Các thuật toán xấp xỉ tìm đường xâm nhập có khả năng bị phát hiện nhỏ nhất trong mạng cảm biến dây (approximate algorithms for solving the minimal exposure path problems in wireless sensor networks)

MINISTRY OF EDUCATION AND TRAININGHANOI UNIVERSITY OF SCIENCE AND TECHNOLOGY  NGUYEN THI MY BINH APPROXIMATE ALGORITHMS FOR SOLVING THE MINIMAL EXPOSURE PATH PROBLEMS IN WIRELESS SENS

MINISTRY OF EDUCATION AND TRAINING

HANOI UNIVERSITY OF SCIENCE AND TECHNOLOGY



NGUYEN THI MY BINH

APPROXIMATE ALGORITHMS FOR SOLVING THE MINIMAL EXPOSURE PATH PROBLEMS IN

WIRELESS SENSOR NETWORKS

Hanoi, 2020

MINISTRY OF EDUCATION AND TRAINING HANOI UNIVERSITY OF SCIENCE AND TECHNOLOGY



NGUYEN THI MY BINH

APPROXIMATE ALGORITHMS FOR SOLVING THE MINIMAL EXPOSURE PATH PROBLEMS IN

WIRELESS SENSOR NETWORKS

Major : Computer Science

Code : 9480101

SUPERVISORS:

DECLARATION OF AUTHORSHIP

I assure that this dissertation "Approximate algorithms for solving the minimal exposure path problems in wireless sensor networks" is my own work under the guidance of my co-supervisors, Associate Professor Huynh Thi Thanh Binh and Associate Professor Nguyen Duc Nghia All the research results are presented in the dissertation which have never been

published by others

Hanoi, October 16, 2020Ph.D Student

Nguyen Thi My Binh

SUPERVISOR

Asso Prof Huynh Thi Thanh Binh

i

This dissertation was completed during my doctoral course at the School of Information Communication and Technology (SoICT), Hanoi University of Science and Technology (HUST) I

am so grateful for all the people who always support and encourage me to complete this study.

First, I would like to express my sincere gratitude to my co-supervisors, AssociateProfessor Huynh Thi Thanh Binh and Associate Professor Nguyen Duc Nghia I amindebted to have had advisors who gave me all the freedom, resources, guidance andsupport during the period that led up to this dissertation Their broad knowledge in di erentareas inspired me and helped me overcome many di culties in my research

Furthermore, I would like to thank all the members of Modeling and Simulation Lab,Computer Science Department, SoICT, HUST, as well as all of my colleagues in theFaculty of Information Technology, Hanoi University of Industry They assisted me a lot inthe research process and gave me helpful advice to overcome my own di culties.Furthermore, attending at scienti c conferences has always been a great opportunity for

me to receive many useful comments from the academic community

Last but not least, I would like to express my utmost gratitude to my family, my ents, my husband and my children, for their unconditional love, support, understandingand encouragement I would not be able to achieve this accomplishment without their loveand support

par-Hanoi, October 16, 2020Ph.D Student

Nguyen Thi My Binh

1.1 Wireless sensor networks 10

1.1.1 Sensors 10

1.1.2 Sensor nodes 11

1.1.3 Sensor coverage model 11

1.1.4 Sensing intensity models 12

1.1.5 Terminologies 12

1.1.6 Wireless sensor network scenarios 14

1.2 Optimization problems 15

1.3 Approximate algorithms 17

1.3.1 Single-solution-based metaheuristic 21

1.3.2 Population-based metaheuristics 22

1.3.2.1 Evolutionary algorithms 23

1.3.2.2 Particle swarm optimization algorithm 26

1.4 Conclusion 29

2 MINIMAL EXPOSURE PATH PROBLEMS IN OMNI-DIRECTIONAL SENSOR NETWORKS 30 2.1 Minimal exposure path problem in mobile wireless sensor networks 30

2.1.1 Motivations 30

2.1.2 Preliminaries and problem formulation 31

2.1.2.1 Preliminaries 31

2.1.2.2 Problem formulation 33

2.1.3 Proposed algorithms 34

2.1.3.1 The GAMEP for solving the MMEP problem 34

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2.1.3.2 The HPSO-MMEP algorithm for solving the MMEP problem 38

2.1.3.3 Complexity analysis 42

2.1.4 Experimental results 43

2.1.4.1 Experimental settings 43

2.1.4.2 Computation results 44

2.2 Minimal exposure path problem in probabilistic coverage model 50

2.2.1 Motivations 50

2.2.2 Preliminaries and problem formulation 51

2.2.2.1 Preliminaries 51

2.2.2.2 Problem formulation 53

2.2.3 Proposed algorithms 55

2.2.3.1 Grid-based algorithm for solving the PM-based-MEP problem 55 2.2.3.2 Genetic algorithm for solving the PM-based-MEP problem 56

2.2.4 Experimental results 64

2.2.4.1 Experimental setting 64

2.2.4.2 Computation results 66

2.3 Conclusion 81

3 MINIMAL EXPOSURE PATH PROBLEM IN WIRELESS MULTIME-DIA SENSOR NETWORKS 82 3.1 Motivations 82

3.2 Preliminaries and problem formulation 83

3.2.1 Preliminaries 83

3.2.1.1 The Boolean directional coverage model 83

3.2.1.2 The attenuated directional sensing model 83

3.2.1.3 Accumulative intensity function 84

3.2.1.4 Closest-sensing intensity function 85

3.2.1.5 Minimal exposure path 85

3.2.2 Problem formulation 86

3.3 Proposed algorithms 87

3.3.1 Individual representation 87

3.3.2 Individual initialization 88

3.3.2.1 HEA individual initialization 88

3.3.2.2 GPSO individual initialization 89

3.3.2.3 Fitness function 90

3.3.3 Evolutionary operators 91

3.3.3.1 Evolutionary algorithm 91

3.3.3.2 Particle swarm optimization algorithm 94

3.4.1 Experimental setting 98

3.4.1.1 Datasets 98

3.4.1.2 Parameters and system setting 99

3.4.2 Computational results 100

3.4.2.1 Algorithm parameters trials 101

3.4.2.2 Comparison under our datasets 104

3.4.2.3 Comparisons under the datasets of previous algorithms 109

3.5 Conclusion 111

4 OBSTACLES-EVASION MINIMAL EXPOSURE PATH PROBLEM IN WIRELESS SENSOR NETWORKS 112 4.1 Motivations 112

4.2 Preliminaries and problem formulation 112

4.2.1 Preliminaries 112

4.2.1.1 The truncated directional coverage model 112

4.2.1.2 The accumulative sensing intensity 113

4.2.1.3 Obstacle model 113

4.2.1.4 Minimal exposure path 114

4.2.2 Problem formulation 115

4.3 Proposed algorithm 116

4.3.1 A novel characteristic of FEA algorithm 117

4.3.1.1 Individual 117

4.3.1.2 Population 119

4.3.2 Algorithm progress 120

4.3.2.1 Initialization 120

4.3.2.2 Family pairing 120

4.3.2.3 Crossover 121

4.3.2.4 Mutation 122

4.3.2.5 Update 123

4.3.2.6 Selection 123

4.3.2.7 Family system based evolutionary algorithm 124

4.3.3 Complexity analysis 124

4.4 Experimental results 124

4.4.1 Dataset 124

4.4.2 Parameters 126

4.4.3 Computational results 126

4.4.3.1 The performance of FEA when using di erent A and D values 126 4.4.3.2 The performance of FEA when using di erent pmin and pmax values 127

