A Genetic Algorithm for a Multi–Objective Nodes ... - Semantic Scholar

This regular paper was presented as part of the main technical program at IFIP WMNC'2011

A Genetic Algorithm for a Multi–Objective Nodes Placement Problem in Heterogeneous Network Infrastructure for Surveillance Applications Ons Abdelkhalek

Saoussen Krichen

Adel Guitouni

LARODEC Laboratory, LARODEC Laboratory, Institut Sup´erieur de Gestion, Faculty of Law, University of Tunis, Economics and Management, Bardo, Tunisia, University of Jendouba, Email: [email protected] Jendouba, Tunisia, Email: saoussen.krichen@isg. rnu.tn

Abstract—In this paper, we adress a Multi–objective communication nodes (e.g., antennas, relays. . . ) placement problem for heterogeneous network infrastructure. The proposed model considers three conflicting objective functions: maximizing the communication coverage, minimizing the cost of nodes placement and communication devices and the maximizing of the total capacity bandwidth in the network. The empirical validation of the model is done in a simulation environment called “Inform Lab”. We consider a large volume of surveillance missions. To solve such an NP-Hard problem, we propose a Multi-objective Genetic Algorithm (MOGA). The empirical results show that the proposed algorithm has good performance with good quality’s result in a practicable CPU time. Index Terms—Antennas placement problem, Genetic Algorithm, Multi-objective optimization problem, Heterogeneous network planning.

I. I NTRODUCTION The large volume surveillance problem is characterized by the employment of mobile and fixed surveillance assets to a large geographic area in order to identify, assess and track the maximum number of moving, stopped or drifting objects. At any given time, there are many observable dynamic and static objects travelling in that geographic area. These objects have different characteristics and behaviours. Platforms include satellites, airborne platforms (e.g., helicopters, marine patrol aircraft and UAVs), seaborne platforms (e.g., coastguard, military and police vessels), stationary and land platforms (e.g., radar stations, land vehicles). Coastal and Arctic surveillance are good examples of large volume surveillance. The execution of any surveillance mission requires a web of heterogeneous communication networks to exchange information and coordinate actions. For example, network antenna placement and ad hoc mobile networks might also be considered as key components of the required infrastructure. Therefore, there is a requirement for better planning the communication network infrastructure placement and effective dynamic extension of that infrastructure as the different platforms roam the area.

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©2011 IEEE

Peter B. Gustavson School of Business University of Victoria, Victoria B.C, Canada, Email: [email protected]

Snezana Mitrovic-Minic Simon Fraser University, Vancouver, B.C. MacDonald, Dettwiler and Associates Ltd,

Richmond, B.C, Canada, Email: [email protected]

Many other problems might have the same characteristics as the large volume surveillance problem. For example, by the increasing number of mobile users and the continuous development of new communication technologies, many wireless communication providers are facing problems managing their communication networks (e.g., unbalanced traffic between different antennas due to limited bandwidth range, congestion of cells resulting in an increase in dropped calls, limited capacity). In addition to the antennas or transmitters placement [4][5] and sensors placement problem [22], we have to optimize the placement of nodes and their connections to the existing infrastructure. In this paper, we assume an initial existing infrastructure and heterogeneous nodes connection where both one–hop and dual–hop connecting modes are used. In the one-hop networks, stations communicate using access points (APs) or fixed Base Station (BS). Users access the system through a fixed BS - wireless network - or an AP WLAN - that is connected to a wired infrastructure. Whereas, in multi-hop networks, mobile Stations (MSs) may communicate directly with each other without antennas to establish the access. The communication is established without the use of BS or AP. For example, nodes can be considered relays, antennas, getaways, etc, depending on the connection needs. This configuration allows for versatility of functions to be carried out by the same the node. There has been a growing interest for the integration of different kind of networks in order to support different services (e.g., data, voice, imagery, video). There have been several proposition for the integrations of LAN and wireless LAN (WLAN) [1] [7] [10] [8] [23] [2], Wi-Fi and Wi-Max [5], and the integration of Ad hoc to cellular networks in [12] [9] [6] [13] [3] [14]. Various integrating architectures for heterogeneous networks have been proposed in the literature. However, most of research efforts focused only on specific communication sce-

