits current route and re-inserted right after point 7 Figure 1.6 illustrates two-point-move neighborhood in which points 3 and 6 are removed from its currentroute and then, point 3 is re-inserted right after point 5 and point 6 is re-insertedright after point 2 Figure 1.7 illustrates two-opt-move in which links (2,3) and(7,8) are removed from their current routes Then, the disconnected parts of theseroutes are re-linked together Figure 1.8 illustrates or-opt-move neighborhood inwhich a sequence of points ⟨3, 4, 5⟩ of a route is removed from its current routeand re-inserted to another route Figure 1.9 illustrates the three-opt-move neigh-borhood in which three links (2,3), (4,5), and (6,7) are removed from their currentroute, then disconnected parts of this route will be re-linked together Figure 1.10illustrates the three-point-move in which the positions of a link (7,8) and a point

3 are exchanged: link (7,8) is re-inserted at the position of point 3 and point 3 isre-inserted at the position of link (7,8) Figure 1.11 illustrates the cross-exchangeneighborhood in which we select two routes, two links of each route are selectedand removed Then the disconnected parts of these routes are re-linked together

(a) Current solution (b) A neighbor

Figure 1.6: Illustration of two-point move

Figure 1.7: Illustration of two-opt move

Figure 1.8: Illustration of or-opt move

Figure 1.9: Illustration of three-opt move

Figure 1.10: Illustration of three-point move

Figure 1.11: Illustration of cross-exchange move

and diversification are two main features of metaheuristic algorithms [65, 82] erally, the concept of "diversification" refers to the exploration of the search space,whereas "intensification" defines the exploitation of the accumulated search experi-ence Therefore, all metaheuristic algorithms use some trade-off of local search andglobal exploration For summarizing, fundamental properties that characterize mostmetaheuristics are listed as follows [82, 83, 84].

Gen-• Metaheuristics are strategies referred to as "heuristics guiding other heuristics"

• Metaheuristics are used to find efficiently near-optimal solutions

• Techniques which constitute metaheuristic algorithms range from simple localsearch procedures to complex learning processes

• Metaheuristics usually incorporate mechanisms to continue the exploration of thesearch space after a local minimum is encountered

• The basic concepts of metaheuristics permit an abstract level description

• Metaheuristics are not problem-specific and usually non-deterministic

• Metaheuristics are high-level strategies that control the using domain-specificknowledge in the form of heuristics

• Today’s more advanced metaheuristics use search experience (embodied in someform of memory) to guide the search

The notable performance of metaheuristic algorithms is due to how they imitate thebest features in nature For example, Greedy Randomised Adaptive Search Procedure(GRASP), Adaptive Large Neighborhood Search (ALNS) [85, 86], Genetic algorithms(GA), Ant Colony System (ACS) and Particle Swarm Optimisation (PSO) are the mostcommon and studied metaheuristics which have been used for solving VRPs and otherOPs Each algorithm has its own advantages or drawbacks It is clear that some algo-rithms only outperform others for given types of optimization problems [83, 87] statedthat an algorithm outperforms another algorithm for some optimization functions butmay be inferior for other functions In other words, there are no universally betteralgorithms We believe that there is no universal framework based on our experiences.Thus, the main objective would be either to choose the most suitable algorithm for agiven problem or to design better algorithms for specified problems, not necessarily forall the problems Among many metaheuristic methods, other metaheuristic algorithmsthat are not local search-based are usually population-based metaheuristics (e.g., GA,ACS, PSO) and some metaheuristic algorithms were proposed to improve local searchheuristic in order to find better solutions (e.g., GRASP, ALNS)

The static VRP requires the best solution found in reasonable execution time withsufficient computational resources Therefore, the used algorithm can explore a large

solution space However, the search should be guided by an effective strategy to balancediversification and intensification Recently, the ALNS algorithm proposed by [85] is

an efficient guidance strategy that has yielded excellent results for several differentrouting problems (see [88]) The ALNS algorithm extends the large neighborhoodsearch framework of [89], a problem solving approach which can also be related tothe ruin-and-recreate principle [85] The basic idea is to search for a better solution

at each iteration by destroying a part of the current solution and by reconstructing

it in a different way When solving VRPs, a new solution is typically obtained byfirst removing a number of customers and then by reinserting these customers intothe solution In general, a number of destruction and reconstruction operators areavailable and a destructionreconstruction pair is randomly chosen at each iteration

In the adaptive extension, a weight is associated with each operator and the selectionprobability of an operator is related to its weight, which is adjusted during the searchbased on its past successes

In dynamic VRP problems, the time to find a solution is often limited These lems usually require a limited time to provide the best or valid solution, even if thesystem’s interrupted at any time before the algorithm ends This is particularly prob-lematic for certain types of systematic algorithms that search through spaces of partialsolutions without computing complete solutions early in the search Local search-basedalgorithms are often advantageous in these situations, particularly if reasonably goodsolutions are required within a short time Local search heuristics are often built onneighborhood moves that make small changes to the current solution However, sincethe local search depends on the initial solution, there is a high probability of gettingtrapped in a local optimum Therefore, in this thesis, local search-based algorithmsare studied and improved to make more applicability for RVRP models for solvingreal-world problems The improvement provides a closer look at the applications of LS

prob-to the RVRP problems This work focuses on the adaptation of LS for several realisticRVRP problems in the following chapters