4.4.3.3 Comparison between FEA and previous algorithm in OE-MEP problem 128

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4.4.3.4 Comparison between FEA and GA-MEP 1304.5 Conclusion 133

No Abbreviation Meaning

8 MWSN Mobile Wireless Sensor Networks

9 GPSO Gravitation Partical Swarm Optimization

12 HoWSNs Homogeneous Wireless Sensor Networks

13 HeWSNs Heterogeneous Wireless Sensor Networks

14 SWSN Static Wireless Sensor Networks

26 HeWMSN Heterogeneous Wireless Multimedia Sensor Networks

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LIST OF TABLES

Table 2 Comparative table of related works on MEP problem 4

Table 1.1 Evolution process versus solving an optimization problem 25

Table 2.1 Experimental parameters for attenuated disk model and truncated atten-uated disk model 44

Table 2.2 Parameters setting for GAMEP 45

Table 2.3 Experimental parameters for HPSO-MMEP algorithm 45

Table 2.4 Parameters setting for HPSO 45

Table 2.5 Di erent version of HPSO-MMEP using di erent genetic operators 46

Table 2.6 Computation results of HPSO-MMEP in comparison with GAMEP in uniform distribution of sensors (Mev: minimal exposure value, Sd: standard deviation) 48

Table 2.7 Computation results of HPSO-MMEP in comparison with GAMEP in Gauss distribution of sensors (Mev: minimal exposure value, Sd: standard devi-ation) 48

Table 2.8 Experimental parameters of probabilistic 65

Table 2.9 Experimental parameter of GA-MEP 65

Table 2.10 Experimental Parameter of HGA-NFE 66

Table 2.11 The comparison minimal exposure value, computation time and saw-tooth degree between GA-MEP and GB-MEP when using di erent subinterval s, the topology used is u 50 1 (Mev: minimal exposure value; Time(s): computation time per unit second; Dst: saw-tooth degree) 67

Table 2.12 The minimal exposure value obtain from GB-MEP and the best solution of GA-MEP when threshold A varies from 3 to 7 on the topology used is u 50 1 (GB-Mev: the minimal exposure value obtains by GB-MEP; GA-(GB-Mev: the minimal exposure value obtains by GA-MEP) 69 Table 2.13 Computation time comparison of OGB and GB-MEP when subinterval

Table 2.14 The best minimal exposure value, running time and saw-tooth degree

obtained from GA-MEP1, GA-MEP2 and GA-MEP on topology u 30 1, u 40 1, u 50

1, u 60 1, u 70 1, u 80 1, u 90 1 and u 100 1 (Mev: the minimal exposure value, Time: the computation time, Dst: the saw-tooth degree of each version GA-MEP algorithms) 71

Table 2.15 Result on Sign test for pairwise comparisons between Minimal Exposure values obtained by GA-MEP and HGA-NFE (Mev: the minimal exposure value) 76

Table 2.16 Comparison of experimental results between GB-MEP and GA-MEP (Num: number of sensors, Ord: the order of the topology, Mev: the minimal exposure value, Time: the computation time, Sd: standard deviation, Dst: the saw-tooth degree, BMev: best minimal exposure value, AMev: Average minimal exposure

value) 79

Table 3.1 Experiment instance for homogeneous binary - Dataset 1 99Table 3.2 Experiment instance for heterogeneous binary - Dataset 2 100Table 3.3 Experimental instances for homogeneous network using attenuated model

- Dataset 3 100 Table 3.4Parameters for HEA 101 Table 3.5 Parameterssetting for GPSO 101

Table 3.6 Operators setting for four versions of HEA 101

Table 3.7 Comparison between four HEA versions when running on the Dataset 1

(Heterogeneous, Binary) (Mev - Minimal exposure value, Time - Computationtime (second)) 102

Table 3.8 Parameters setting for four versions of GPSO 103

Table 3.9 Comparison between four versions of GPSO when running on the Dataset

3 (Heterogeneous, Binary) (Mev - Minimal exposure value, Time - Computationtime (second)) 104

Table 3.10 Comparison between HEA, GPSO and previous algorithms when running

on Dataset 1 (Homogeneous - Binary) (Mev- Minimal exposure value,

Time-Computational time (second)) 104

Table 3.11 Comparison between HEA, GPSO and previous algorithms when running

on Dataset 2 (Heterogeneous - Binary) (Mev- Minimal exposure value,

Time-Computational time (second)) 105

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Table 3.12 Comparison between HEA, GPSO and previous algorithms when run-ning

on Dataset 3 (Homogeneous - Attenuated) (Mev - Minimal exposure value, Time - Computational time (second)) 107

Table 3.13 Comparison between HEA and HGA-NFE when using di erent x values

(Mev - Minimal exposure value, Time - Computational time (second)) 109Table 3.14 Comparison between HPSO and GPSO when using di erent x values

(Mev - Minimal exposure value, Time - Computational time (second)) 110

Table 4.1 Parameters for FEA 126

Table 4.2 The Minimal exposure value (Mev), the computational time (sec) and

the standard deviation (Std) of FEA when using di erent pmin and pmax valueswith topology Data 3 0:15 60 2 128

LIST OF FIGURES

Figure 1 Examples of area coverage (a), point coverage (b), and barrier coverage (c) 2

Figure 2 Illustration of a general minimal exposure problem in WSNs 4

Figure 1.1 Demonstration of acoustic sensor 10

Figure 1.2 Illustration of an sensor node 11

Figure 1.3 Illustration of (a) the Boolean disk coverage model in which the red stars are the target points respectively belonging inner and outer the green sensing area of a sensor, (b) the truncated attenuated coverage model 12

Figure 1.4 Demonstration of region of interest and crossing path 13

Figure 1.5 Illustration of crossing path types 14

Figure 1.6 Demonstration of sensor network scenarios: (a) single-hop, heterogeneous, stationary network; (b) hop, homogeneous, stationary network; (c) multi-hop, heterogeneous, stationary network; (d) single-multi-hop, homogeneous, stationary network with a mobile sink 15

Figure 1.7 Illustration of local search using a binary representation of solutions, a ip move operator, and the best neighbor selection strategy The objective function to maximize is x3 x2 + x The nal local optima found is x = (11110), starting from the solution x0 = (11010) 21

Figure 1.8 Illustration of local search behavior in a given landscape 22

Figure 1.9 Illustrate of main principles of P-metaheuristic 22

Figure 1.10 A generation in evolutionary algorithms 24

Figure 1.11 Genotype versus phenotype in evolutionary algorithms 25

Figure 1.12 Illustration of particle swarm with their associated positions and veloc-ities At each iteration, a particle moves from one position to another in the decision space PSO uses no gradient information during the search 27