narios, on integrated technical architectures and on routing protocols in heterogeneous environment [6]. We address the Multi–Objective Nodes placement problem for heterogeneous network infrastructure. It consists in finding the optimal placement of nodes from a set of candidate sites and their optimal connections to an existing hierarchical network structure. In this problem, both placement and connections problems are modelled as multi–objective optimization problem where the following objective functions are considered: maximizing the communication coverage, minimizing nodes placement with communication devises costs and maximizing of the total capacity bandwidth in the network. The system constraints include multiple communication and energy management constraints. As nodes and transmitters placement problem are NP-hard [5] the problem is consequently NPhard. We propose a Genetic Algorithm to solve the problem. A simulation environment called Inform Lab is used to generate problem instance for empirical validation [19]. The empirical validation is generated based on surveillance problem application. The rest of the paper is organized as follows. Section 2 reviews the related literature. The proposed problem is presented in section 3 followed by the environment description in section 4. In section 5, we present the proposed problem formulation as an integer non-linear multi-objective mathematical program. Section 6 describes the proposed solving approach. In section 7, computational results are presented and discussed. Finally, the conclusion and further works are presented in section 8. II. L ITERATURE REVIEW The management of wireless networks infrastructure plays a significant and crucial role in increasing the performance and efficiency for its robustness, self management, flexibility and supporting the mission such as: vehicular wireless ad hoc networks [21], cellular networks [1] [7] [10] [8] [23] [2] [5], surveillance, etc. However it is worth mentioning that, the placement of a new antenna could be very expensive because of not only the equipment cost but also the right way to install the equipment and the cost for system planning, which make the conventional approaches (such as cell splitting) unattractive to increase the system capacity. In addition, due to the limited radio bandwidth, the network cannot support a large number of users simultaneously, especially for applications requiring large and fast data transmission rate. The integration of wireless heterogeneous networks may provide services with high transmission data rate with cost savings. For example, the integration of cellular and WLAN can provide better service by minimizing call blocking probability [8] and handoff [23]. However, WLAN has a very small radio coverage (especially in urban areas) and can only provide services to users in its covered area by its fixed access points. To overcome this drawback and be able to serve most of the users, a high density of WLAN access points have to be deployed. But this solution leads to increase costs and reduce the efficiency of the fixed infrastructure.

Many authors studied the Heterogeneous Integrated Wireless Networks (HIWN) problem. Since the development of 3G systems(or 3rd generation [25]), there have been several studies to investigate the integration of wireless LAN (WLAN) [1] [7] [10] [8] [23] [2], Wi-Fi and Wi-Max [5], and to integrate ad hoc to cellular networks in [12] [9] [6] [13] [3] [14]. Lee and Kang [4] addressed the problem of cell planning problem that consists in deciding the location and capacity of each new BS to cover expanded and increased traffic demand. The authors formulated this problem as an integer linear uni-objective mathematical programming problem and solved it by using a Tabu Search (TS) algorithm. The main objective is to minimize the cost of new base stations. Ting et al. [5] presented a multi-objective variable-length genetic algorithm (GA) to solve the problem of transmitters’ placement in order to determine the optimal number, type and positions of heterogeneous transmitters in integrating Wi-Fi and Wi-MAX networks. The heterogeneity in this problem came from the fact of including two different nodes type: large and small power radius nodes. The problem optimize four objectives functions: maximizing coverage, minimizing cost, maximizing capacity satisfaction, and minimizing overlap. The wireless transmitter placement problem is defined as an multi-objective minimization problem. See Toumpis and Toumpakaris [21] for a summary of the literature related to the topology of Ad Hoc networks that have evolved over time, the different applications (military, vehicular, sensors. etc.) and future challenges. St-Hilaire et al. [17] introduced the global planning problem that consists in selecting the number, the location and the type of network nodes as well as the interconnections between them. This problem is composed of three NPhard subproblems: the cell, the access network and the core network planning problems. They [17] proposed a mathematical formulation and a local search (LS) algorithm to find feasible solutions rapidly. They showed that the problem can be solved to optimality only for small-size instances within a reasonable amount of time using a branchand-bound algorithm. LS algorithm can find solutions that are, on average, at 6.53% of the optimal solution. St-Hilaire et al. [18] revisited the proposed model in [17] and proposed a Tabu Search (TS) algorithm to improve the result obtained by LS algorithms. The aim of this algorithm is to find solutions with acceptable difference to the optimal (with Cplex) and feasible (with TS) solutions, at a relatively good running time. Hsu and Lin [24] combined the features of Single-Hop Cellular Networks (SCN) with Ad hoc networks and proposed a new integrated architecture called the Multi-hop Cellular Network (MCN). In MCN, MHs can connect with each other and communicate with the BTS through multiple hops. The direct communication between MHs can improve the throughput of intra-cell traffic. Many applications for heterogeneous networks are reported in the literature: Vehicular wireless ad hoc networks [21],