Chapter 2 MODELLING AND SOLVING A NEW VARIANT OF

STATIC VEHICLE ROUTING PROBLEM

of 10 tons carries an amount of good which is 100 kg, which is not realistic Thesetrips are cancelled because this schedule provides low profitability and causes resourceimbalances Due to this reason, new lower-bound capacity constraints on vehicles areconsidered as the hard constraints in this study More precisely, the total weight ofproducts transported in each trip must be within a given range depending on thecapacity of the operating vehicle The presence of lower-bound capacity constraintsmakes the problem more challenging One of the strategies we apply is to handle lower-bound capacity constraints as soft constraints (accept violating trip), then transfersome customers of a feasible trip to other underweight trips as illustrated in Figure2.1 In this figure, the bound of capacity is [70, 110] for each vehicle If a vehicle isscheduled to perform two trips according to a sequence of points 0, 1, 2, 3, 4, 5, 1,

8, 7, 6, 0 (see Figure 2.1a) then the second trip of the vehicle is violated the capacityconstraint In this case, there are three unserved customers However, if we transfercustomer 5 from the first trip to the second trip, the vehicle can perform both trips(i.e., there are no unserved customers) The same transfer is also applied to trips

of different vehicles (see Figure 2.1b) These transfers increase the number of served

customers without increasing the number of vehicles needed.

(a) Node transfer on different trips (b) Node transfer on different vehicles

Figure 2.1: An example of node transfers to satisfy the capacity constraints, where the lower and the upper boundaries are 70 and 110, respectively.

These realistic requirements come from one of the biggest dairy distribution panies in Vietnam With over 1000 customer points included in a plan on average,the company takes at least one working day to make a route plan To the best of ourknowledge, the lower-bound capacity constraint has not been investigated in the liter-ature for the static VRP class Besides, the combination of these real-life constraintsmakes the problem more challenging

com-The motivation of this study is to solve the problem of the company in Vietnam

as well as similar delivery problems around the world This study fills a gap in theliterature on the problem by combining some real-world factors, some of which exist

in literature while the others have not been reported The innovations of this Chapterare as follows:

• This Chapter defines a novel static VRP for real-world applications that combinethe following features:

– There are three types of spatial points in a geographical region: parkingpoints, distribution center points, and customer points

– Each vehicle can operate multiple trips and load dairy products at differentdistribution centers on different trips

– The total weight of dairy products loaded on the vehicle must be greater than

or equal to the minimum weight on each trip

– The service-dependent loading times at points are considered The loadingtime at distribution centers and the unloading time at customers depend onthe demand of customers served on each trip

– Each vehicle has a set of forbidden customers and a set of prespecified tomers

cus-• The considered problem is formulated as a mixed-integer linear programming(MILP) model Some experiments are performed on small-scale real instances,adapted benchmark instances, and generated instances by using GUROBI Opti-mizer to validate the model.

• We analyze the challenges of the new lower-bound capacity constraints, considerthis fact as a soft constraint and put it (with a specified coefficient) to the ob-jective function for comparison We propose three efficient adapted constructionalgorithms to solve this problem The results reveal that our algorithms caneffectively solve large-scale instances with up to 1256 customers, four distribu-tion centers, and two parking areas The instances and results are available onhttps://github.com/sonnv188/MTDLC-VR.git for further research and compari-son

2.2 Problem description and formulation

In this section, we formally define the MTDLC-VR problem and then formulate aMILP model that can be directly solved by commercial solvers A detailed description

of this problem is as follows

2.2.1 Problem description

A vehicle scheduling system receives a large number of requests to transport dairyproducts from distribution centers to customers during fixed working hours Eachrequest consists of information about the customer location, a valid time window, anddemand weight The system performs scheduling and routing a fleet of heterogeneousvehicles that execute their itinerary consisting of several trips: a vehicle departs fromits parking area, operates a sequence of trips, and returns to its parking area on aworking day This problem aims to obtain the maximum number of served customers,the minimum number of vehicles needed, and the best routes of vehicles to minimizethe total travel distance

The problem can be formally defined as an optimization problem (called the

MTDLC-VR problem) on a directed network G = (V, E), where V is a set of vertices that consists

of a set of parking areas PK, a set of distribution centers D and a set of customers C,and set E is an arc set that corresponds to connections between the vertices In thiscontext, no arc starts from a parking area to the other parking areas, from parkingareas to customers, from a distribution center to parking areas, and from a distributioncenter to the other distribution centers A travel time ti,j and a travel distance di,j isassociated with each arc (i, j) ∈ E We denote a set of products by P Each product

p ∈ P has weight w(p) and is available for delivery at each distribution center Eachdistribution center dp ∈ D has a window of working time [e(dp), l(dp)], the waiting