Figure 1.13 Demonstration of movement of a particle and the velocity update 28

Figure 2.1 Illustration of (a) the attenuated disk model; (b) the truncated attenuated disk model 31

Figure 2.2 Demonstration of input and output data 34

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Figure 2.3 Illustration of individual representation of GAMEP 34

Figure 2.4 Illustration of the single-point crossover 37

Figure 2.5 Illustration of the mutation operator 38

Figure 2.6 Individual representation for HPSO-MMEP 39

Figure 2.7 Red stars are the control points that drives the path 40

Figure 2.8 Illustration of the crossover operator of HPSO-MMEP 42

Figure 2.9 Mutation operators: (a) Inverse mutation; (b) Symmetric mutation 42

Figure 2.10 Sensor trajectory: (a) Rectangle trajectory; (b) Random point trajectory 43 Figure 2.11 E ect of s on minimal exposure value (a); computation time (b) of HPSO-MMEP 46

Figure 2.12 E ect of the genetic operators on the minimal exposure value and the computation time among di erent versions of HPSO-MMEP 47

Figure 2.13 Comparison of the minimal exposure value between random and control-point initialization methods: (a) Gauss distribution (b) Uniform distribution 47

Figure 2.14 Comparison between HPSO-MMEP and HPSO algorithm 49

Figure 2.15 E ects of the speed of intruder on the minimal exposure value from GAMEP (a) and HPSO-MMEP (b) 50

Figure 2.16 Movement of an intruder on grids 56

Figure 2.17 Individual representation 57

Figure 2.18 Execution of creating an individual in sensor eld < 59

Figure 2.19 Demonstration of executing ALXcrossover operator 59

Figure 2.20 An example of the M SP B crossover operator 63

Figure 2.21 Demonstration of the Gene-removal mutation operator 63

Figure 2.22 The computation of the saw-tooth degree 66

Figure 2.23 The chart presents the minimal exposure values, the computation times and the saw tooth degrees of GB-MEP and GA-MEP when using di erent subin-terval s values on topology u 50 1 68 Figure 2.24 The chart presents the minimal exposure values obtained from GA-MEP

Figure 2.25 Comparison of minimal exposure values between GA-MEP and GB-MEP when using: (a) Uniform distribution method, (b) Gaussian distribution method,

(c) Exponential distribution method 73

Figure 2.26 Comparison of computation times between GA-MEP and GB-MEP when using: (a) Uniform distribution method, (b) Gaussian distribution method, (c) Exponential distribution method 73

Figure 2.27 Comparison of sawtooth degrees between GA-MEP and GB-MEP when using: (a) Uniform distribution method, (b) Gaussian distribution method, (c) Exponential distribution method 74

Figure 2.28 Comparison of MEPs by GA-MEP (a, c, e) and GB-MEP (b, d, f) for some noble topologies with di erent deployment distributions: ((a),(b)) Uniform; ((c),(d)) Gaussian ((e),(f)) and Exponential, the number of sensors is 50 75

Figure 2.29 Comparison of convergence level of GA-MEP for for Uniform distribution deployment method, Gaussian distribution deployment method and Exponential deployment method 76

Figure 2.30 Comparison of minimal exposure values between GA-MEP and HGA-NFE when using: (a) Uniform distribution method, (b) Gaussian distribution method, (c) Exponential distribution method 77

Figure 2.31 Comparison of saw-tooth degree between GA-MEP and HGA-NFE when using: (a) Uniform distribution method, (b) Gaussian distribution method, (c) Exponential distribution method 77

Figure 2.32 Comparison of standard deviation values between GA-MEP and HGA-NFE when using: (a) Uniform distribution method, (b) Gaussian distribution method, (c) Exponential distribution method 78

Figure 2.33 Comparison computation time between GA-MEP and HGA-NFE when using: (a) Uniform distribution method, (b) Gaussian distribution method, (c) Exponential distribution method 78

Figure 3.1 Sensing capability of directional sensor 83

Figure 3.2 Illustration attenuated directional sensing model with di erent 0s and 0s 84 Figure 3.3 The individual representation 88

Figure 3.4 Execution of creating an individual in sensor eld < 89

Figure 3.5 Execution of LC crossover operator 91

Figure 3.6 Execution of C crossover operator 92

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Figure 3.7 Illustration how to calculate accelerate parameter causing by the tational forces when having one sensor (a), 3 sensors (b) 96Figure 3.8 Illustration how to calculate accelerate parameter causing by the gravi-tational forces when having two sensors with their di erence position 97Figure 3.9 Comparison of convergence level among versions of HEA 102Figure 3.10 Comparison of standard deviation degree of HEA versions under Binarysensing coverage model 103

gravi-Figure 3.11 The standard deviation degrees of the algorithms on Dataset 1 105Figure 3.12 Illustration of the minimal exposure path found by HEA (a) and GPSO

(b), the topology is HeB2 106Figure 3.13 The standard deviation degrees of the algorithms on Dataset 2 106Figure 3.14 Illustration of the minimal exposure path acquired by HEA (a) and GPSO

(b), the topology is HoA3 107Figure 3.15 The standard deviation degrees of the algorithms on Dataset 3 108Figure 3.16 Comparison of standard deviation degree between HEA and GPSO under

the attenuated sensing coverage model 108Figure 3.17 Comparison of standard deviation degree between GPSO and HPSO in

di erent scenarios 110

Figure 4.1 Sensing capability of truncated directional sensor 113Figure 4.2 Sensing ability of the sensor s being absorbed by the hatched polygon

obstacle 114Figure 4.3 Illustration of the Individual representation in FEA 118Figure 4.4 Illustration of the invalid individual without the normalization opera-tor

(a), the valid individual with the normalization operator by replacing theobstacle-crossing path (b) 119

Figure 4.5 The algorithm process of EA (a) and FEA (b) 120Figure 4.6 Illustration of Leaning crossover operator, the father individual (red path)and the mother individual (blue path) perform crossover operator (a) and repro-

duce a child individual as purple path (b) 121

Figure 4.8 The minimal exposure value when using di erent A-D values 127Figure 4.9 The minimal exposure value comparison between FEA and Grid basedmethod on some noble topologies 129Figure 4.10 The computational time (sec) comparison between FEA and Grid basedmethod on some noble topologies 129Figure 4.11 The minimal exposure value comparison between FEA and GA-MEP onsome noble topologies 130Figure 4.12 The computational time (sec) comparison between FEA and GA-MEP

on some noble topologies 131Figure 4.13 The Minimal Exposure Path is achieved by FEA, GA-MEP and Grid-

based method on some noble topologies 132

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It is established beyond doubt that the common vision of smart systems today, is associated with one single concept, the Internet of Things (IoTs), where the whole physical infrastructure is linked with intelligent monitoring and communication technologies through the use of Wire-less Sensors Networks (WSNs) [1, 2, 3, 4, 5, 6, 7] The WSN consists of thousands of sensor nodes, deployed either randomly or according to some prede ned statistical distributions, over a geographic region of interest A sensor node by itself has resource constraints, such as low battery power, limited signal processing, limited computation and communication capabilities, and a small size of memory; hence it can sense and store only a small amount of sensing infor-mation before transmitting to the other nodes and/or base stations However, by collaborating with each other, they can accomplish many bigger tasks e ciently [8, 9, 10].