cars equipped with wireless transceivers. Cavalcanti et al. [6] summarized the possible communication scenarios, the integrated architecture and routing protocols in an heterogeneous environment. They integrated Mobile Ad hoc Networks (MANETS), WLAN and cellular networks and supposed the general case for the integration when both of systems are supposed to have dual mode capability. Pandey et al. [20] defined a two-tier hierarchical heterogeneous wireless sensor network. They presented the placement problem as an optimization problem in order to place the minimum number of nodes to handle the traffic, under a set of system constraints. The majority of research reviewed are concerned with possible communication scenarios, the integrated architecture and routing protocols in an heterogeneous environment [6]. All previous works, focused on only one system criteria for expanding coverage [13] or assumed static and certain wireless environment [5]. To our knowledge, none of the previous works considered a multi–objective optimization model for extending the network communication coverage using heterogeneous communication devices in the networks. III. P ROBLEM DESCRIPTION We address nodes placement problem for heterogeneous network that consists to optimize the extension of communication coverage of an existing network by deploying new nodes and integrate them with the existing infrastructure. Given a set of N nodes, a set of D communication device and Z d a set of existing networks infrastructure related to each communication device d. The purpose is to find the optimal number, position, communication types and connections in a special area of coverage. In this paper, we consider Vancouver Island as a special area of interest to extend the communication coverage. We assume that each node ni can only communicate with a set of communication devices. Thus, a nodde ni can have multiple communications devices to connect to different communication networks. Each of the communication devices d is characterized by τ = (p, s, c, t, w, b); where p denotes the power (to connect receivers to nodes), s the capacity (bandwidth) provided by the node to manage the data demand of test points, c denotes the cost of the communication device, t denotes the communication device type, w denotes the power range (to connect nodes in the network) and b denotes the bandwidth where connecting the network. A set of M candidate sites with spatial coordinates (αk , βk ) are considered to represent the potential placement of nodes. Each node should be assigned to only one candidate sites. To simulate the traffic communication demand, we introduce a set of test points. These test points require particular signal strenght from that communication device d to connect to a communication network. A test point can represent one or a set of mobile terminals. In our case study, test points are assumed to be uniformally distributed all over the land and used to maximize the communication coverage of our network.

It is important to consider a sufficient number of test points in order to test the quality of the coverage. We assume that each test point has spatial coordinates (αfd , βfd ). A distributed data rate σfd represents the priority for each receiver to be covered and a signal threshold θfd . The first objective function maximizes the number of test points covered by the placed nodes. The second objective function minimizes the total cost that includes fixed cost Ci for each node and total cost for each communication device d on each node. The third objective function maximizes the total bandwidth capacity in the network. In the remaining of this paper, we propose a mathematical formulation of the multi-objectives optimization problem. We consider an empirical validation using a multi-agents based simulation environment called Inform Lab (IL) [19]. It is a testbed to support the development of two groups of algorithms, which are particularly useful for wide-area surveillance applications: Distributed Dynamic Information Fusion (DIF) and Distributed Dynamic Resource Management (DRM). In IL simulator, we model each node as an agent. Ech agent is associated to a node in the network structure and controls a set of communication devices installed on that node. In this application, we do not take into consideration the Handover constraints [16][11] which define a maximum handover percentage used to consider the viability of the handover region when commissioning a new cell. IV. E NVIRONMENT DEFINITION The problem of nodes placement and communication device assignment can be defined as follows: •

A set of nodes to be placed: Each node ni is defined by a set of specific characteristics such as: limited capacity, setup cost c, etc, and each one has a possible relationships with nodes of the network as compatibility, complementarity, accessibility,. . . We suppose a known demand distribution over the time horizon. Additional nodes are placed only if there is a great need. Each node has to satisfy system constraints. These nodes are able to communicate, collaborate and negotiate via the network. In general, node placement are expensive.