WSNs have a great potential for various applications in many scenarios [11, 12, 13, 14,

15, 16, 17, 18, 19, 20, 21] ranging from military target tracking and surveillance, naturaldisaster relief, biomedical health monitoring, hazardous environment exploration, to seismicsensing In military target tracking and surveillance, a WSN can assist in intrusion detectionand identi ca-tion Speci c examples include spatially-correlated and coordinated troop andtank movements With natural disasters, sensor nodes can sense and detect the environmentfactors to forecast disasters before they occur In biomedical applications, surgical implants ofsensors can help monitor a patient’s health For seismic sensing, ad hoc deployment ofsensors along the volcanic area can detect the development of earthquakes and eruptions

To evaluate the e ciency of a WSN, coverage measurement is considered as one of thefundamental problems [22, 23, 24, 25, 13, 26, 27, 28] By this means, the coveragemeasurement is called coverage problems which can be classi ed into three categories based

on the coverage type [29]: point-coverage, area coverage and barrier coverage In pointcoverage, the sensor nodes are deployed to cover all given speci ed points, whereas the goal

of area coverage is that the whole region of interest (ROI) is covered by the WSN Unlikethese coverage types, in barrier coverage, the subjects to be covered are not xed or knownbefore node deployment The main focus of barrier coverage (BC) is on dynamic targetstracking and surveillance Due to the mobility of targets, BC is considered to be complex ascompared to the static ones such as area coverage and point coverage Moreover, to detectobjects penetrating the ROI, it is not necessary to guarantee that every point in the ROI iscovered by one or multiple sensor nodes Therefore, full area coverage model is not suitablefor intruder detection anymore In contrast, barrier coverage [30, 31, 32], was proposed speci

Figure 1 Examples of area coverage (a), point coverage (b), and barrier coverage (c)

Related works

Barrier coverage is a vital problem in WSNs, and has received extensive attentionfrom the academic community in recent years, especially for military and securityapplications [29, 32, 12, 33, 20] In reality, a lot of security applications need to detectintruders who attempt to penetrate the ROI such as national border protection, criticalresource protection, disaster warning and so on [19, 18, 17, 16, 15, 34, 21]

According to a particular application, the requirements in solving the BC problem are ferent Finding penetration path, especially the minimal exposure path problem is the superiorversion of the barrier coverage [29] The minimal exposure path (MEP) problem is addressed

dif-by searching a path through the sensing region, such that an object moving along that path will

be the least monitored by the sensor nodes Hence, the probability of detecting the movingobject/intruder would be minimum The MEP problem is very meaningful for both theoreticalstudies and practical applications The MEP problem in WSNs strongly e ects by several fac-tors such as type of sensors, environment, deployment strategy, sensor density, and approachmethods, etc Therefore, this part provides a brief overview of the MEP problem in WSNs

Regarding static WSNs, many studies have focused on the MEP problem with several di erent approaches: computational geography, grid-based and heuristic/metaheuristic Com-putational geography- Voronoi diagram and grid-based approaches were the earliest methods to address the MEP problem The authors in [35, 22, 36, 37, 26] had used the Voronoi-diagram method for solving the MEP problem with di erent assumptions In [35], Meguerdichian et al had de ned the exposure

of a moving object in a sensing eld during the time interval [t 1 ; t 2 ] along with a path p(t) as the integral path of the sensing function which is a measure of sensitivity at a point on the path by the closest sensor intensity or by the all-sensors intensity in the sensing eld Megerian et al [37] de ned a very similar concept to the MEP which is the maximal breach path (MBP) The MBP comes through a sensing eld beginning at the point B and ending at the point E is a path for any point on the path }, the distance from } to the closest sensor is maximum They then designed an algorithm using Voronoi diagram for searching the MBP in the sensing eld In [35, 38] the authors designed

an algorithm to search the MEP under attenuated coverage model based on the intrinsic properties

of the Voronoi

2

diagram The method rst transfers the sensing eld into a discrete Voronoi diagram, thenthe shortest path through vertices is discovered to gain the solution for the MEP problem.Another approach to solving the MEP problem is the grid based method [39, 40, 41, 42,43] In this approach, the continuous domain of the MEP problem is transformed into adiscrete one by dividing the sensing eld into square grid cells, then each edge of the cells

is assigned a weight corresponding to the exposure value The MEP problem is thenconverted to the shortest path problem on the graph of grid cells and the path is found out

by the Dijkstra algorithm However, the existence of MEP is limited within grid elements,thus making the solution less accurate

Both grid-based and Voronoi-diagram-based methods are simple in implementing, but have some drawbacks For Voronoi-diagram-based method, the algorithm computes minimum exposure paths in a sensor network with guaranteed performance characteristics, but cannot solve the MEP problem for the all-sensor intensity model which is needed to measure the exposure Secondly, when the source point and destination point of the penetration path do not lie on the edges of Voronoi diagram, the algorithm will not result in the optimal solution for the MEP problem Lastly, when the sensing capabilities of sensors are di erent or in the case of heterogeneous sensor nodes scenarios, the MEP will not lie on the segments of the edges of the Voronoi diagram Meanwhile, for the grid-based method, the downside comes from the size of the grid The trade-o between grid size, which is directly proportional to the computational cost of the method, and solution accuracy is a big disadvantage in large-scale WSNs Besides, objects can only move on the grid with xed directions, which does not follow realistic scenarios.

Because the MEP problem is a NP-Hard [27], recently, another approach to this problem

is applying algorithms inspired from biology such as particle swarm optimization and geneticalgorithm All of these methods convert the MEP into a numerically function extreme (NFE)[44] by xing the x-coordinate values of points on the penetration path Then, variables in NFEare only an ordered set of corresponding y-coordinate values However, the objective function

is still highly nonlinear and high dimensional, so [45] proposed a PSO and [46] applied a GA tohandle the MEP problem Because of the complex objective function, both algorithms result insaw-tooth solutions if they are directly applied Therefore, [45] adjusted the standard PSOalgorithm with a projection operator while [45] designed a crossover based on a metricmeasuring the saw-tooth jumping degree and local searching to tackle this issue The authors

[46] also introduced an upside-down operator to reduce the saw-tooth jumping degree of ay-coordinate value in their GA However, the operators are not yet e cient since theobtained solutions still have a high saw-tooth degree Moreover, the complexity of thesealgorithms is quite high and the cost of the computational time is not applicable in realisticlarge-scale WSNs

sure path under static sensors that could avoid mobile sensors was introduced The approach

of this work was Voronoi diagram method which cannot be generalized to deal with othernetwork models such as entirely mobile sensor network or heterogeneous sensor network

All the related works to the MEP problems in WSNs are presented and summarized inTable 2 as follows:

Table 2 Comparative table of related works on MEP problem

Voronoi diagram Grid-based Metaheuristic Static Mobile

Figure 2 Illustration of a general minimal exposure problem in WSNs

is to nd a path on which an intruder can penetrate through the sensing eld with the lowestcapability of being detected Exposure value is directly related to coverage degree of asensor network Knowledges of the MEP in WSNs play an important role in both defendersand intruders who are actors of military and security applications An intruder would like to

nd the safest penetration path such that by moving along the path, he is mostly unlikely to

be detected and tracked On the contrary, from the point of view of a defender, the safestpenetration path to the intruder is its weakest path Defenders or network designers need

to identify such the worst coverage crossing paths and takes some measures to improvethe network monitoring performance The minimal exposure value is a good metric todeploy sensor networks with optimal cost, which can be used to measure the quality ofsurveillance system or coverage quality of the sensor network

The MEP problem has several applications in di erent elds such as manufacturingpath-nding robots or evaluating the quality of radio signal propagation etc The detailedinforma-tions about the motivation behind the MEP problem are presented in theliteratures [35, 39, 37] The MEP problem can be brie y formulated as follows: given awireless sensor network to be deployed in the region of interest <, the WSN has di erentcharacteristics depending on par-ticular scenarios, there are two arbitrary points which arethe source point and the destination point, lie on the opposite sides of < respectively Thegoal of the MEP problem is to search a penetration path } from the source point todestination point such that any object going through < along path } has the least detectionprobability Figure 2 demonstrates a general MEP problem

Obviously, solving the MEP problem provides many usefulnesses for designing, deploying and maintaining WSNs in the real world We have strongly desire to address the MEP problem completely However, the MEP problem is a NP-Hard [27], and depends on several aspects such

as characteristics of sensors or type of sensors, deployment methods, deployment environment, approach method for solving the problem Thus, we would like to propose the practical MEP problems and devise e cient heuristic/metaheuristic algorithms for solving these problems.

However, most prior research worked on the problem under ideal assumptions that there are

no environmental factors such as vibration, temperature, obstacle, etc., making a big gap between the research results and applications the results to practical WSN systems Therefore, motivating

us to do further research on the MEP problem with several aspects as follows:

ˆ Moving ability of sensor nodes or mobile wireless sensor networks

ˆ Realistic sensing coverage model

ˆ Heterogeneous wireless networks

The methodology of this dissertation are as follows:

ˆ Theoretical study of barrier coverage problems as optimal problems.

ˆ Analyzing the related works to the barrier coverage problems Especially, the minimalexposure path problem is comprehended and considered

ˆ Proposing the practical and useful models of the minimal exposure path problem in wireless sensor networks

ˆ Pro ering e cient metaheuristic algorithms to solve the proposed minimal exposure path problems

Scope of research

The scope of dissertation is to investigate the MEP problem in 2-Dimension WSNswhich is a typical type of the barrier coverage problems in WSNs The MEP problem is aNP-Hard, a practical optimization problem with high dimension, non-di erentiation and non-linearity To e ciently cope with these characteristics, the dissertation mainly investigatesthe strength of metaheuristic algorithms Especially, the dissertation focuses on the MEPproblem in real-world WSN scenarios as follows:

Mobile wireless sensor networks

There are several existing algorithms for solving the barrier coverage problems in WSNsuse mobility in favor of improving the quality of coverage and connectivity [49, 50, 51, 52].However, most of the algorithms assumed the random movement of nodes without consideringany mobility models In applications where nodes move around in a certain pattern, mobilitycould further be exploited to improve coverage and connectivity [53, 54, 55] However, mobilityposes challenges in guaranteeing coverage at all times, while it enables nodes to cover areasthat would have been left uncovered using only static nodes Further research in the barriercoverage problem in mobile sensor networks, especially, the MEP problem promises toprovide better application-speci c evaluate the quality of coverage of mobile sensor networks

Practical sensing coverage model

Most of existing barrier coverage solutions, the sensing coverage models were simpleand ideal, i.e they are not e ected by environmental factors such as temperature,humidity, and vibration However, in real deployments, the sensing capability of sensors isvulnerable to these environmental factors, which causes deviation of the detectionprobability from its exact value Thus, the gap between theory and practice will cause thatlaboratory researches cannot be applied in large-scale practical systems To overcomethis drawback, it is crucial to carefully consider practical sensing coverage model at thedesign stage, which allows all realistic cases to be covered

6

Heterogeneous wireless sensor networks

In real-world applications, we may need heterogeneous wireless sensor networks todeal with the problem of barrier coverage, since the sensor nodes may come from di erentmanufacturers and thus have di erent sensing characteristics Besides, it is possible totake the advantages of various kinds of sensors to form a hybrid barrier, to improve thequality of coverage and/or reduce the deployment cost [56, 57] It is interesting to considerthe problem of barrier coverage with heterogeneous sensors

Deployment environments with obstacles

Barrier coverage in a deployment environment with the presence of obstacles is a lenging problem and has not been addressed much in the literature Furthermore, modelingobstacles with arbitrary shapes that are present in arbitrary locations and realistic objects indeployment environments is an open problem and the existing tools and techniques for thebarrier coverage problems need to be substantially extended to meet these above challenges

chal-Contributions

This dissertation explores the barrier coverage problems in WSNs, especially, theminimal exposure path problem which is a well-known method for evaluating the coveragequality of WSNs, and is ultimately useful for sensor network designers Our maincontributions in the dissertation are as follows:

ˆ Presenting a rigorous theoretical analysis, and devise the formulation of the MEPproblem in mobile wireless sensor networks, called MMEP Based on the characteristics ofthe MMEP problem, two e cient meteheuristic algorithms are proposed to solve it The rstone is a genetic algorithm named GAMEP To improve the quality of solution obtaining byGAMEP, the sencond one, HPSO-MMEP algorithm is proposed, which is combined thestrength of genetic algorithm and particle swarm optimization Analyzing experimentalresults, we give some insights into the important parameters and obtained performance ofthe proposed algorithms

ˆ Formulating a minimal exposure path problem under practical sensing coverage model,

i.e the probabilistic coverage model with noise in a WSN, called PM-based-MEP A new denition of exposure measure for this model is also introduced We then propose GB-MEPalgorithm to obtain the solution based on the traditional grid-based method incorporated withseveral improvements To enhance the search space and more e ciently solve the problem,

we design a new individual representation, an e cient crossover and a suitable mutationoperator to form a genetic algorithm Conduct experiments in various scenarios to examine the

ˆ Establishing mathematical models to represent the MEP problem in heterogeneouswire-less multimedia sensor networks, called HM-MEP and convert HM-MEP into an opti-mization problem with an objective function and constraints which permit the use of themathematical optimization methods to solve We also propose two e cient meta-heuristicalgorithms: HEA - a hybrid evolutionary algorithm in combination with local search andGPSO - a novel particle swarm optimization based on the gravity force theory Analysis,evaluate and compare the experimental results and show that our proposed al-gorithmsoutperform the previous methods for most cases regarding quality solution andcomputation time.