•

Existing infrastructure: The existing infrastructure is a set of homogenous or heterogeneous nodes Z t that are connected via a fixed and hierarchical networks and related to each communication device type. These nodes that form the existing network have a set of characteristics such as: limited energy, capacity power and coverage size. However, these pre-existing nodes are considered to be fixed with only one-hop air interface.

•

A set of constraints: To be feasible and realistic, each planned architecture must satisfy all networks constraints. In this application,

xdik

we consider two types of constraints: communication constraints and connection constraints. When we maximize the communication coverage in the network, each node has to manage the demand rate of receivers (test points) that are assigned to that node. For the connection node constraints, two nodes must have the same communication device type to be able to connect with each other, while respecting power and capacity constraints.

V. P ROBLEM FORMULATION In this mathematical formulation, we search the pareto optimal placement of nodes (agents), types and connection devices based on objectives such as coverage and cost. •

Notations: Symbols N D M R τ = (p, s, c, t, w, b)

AM ×D

N Ld Ci d Sf,i,k (σfd , θfd ) (αf , βf ) (αk , βk ) Zd TZ d

Description Set of nodes (agents) {n1 , ..., nN } Set of communication device{d1 , ..., dP } Set of predefined candidate sites of interest {l1 , ..., lM } Set of test points (or receivers) {r1 , ..., rR } Each communication device has a set of characteristics related to the infrastructure and to the sub node, where: p denotes the power and s denotes the capacity agents and test points, c denotes the cost of (bandwidth) between communication device, t denotes the communication device type, w denotes the power range of the communication device for the connection network and b denotes the bandwidth between two different agents when connecting the infrastructure. Input matrix where akd = |{rf }| denotes the number of test points covered by candidate sites lk with communication device d The maximum number of links allowed for an agent with communication device d Cost of agent ni Signal strength between node ni with communication device d in candidate site lk and test point rf data rate demand and signal threshold of test point rf for the communication device d Coordinates of the test point rf Coordinates of the candidate site lk Initial existing networks infrastructure with communication device d Maximum capacity for Z d in term of bandwidth

d yij

d wif

•

Decision variable, xdik = 1 if agent ni with a communication device d is assigned to candidate site lk d Decision variable, yij = 1 if agent ni is assigned to agent nj with a communication device d d Decision variable, wif = 1 if test point rf is assigned to node ni with communication device d

Objectives: The objective functions considered are: – Maximizing the communication coverage: The maximization of coverage is the must important issue in our problem. The aim of integration heterogeneous networks in to maximize the coverage, allowing terminals (or receivers) to be connected to networks via additional placed agents. As the area range of agents is not specified, choosing the cell size could affect the network performance [25]. We consider a large set of receivers R (or test points) for maximizing the communication coverage. A test point rf is said to be covered by an agent ni if the signal strength is greater than his signal threshold [5]. The communication coverage of the integrating networks can be calculated by: M ax Z1 (X) =

N X D X M X

xdik akd

(1)

d=1 i=1 k=1

Where each follows: ( 1, d xik = 0,

decision variable xdik is expressed as

if node ni using the communication device d is assigned to candidate site lk otherwise. (2) and the matrix AM ×D is computed as follows:   |{rf }|, if ∀f , ∃i ∈ N , ∃k ∈ M and ∃d ∈ D d akd = ≥ θfd where Sf,i,k  φ, otherwise. (3) 2 d d Gf Gi λ Where Sf,i,k = p(4π) is the signal strength be2 d2 k,f tween test point (receiver) rf and agent ni with communication device d placed in candidate site lk [5]. pd is the power of the communication device d, Gf and Gi are the antenna gains of test point rf and agent ni , respectively, λ is the carrier wavelength, and df,k is the Euclidean distance from ff to candidate site lk where is placed node ni . θfd is the signal threshold of receiver rf for communication device d. Each agent ni will be assigned to the candidate site lk that cover maximum set of receivers with the strongest signal.

AM ×D matrix, that computes the number of covered test points, is represented as follows: d1

d2



l1 {r2 , r7 } {r4 , r3 , r2 }  l2  ... ..   ...  .. .. lM {r17 , r10 , r3 , r5 } ... S where | k akd | ⊆ R

.. .. .. .. ..

dD  ...  {r9 }    ..  ...