ˆ The dissertation investigates a systematic and generic MEP problem under real-world

deployment environment networks with presenting obstacles called OE-MEP In detail, an algorithm to create several types of arbitrary shape obstacles inside the deployment area of WSNs

is proposed The OE-MEP problem is then converted into an optimization problem with dimension, non-di erentiation, non-linearity, and constraints Based upon its characteristics, we devise an elite algorithm namely FEA for solving the OE-MEP An extension to a custom-made simulation environment to integrate a variety of network topologies as well as obstacles are created Experimental results on numerous instances indicate that the proposed algorithm is suitable for the converted OE-MEP problem and performs better in both solution accuracy and computation time than existing approaches.

high-Dissertation organization

The dissertation is organized as follows:

Chapter 1 presents background knowledge about the barrier coverage problem such

as wireless sensor networks, optimal problems, approximate algorithms especiallyheuristics and metaheuristics

Chapter 2 focuses on the MEP problems in omni-directional sensor networks Thischapter investigates two crucial issues as the MEP problem in mobile sensor networks andthe MEP problem under probabilistic coverage model in WSNs Especially, in Section 2.1,

we proposed the MEP problem in MSNs, with characteristics of the problem, we devise agenetic algorithm to solve it, and then make experiments to prove the e ciency of theproposed algorithm In Section 2.2, we study the MEP problem under probabilisticcoverage model for WNSs We then proposed two approximate algorithms to deal with theproblem Experimental results on numerous instances indicate that the proposedalgorithms are suitable for the problem and perform well regarding both solution accuracyand computation time compared with existing approaches

Chapter 3 highlights the MEP problem in heterogeneous directional sensor networks Theproblem is speci cally complex and challenging with the unique features of the heterogeneousdirectional sensor networks Base upon these characteristics, two e cient meta-heuristic algo-

8

rithms, Hybrid Evolutionary Algorithm (HEA) and Gravitation Particle Swarm Optimization(GPSO) are proposed for solving the problem We make experiments on extensive instances,and the results indicate that the proposed algorithms are suitable for the problem and performwell regarding both solution accuracy and computation time compared to existing approaches.Chapter 4 investigates the MEP problem under real-world deployment environmentsensor networks with presenting obstacles We devise an elite algorithm for tackling theproblem An extension to a custom-made simulation environment is created that integrates avariety of network topologies as well as obstacles Experimental results on numerousinstances indicate that the proposed algorithm is suitable for the problem and perform well interm of both solution accuracy and computation time compared with existing approaches.

Finally, the summary and evaluation of the achieved results of the dissertation are included.

Additionally, the future work is also described brie y

CHAPTER 1

BACKGROUND

This Chapter will provide basic knowledge relevant to the barrier coverage problems inwireless sensor networks, the concepts of optimal problems, and approximate algorithms forsolving the optimal problems Especially, the theoretical basis of heuristic/metaheuristic algo-rithms are described These concepts will be used throughout the dissertation

1.1 Wireless sensor networks

Wireless Sensor Networks have revolutionized the IoTs industry by building a reliableand e cient communication system With the rapidly growing technology of sensors, WSNsplay an important role in implementing IoTs Recently, wireless communications,computing and sensor technology have enabled the rapid development of low-cost, small-size sensor nodes that integrate sensing, data processing and wireless communication [1,10] Although sensor nodes are usually resource limited, such as limited battery, memoryand computation capacities, they can collaborate with each other to accomplish big tasks eciently A typical WSN consists of thousands of sensor nodes deployed in the region ofinterest, which can be used to monitor physical phenomena of ROI

1.1.1 Sensors

A sensor is a device, module, machine, or subsystem whose purpose is to collectinforma-tion, detect events or changes in its environment (such as heat, light, sound,pressure, mag-netism, etc.) and send the information to other electronics, frequently acomputer processor Figure 1.1 depicts an acoustic sensor

Fixed backplate

Output audio signal

Battery Fixed backplate

Figure 1.1 Demonstration of acoustic sensor

10

A sensor node is the one that is capable of performing some processing, gathering

sensory information and communicating with other connected nodes in the network A

typical archi-tecture of a sensor node is shown in Figure 1.2 which consists of sensor unit,

communication unit, micro-controller unit, and memory and power unit

1.1.3 Sensor coverage model

Sensor coverage models are used to re ect the sensing capability and quality of sensors.

They are abstraction models trying to quantify how well sensors can sense physical phenomena at

some locations, or in other words, how well sensors can cover such locations Sensor cover-age

models can be mathematically formulated as a coverage function or a sensing function of

distances and angles Commonly, most sensing functions share two aspects in common [39].

ˆ Sensing ability decreases as distance increases.

ˆ Due to diminishing e ects of noise bursts in measurements, sensing ability can

improve as the allotted sensing time (exposure) increases

Assume sensor si is deployed at point (xi; yi) For any target point at location l(x; y), the

Euclidean distance between si and the target point as:

qd(si; l) = (xi x)2 + (yi y)2 (1.1)

The Boolean disk coverage model

8

f(d(si; l)) = 1 if d(si; l) r (1.2)

<

: 0 otherwise

11

sensor becomes very large In such cases, the coverage measure might be ignored, and someapproximations can be made by truncating the coverage measure for larger values of distance

1.1.4 Sensing intensity models

The sensing eld intensity models specify the collaboration of sensors in the sensing eld [39] There are two types of sensor eld intensity are usually applied:

The all sensing intensity

In barrier coverage, the ROI is often a long belt domain, which is the boundary of the

monitored area Sensors are deployed in the ROI to detect intruders that attempt across the belt

region into the monitored area The ROI is usually assumed to be a two-dimensional belt region

that is bounded by two parallel lines The ROI can be a closed belt or an open belt region, that is

described in Figure 1.4 Close belt area is a close belt area having no boundaries.

Closed belt region

Open belt region

Protected

Protected area area

Open belt area is a belt area that has two boundaries orthogonal to the two parallel

lines Rectangle belt is one of the common open belts studied in existing literatures, and

also in this dissertation

Penetration path

A penetration path, or a crossing path is a path that connects two the opposite sides in

the ROI, where the entry point and the exit point reside on two opposite sides of the region

[32] For a two dimensional belt, orthogonal crossing paths are straight lines, whose length

is equal to the width of the belt, as shown in Figure 1.5

Static sensor node

A static sensor node has the ability to collect sensed data, send or receive messages,

process data and messages, and do other types of computation in static WSNs Typically,

these sensor nodes do not move once they are deployed

Mobile sensor node

A mobile node not only has all the characteristics of the static sensor nodes, but also

has some mobility A mobile sensor node can move after deploying and acts as a router

when it is in a low or even no coverage area, and accomplish the recovery task

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Perpendicular crossing path

(a) Any crossing path

(b)

Figure 1.5 Illustration of crossing path types

1.1.6 Wireless sensor network scenarios

Sensor nodes are deployed in a ROI to monitor some physical phenomena Such aeld is called a sensor eld, and the sensor nodes form a sensor network Diverse scenariosexist in the architecture and management of sensor networks

Homogeneous versus heterogeneous wireless sensor networks

A homogeneous WSN (HoWSN), all sensor nodes have the same sensing, processing,communi-cation, and other capabilities Figures 1.6(b) and (d) illustrate two homogeneousnetworks A heterogeneous WSN (HeWSN), sensor nodes have di erent capabilities e.g anode may have a stronger sensor unit and can cover a larger area Figures 1.6(a) and (c)depict two examples of HeWSN

Static versus mobile wireless sensor networks

A static wireless sensor network (SWSN), all sensor nodes are xed and cannot movearound after they have been deployed Figure 1.6(a)(b)(c) demonstrate SWSNs A mobilesensor node is equipped with a locomotive unit and can move around after deployment Amobile wireless sensor network (MWSN) is a network consisting of only mobile nodes, and

a hybrid sensor network is a network consisting of both stationary nodes and mobilenodes As mobile nodes can move to desired locations, it is certain that using mobilenodes can improve sensor network performance Such performance improvements are

Single-Hop versus multi-Hop wireless sensor networks

There are two elementary communication models between sensor nodes and sinks,

namely, single-hop communication and multi-hop communication Figure 1.6(a) represents

a single-hop WSN A multi-hop sensor network, instead of transmitting to the sink directly,

some sensor nodes use a multi-hop path consisting of other nodes as relays to deliver

their data to the sink Figure 1.6(c) depicts a hierarchical multi-hop sensor network

Sensor Field Sensor Field

Figure 1.6 Demonstration of sensor network scenarios: (a) single-hop, heterogeneous, sta-tionary

network; (b) multi-hop, homogeneous, stationary network; (c) multi-hop, heterogeneous, stationary

network; (d) single-hop, homogeneous, stationary network with a mobile sink

1.2 Optimization problems

Applications of optimization are everywhere countless Every process has the potential to

be optimized [58] There is no company that is not involved in solving optimization prob-lems

Actually, many challenging applications in science and industry can be formulated as

optimization problems Optimization occurs in the minimization of time, cost, and risk or the

maximization of pro t, quality, and e ciency For example, there are many ways to go from

home to work, some people choose the shortest way, others choose to go with the least tra c

jams or the least tra c lights; there are many possible ways to design a network to optimize

15

the cost and the quality of service; there are many ways to schedule a production with optimal time.

The optimization problems are often classi ed into several categories as follows [58]:

ˆ Continuous optimization: An optimization problem is called a continuous optimiza-tion

if the variables which demonstrate the objective function must be continuous A continuousvariable is a variable which is chosen from a set of real values

ˆ Discrete optimization: An optimization problem is called a combinatorial optimization

if the variables which decides the objective function must be discrete

De nition 1.2.1 A continuous optimization problem can be de ned as follows:

minimize=maximizef(x)

Subject to : gi(x) 0; i = 1; 2; :::; m

hi(x) = 0; i = 1; 2; :::; pwhere

ˆ f(x) : Rn ! R, is the objective function which is minimize (maximize).

ˆ gi(x) 0, is the unequal constraints

ˆ hi(x) = 0, is the equal constraints

ˆ m; n 2 N

De nition 1.2.2 A discrete problem P = D(X; f) can be de ned by:

ˆ A set of variables X = fx1; x2; :::; xng;

ˆ Variable domains D1; D2; :::; Dn

ˆ An objective function f to be minimized (maximized), where f : D1 D2 ::: Dn ! R+; X = fx

= f(x1; v1); (x2; v2); :::; (xn; vn)gjvi 2 Di; xi satis es all the constraintsg

X is usually called a search (or solution) space, as each element of the set can beseen as a candidate solution To solve a discrete optimization (DO) problem one has to nd

a solution x 2 X with minimum objective function value, that is, f(x ) f(x)8x 2 X (or

f(x ) f(x)8x 2 X) x is called a globally optimal solution of (X; f) and the set X X is called theset of globally optimal solutions

Many real-world DO problems are the Timetabling and Scheduling problems (TaSP);Trav-elling Salesman problem (TSP), the Quadratic Assignment problem (QAP) Due to theprac-tical importance of DO problems, many algorithms to solve them have been developed

worst-case This often leads to computational times too high for practical purposes Thus,us-ing of approximate methods to deal with DO problems has received more and moreattention In approximate methods, one gives up the guarantee of nding optimal solutionsfor achieving good solutions in a signi cantly reduced amount of time.

1.3 Approximate algorithms

Approximate algorithms can further be decomposed into two classes: speci cheuristics and metaheuristics [60, 61] Particular heuristics are problem dependent; theyare designed and applicable to a speci c problem The term metaheuristic was the rstintroduced in [62] Generally, metaheuristics deal with instances of problems that arebelieved to be hard, by exploring the usually large solution search space of theseinstances These algorithms achieve this by reducing the e ective size of the space and byexploring that search space e ciently Metaheuristics serve three main purposes: solvingproblems faster, solving large problems, and obtaining robust algorithms Furthermore,they are simple to design and implement, and very exible

In summary, fundamental properties which characterize metaheuristic algorithms are

as follows [61, 63, 58, 64]:

ˆ Metaheuristics are strategies that \guide" the search process.

ˆ The goal is to e ectively explore the search space to nd (near-)optimal solutions.

ˆ Techniques which form metaheuristic algorithms range from simple local search proce-dures to complex learning processes

ˆ Metaheuristic algorithms are approximate and usually non-deterministic.

ˆ They may integrate di erent mechanisms to evade getting trapped in con ned areas

of the search space

ˆ The basic concepts of metaheuristics allow an abstract level description.

ˆ Metaheuristics are not speci c problem

ˆ Metaheuristics may make using of speci c domain knowledge in the form of heuristicsthat are controlled by the upper level strategy

ˆ Today, more advanced metaheuristics use search experience to guide the search.

Metaheuristics are high level strategies for exploring search spaces by using variousmeth-ods One of the most extreme importance hereby is that a dynamic balance is givenbetween diversi cation and intensi cation Generally, the term "diversi cation" relates to theexplo-ration of the search space, whereas the concept "intensi cation" refers to the exploitation

of the accumulated search experience The use of the notions diversi cation and intensi cation

in their initial meaning becomes more and more accepted by the whole eld of

metaheuris-17

tics Therefore, these concepts are used throughout this dissertation The balancingbetween diversi cation and intensi cation as mentioned above is crucial, on one side toquickly identify regions in the search space with high quality solutions and on the otherside not to waste too much time in regions of the search space which are either alreadyexplored or which do not o er high quality solutions.

Categorization of metaheuristics

There are di erent ways to categorize and describe metaheuristic algorithms.Depending upon the features selected to di erentiate among them, several classi cationsare possible, each of them being the result of a speci c viewpoint The following will brie ysummarize the most important ways of classifying metaheuristics [65, 66]

Nature-inspired versus non-nature inspired

Other way of categorizing metaheuristics is based upon the roots of the algorithm There are nature-inspired algorithms, such as Genetic Algorithms (GA) and Ant Colony Optimization (ACO), and non nature-inspired ones such as Tabu Search (TS) and Iterate Local Search (ILS).