– Minimizing cost: An other objective, is to minimize costs of placing agents. The cost of each placed node is evaluated by the agents placement cost and the communication devices cost. We also solve the problem of minimizing the number of nodes placed ( i.e. the number of agents that can achieve full coverage at the lowest cost) implicitly while minimizing placement cost. Generally, the problem of how many nodes to be used must be solved before dealing with the placement. The second objective can be formulated as follows: M in Z2 (X) =

N D X X d=1 i=1

(Ci + cd )

M X

f =1 k=1

Where if test point rf is assigned to node ni with communication device d 0, otherwise. (8) ∗ The sum of capacity of all agents connected to an existing network Zd , should not exceed the maximum capacity of this network TZd d wif

(

=

1,

N N D X X X

d bd yij ≤ TZd ∀Zd

(9)

i=1 j=1,j6=i d=1

– Links constraints: All agents n ∈ N −{j} connected to agent nj should not exceed the maximum capacity of links N Ld allowed for nj and related to his communication device. X d yij ≤ N Ld ∀j ∈ {1, . . . , N } (10) ∀i∈N −{j}

xdik

(4)

k=1

where Ci represents the cost of agent ni and cd the communication device cost. – Maximizing bandwidth: The third objective function is to maximize the minimum capacity bandwidth of the network and formulated as follows: d M ax (Z3 (X) = M in{d,i6=j} yij bd ) •

exceed the capacity sd of communication device d. R X M X d d σfd wif xik ≤ sd ∀i, d (7)

(5)

Constraints: Our problem includes various types of constraints differing in difficulty and complexity which make the problem extremely hard to solve. The constraints include: – Energy constraints: There are two types of energy constraints: agent (node) connection constraints and agent energy constraints. ∗ Connection constraints: two agents ni and nj can be connected only if they share the same communication device d and have the Euclidean distance dk,k′ from lk to candidate site lk′ less or equal to the maximum power range between wd ′ and wd related to communication devices d and d′ .  ′  1, if xdik xdjk′ = 1 with td = td′ and d yij = dk,k′ ≤ M ax(wd , wd′ ), i 6= j and k 6= k ′  0, otherwise. (6) ∗ Agent capacity constraints: the sum of data rate demand for all assigned test points associated to agent ni with communication device d cannot

– Assignment constraints: ∗ We can assign more than one communication device to an agent ni . D X

xdik Tit ≥ 1 ∀i ∈ N

(11)

d=1

∗ Each agent ni is assigned to one candidate site lk . M X

xdik = 1 ∀i ∈ {1, . . . , N }, ∃d ∈ D

(12)

k=1

∗ Each candidate site lk is assigned to at most one agent ni . N X

xdik ≤ 1 ∀k ∈ {1, . . . , M }, ∃d ∈ D

(13)

i=1

∗ Each receiver rf can be assigned to at most one agent ni with communication device d. N X M X

d xdik wif ≤ 1 ∀d ∈ D

(14)

i=1 k=1

∗ Each agent ni should be connected at least to another agent nj N X

d yij ≥ 1 ∀j, t and j 6= i

(15)

i=1

∗ At least one node ni should be connected to the existing networks Z d N X i=1

d yiZ d ≥ 1 ∀d

(16)

– Binary constraints: xdik

∈ {0, 1}

∀i, k, d

(17)

d wif ∈ {0, 1}

∀i, f, d

(18)

d yij ∈ {0, 1}

∀i, j, d

(19)

VI. A LGORITHMIC APPROACH If we reduce the proposed problem to the antenna placement or transmitter placement problem, we will clearly conclude that it is a NP-hard problem. Considering the problem formulation above, we propose a metaheuristic to find pareto optimal solutions. We propose to adopt the Genetic algorithm as solution approach since it gave good results in similar constrainted problems [5][11][16]. A. Multi-objective Genetic Algorithm Figure 1 represents the proposed encoding of a chromosome. Each node, encoded into one chromosome, presents a substring as follows: the position of a candidate site where it is located, its communication device and all other agent with which it is connected. For the position of each agent, we assign the index the candidate site where each index represents a specific and unique potential placement of the agent. The index of the potential sites varies from 0 to (M − 1). Candidate sites corresponds in our empirical application to the spacial coordinates of different cities in Vancouver Island. As we assume that each agent can connect to more than one communication networking using different devices, the length of the second part of our substring will be equal to the number of different available communication devices in the network D. The last part of the substring coding is equal to the set of different nodes in the existing infrastructure with which the node ni is connected. The total number of agents is equal to |Z d | where we assume that each existing network is a super node and equal to 1. The number of existing networks vary from 1 to D depending on the communication device used.

The initial population is randomly generating the assignment of substrings in a chromosome, where positions is one of possible candidate sites’ index {1, 2, , M }, communication device types are chosen from a the set of communication devices D and the number of other nodes to which they are connected are generated randomly from {1, ..., |Z d |}. Each chromosome is then adjusted in order to verify the constraints and thus come–up with a set of feasible that will represent our initial solution. G Fitness Evaluation The dominance is verified based on the fitness function evaluation. The proposed fitness evaluation is based on NSGA II [15]. G Sorting process In each iteration a sorting process is used to generate the list of non-dominated set Qi . The non-dominated sorting approach (NDS) is used only to rank the best Pi individuals and thus assign a rank to each solution of the potential Pareto-set. Qi is defined as: Qi = Qi−1 ∪ Rank(Pi )

G Crossover In each iteration, a crossover process is applied based on these steps: 1) two chromosomes ch1 and ch2 are randomly chosen from the current population Pi 2) a probability p is randomly generated 3) if p < pc then the substring for a new child is chosen from the first chromosome ch1 otherwise it’s taken from the second chromosome ch2 4) repeat until the end of ch1 and ch2 The new population Pi+1 is defined as follow: Pi+1 = Qi ∪ Ri

Chromosome and substring representation

G Initial Population

(21)

where Ri includes the set of new offsprings. Figure 2 illustrates this procedure.

Fig. 2.

Fig. 1.

(20)

Example of probability crossover for chromosomes

G Mutation During each iteration, a probability p is randomly generated where the probability of mutation is set to pm = (1/substring − lengh). If p > pm then the mutation process is activated on a random chromosome from Pi by making small changes on the assignment of nodes to the

existing network. The basic outline of the algorithm is summarized as follows:

in Vancouver island. We use a GMLParser in order to run the GML file “Cities.gml” and to extract all cities’ coordinates. In Table II, we present the parameters used in this empirical application. The empirical results are shown in table III where the CPU

Multi-Objective Genetic Algorithm it = 0 Randomly generate the first population P0 of size N Repair the first population to make it feasible Fitness evaluation of P0 Apply the sorting process for each solution based on the fitness evaluation Do it = it + 1 Crossover: generate the set Ri of offspring of size N If p > pm Then activate the Mutation process Apply the sorting process for each solution in Ri Fitness evaluation for Pi Update the non dominated list Qi Evaluate and select best N solution from Pi While stopping criteria VII. E XPERIMENTAL RESULTS The performance of the MOGA is evaluated in IL. A wide range of synthesized test problems could be generated in IL by varying the size of the area in which nodes are placed, the number and positions of candidate sites, the density of test nodes and the power radius of the existing agents. In this empirical validation, we vary the density distribution of test points and the region size. The MOGA algorithm parameters are listed in Table I. Our algorithm will help to optimize the placement of extra TABLE I PARAMETERS OF THE PROPOSED GA

Parameters Representation Substring length Crossover rate pc Mutation rate pm Number of iterations Generations

IN THE EXPERIMENTS

Values Binary and integer code N + D + Zd 0.7 (1/substring − length) 300 40

nodes in an existing network in order to improve the communication coverage. CPU time, number of potentially non dominated solutions (|PN D |) and the mean average of the best values for each objective function are reported. A. Illustrative example Before presenting the empirical results, we start by an illustrative example to explain the execution program with the resulting outputs. We adopted an existing networks topology illustrated in the XML file “BaseTest.xml” including 46 heterogeneous nodes and 3 communication devices. Candidate sites represent the coordinates of the existing cities

TABLE II P ROBLEM

PARAMETERS FOR THE ILLUSTRATIVE EXAMPLE

Parameters Region size (Km2 ) Distribution distance between test points (Km) Number of candidate sites Number of existing nodes Number of communication devices Number of different modes Number of extra-nodes

Values (40 x 40) 2 17 46 3 4 10

time, |PN D | and values of objective functions are reported. Table IV illustrates a potential Pareto Optimal placement form the set of non dominated solutions that we generated by the MOGA. The first column represents the Index of the agent. Column 2 contains the optimal placement for a given agent according to the list of candidate sites previously described. Finally the last columns represent the number of communication devices (NCD) assigned to a given agent and the number of nodes to which the new argent is connected (NCN). TABLE III E XAMPLE RESULTS