Population-based versus single-solution-based search

Other features can be used for categorizing metaheuristics is the number of solutionsused at the same time: does the algorithm employ on a population or on a single solution

at any time? Algorithms performing on single-solutions based are called trajectorymethods and encompass local search-based metaheuristics, like TS, ILS and VariableNeighborhood Search On the contrary, population-based metaheuristics, perform searchprocesses which describe the evolution of a set of points in the search space

The main characteristics of DO justifying the use of metaheuristics are described as follows:

ˆ A problem is in P class (i.e if it can be solved by an algorithm in polynomial time)with very large instances In this case, exact polynomial-time algorithms are known but aretoo expensive with the size of instances

ˆ An easy problem is in P class with hard real-time constraints In real-time optimization

problems, metaheuristics are widely used Indeed, in this class of problems, one has to nd a \good solution" online Although e cient exact algorithms are available to solve the problem,metaheuristics are used to reduce the search time

ˆ A problem is in NP-hard class with medium size and/or di cult structures of the in-putinstances An NP-hard problem where state-of-the-art exact algorithms cannot deal withthe handled instances (size, structure) within the required search time, the use ofmetaheuristics is justi ed

ˆ DO problems with non-analytic models that cannot be solved in an exhaustive manner

Many real-life problems are de ned by a black box scenario of the objective function

Some common concepts for metaheuristics

There are two common design questions referred to all iterative metaheuristics: how

to represent of solutions handled by algorithms and how to de ne of the objective functionthat will guide the search [67, 68]

of a representation is also related to the search operators applied on this representation(neighbor-hood, recombination, etc.) In fact, when de ning a representation, we have to bear

in mind how the solution will be evaluated and how the search operators will work

Many di erent representations may exist for a given problem A representation musthave the characteristics as follows:

ˆ Completeness: one of the main characteristics of a representation is its completeness;

mean that, all solutions associated with the problem must be represented

ˆ Connectivity: the connectivity characteristic is very crucial in designing any search

al-gorithm A search path must exist between any two solutions of the search space Any solution

of the search space, especially the global optimum solution, can be obtained

ˆ E ciency: the representation must be easy to manipulate by the search operators.The time and space complexities of the operators regarding the representation must be re-duced

Objective function

The objective function, which can be de ned as the cost function, evaluation function,and utility function f, formulates the goal to achieve It associates with each solution of thesearch space a real value that describes the quality or the tness of the solution, f : S ! R Itthen represents an absolute value and allows a complete ordering of all solutions of thesearch space As shown in the previous section, from the representation space of thesolutions R, some decoding functions d may be applied, d : R ! S to generate a solutionthat can be evaluated by the function f

The objective function is an important aspect in designing a metaheuristic It will guide thesearch toward \good" solutions of the search space If the objective function is improperly

19

de ned, it can lead to unacceptable solutions whatever metaheuristic is used.

Constraint handing

Handing constraints in optimization problems is also an important topic for the e cient design

of metaheuristics Indeed, many continuous and discrete optimization problems have constraints, and it is not trivial to deal with those constraints The constraints may be of any kind: linear or nonlinear and equality or inequality constraints In this section, constraint handling strategies, which mainly act on the representation of solutions or the objective func-tion, are presented They can be classi ed as reject strategies, penalizing strategies, repairing strategies, decoding strategies, and preserving strategies Other constraint handling approaches using search components not directly related to the representation of solutions or the objective function may also

be used, such as multi-objective optimization and co-evolutionary models.

Parameter tuning

For any metaheuristic, many parameters have to be tuned Parameter tuning maypermit a larger exibility and robustness, but requires a careful initialization Thoseparameters may have a strong in uence on the e ciency and e ectiveness of the search It

is not obvious to de ne a priori which parameter setting should be used The optimalvalues for the parameters depend mainly on the problem and even the instance and on thesearch time that the user wants to spend in solving the problem A universally optimalparameter values set for a given metaheuristic does not exist

Performance analysis of metaheuristics

Performing analysis of metaheuristics is an essential task to execute and must be done

on a fair basis A theoretical approach is generally not su cient to evaluate a metaheuristic.This section addresses some guidelines for evaluating experimentally a metaheuristic and/orcomparing metaheuristics in a rigorous way To evaluate the performance of a metaheuristic in

a rigorous manner, three steps must be considered as follows:

ˆ Experimental design: in the rst step, the goals of the experiments, the selectedinstances including real-life instances or constructed instances, and factors have to be dened

ˆ Measurement: in the second step, the measures to compute are selected such as quality

of solution, computational e ort, robustness After executing the di erent experiments,statistical analysis is applied to the obtained results The performance analysis must be donewith state-of-the-art optimization algorithms dedicated to the problem

ˆ Reporting: nally, the results are presented in a comprehensive way, and an analysis

to the single solution versus population-based search classi cation This choice ismotivated by the fact that this categorization permits a clearer description of thealgorithms Besides, a current trend is the hybridization of methods in the direction of theintegration of single point search algorithms in population-based ones.

1.3.1 Single-solution-based metaheuristic

Single-solution-based metaheuristics (S-metaheuristics) are called trajectory methods andinclude local search-based metaheuristics, such as LS, TB, ILS, and so on While solvingoptimization problems, S-metaheuristics improve a single solution They could be viewed as \walks" through neighborhoods or search trajectories through the search space of the problem

at hand [69] The walks or trajectories are performed by iterative procedures that move fromthe current solution to another one in the search space S-metaheuristics show their e ciency

in solving di erent optimization problems in various domains

Local search

The simple local search is usually called iterative improvement, since each move which isthe choice of a solution x0 from the neighborhood N(x) of a solution x, is only performed if theresulting solution is better than the current solution [70, 71] The algorithm stops as soon as itnds a local minimum The high level algorithm is outline in Algorithm 1.1 It starts at a giveninitial solution At each iteration, the heuristic replaces the current solution by a neighbor thatimproves the objective function Figure 1.7 When all candidate neighbors are worse than the

Iteration 1 Iteration 2 Iteration 3 Iteration 4

Figure 1.7 Illustration of local search using a binary representation of solutions, a ip moveoperator, and the best neighbor selection strategy The objective function to maximize is x3

x2 + x The nal local optima found is x = (11110), starting from the solution x0 = (11010)

current solution, the search stops, meaning a local optimum is obtained For large neighbor-hoods, the candidate solutions may be a subset of the neighborhood The goal of this restricted neighborhood strategy is to speed up the search Variants of LS may be distinguished according to the order in which the neighboring solutions are generated (deterministic/stochastic) and the selection strategy (selection of the neighboring solution) Figure 1.8.

21

Initial solution

Final solution

Search space

Figure 1.8 Illustration of local search behavior in a given landscape

Algorithm 1.1: Diagram of local search algorithm

s s 0 ; t 0;

repeat

Generate(N(s)); /* Generate of candidate neighbors */

s s0;/* Select a better neighbor s 2 N(s)*/;

t t + 1;

until Termination Criterion(P(t));

output nal solution found or local optima;

1.3.2 Population-based metaheuristics

Population-based metaheuristics (P-metaheuristic) maintain and improve multiplecan-didate solutions, often using population characteristics to guide the search P-metaheuristic algorithms provide a natural, intrinsic way for the exploration of the searchspace They start from an initial population of solutions Then, they iteratively apply thegeneration of a new population and the replacement of the current population Figure 1.9

In the generation phase, a new population of solutions is produced In the replacementphase, a selection is performed from the current and the new populations This processiterates until a satis ed stopping criteria

Generate population Memory Replace population