CPU time(s) 3.175

|PND | 4

Z1 400

Z2 505815

Z3 1.05E8

TABLE IV O PTIMAL ASSIGNMENT FOR THE ILLUSTRATIVE EXAMPLE

Agent Index 1 2 3 4 5 6 7 8 9 10

Optimal placement Port Alberni Gwaii Haanas National Park Reserve Nanaimo North Vancouver CFB Comox Parksville Vancouver Prince Rupert YVR Powell River

NCD 1

NCN 2

2 1 2 2 2 1 3 3 1

2 2 2 2 2 0 2 2 0

Based on the example’s results reported in Tables III and IV, we can conclude that almost all test points were covered which is obvious because we placed the most powerful communication device in the majority of new nodes. Then every agent ni , on average, connected to two others nodes from the existing infrastructure. Only two nodes are not connected to any other node, due to the connexions constraints. Figure 3 illustrates a user view of IL simulator with the integrated MOGA optimizer.

TABLE VI E XPERIMENTAL RESULTS

Problem C1 C2 C3 C4 C5 C6 C7 C8 C9

•

Fig. 3.

Inform Lab simulator’s running

B. Experiments with randomly generated instances As in [16], we classified test problems in two ways: The size of the area and the density of test points in which they are positioned (see Table V). Each test problem gives different location and density of test TABLE V N UMBER OF TEST POINTS DEFINED BY REGION SIZE AND DISTRIBUTION DISTANCE

Region size Km

40 x 40 45 x 45 50 x 50

2

2 400 506 625

Distribution distance of test points (Km2 - number of test points) 3 4 178 100 225 127 278 156

points over the land. A total of 9 test problem instances are generated. We used IL for testing these different distributions to measure the performance of the network and the communication coverage. Each instance is solved 30 independent times. The algorithm stops running after a maximum number of iterations set to 300 iterations as listed in Table I or when no improvement is performing on the objective functions after 100 iterations. For each instance, we report in Table VI the average of the following measures: The average CPU time, size of the non dominated set and the best values for the three objective functions. Based on the experimental results illustrated in Table VI, we can make the following remarks: • The CPU time is positively correlated to the problem size and, in average, is about to 2 seconds. • The cost is proportional to the size of the area of coverage. We can notice that the more we have test points to cover, the more expensive is the cost of our placement due to communication devices’ cost.

•

CPU time(s) 3.175 2.229 1.47 5.012 2.61 1.751 5.957 3.114 1.978

|PND | 4 3 6 4 5 3 3 5 4

Z1 400 178 98 506 225 127 620 278 156

Z2 505815 462198 450250 786405 632175 374231 1003142 470651 450038

Z3 1.05E8 4000 400 1.05E8 1.05E8 4000 400 4000 4000

In all the problem instances, almost all test points are covered and their demands are satisfied by the new placed nodes. It shows that our MOGA almost converges to the optimal solution. The number of potentially efficient solution |PN D | is not really high compared to the generations instances. It can be justified by the small number of candidate sites considered in this problem instances or the communication devices. Other problems should be considered for additional empirical validation. VIII. C ONCLUSION

In this paper, we proposed a multi-objectives mathematical formulation of the heterogeneity nodes placement and communication devices allocation problem. Nodes placement is about allocation of physical infrastructure (e.g., towers, antennas) to specific locations. Then, different communication devices should be installed on each infrastructure in order to connect to different communication networks (e.g., radio, cellular, link 11, Wi-Fi). The large volume of surveillance problem consist of deploying a set of surveillance assets in order to scan, track and identify a set of objects in a large region. Different communication networks are used by these platforms to exchange information and data between them and with ground stations. Therefore, it is critical to plan the communication network carefully to support the changing requirements of every mission. The proposed mathematical formulation can be generalized to other similar complex problem like the management of cellular telephony infrastructure. As the problem is NP-hard, we therefore proposed a multi-criteria genetic meta-heuristic to solve the proposed formulation. We used IL simulation environment to generate a set of empirical problem instances for the validation of the formulation and the solving algorithm. The empirical validation shows that the proposed formulation and the solver are providing potentially Pareto-Optimal solutions. The integration of the solver into IL as a plug-in made it available to solve many other problem instances. However, additional validation should be carried out in future work. R EFERENCES [1] A. Bahri and S. Chamberland. “On the wireless local area network design problem with performance guarantees”. Computer Networks, vol. 48, pp. 856-866, 2005.

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