A New Meta-heuristic Algorithm for Maximizing Lifetime of Wireless

Wireless Pers Commun DOI 10.1007/s11277-014-2249-2

A New Meta-heuristic Algorithm for Maximizing Lifetime of Wireless Sensor Networks Habib Mostafaei · Mohammad Shojafar

© Springer Science+Business Media New York 2015

Abstract Monitoring a set of targets and extending network lifetime is a critical issue in wireless sensor networks (WSNs). Various coverage scheduling algorithms have been proposed in the literature for monitoring deployed targets in WSNs. These algorithms divide the sensor nodes into cover sets, and each cover set can monitor all targets. It is proven that finding the maximum number of disjointed cover sets is an NP-complete problem. In this paper we present a novel and efficient cover set algorithm based on Imperialist Competitive Algorithm (ICA). The proposed algorithm taking advantage of ICA determines the sensor nodes that must be selected in different cover sets. As the presented algorithm proceeds, the cover sets are generated to monitor all deployed targets. In order to evaluate the performance of the proposed algorithm, several simulations have been conducted and the obtained results show that the proposed approach outperforms similar algorithms in terms of extending the network lifetime. Also, our proposed algorithm has a coverage redundancy that is about 1–2 % close to the optimal value. Keywords Imperialist Competitive Algorithm (ICA) · Sensor scheduling · Disjoint set cover · Wireless sensor networks (WSNs)

1 Introduction Wireless Sensor Networks (WSNs) are being used in a variety of applications. A sensor network consists of many small nodes, and energy efficiency is one of the most critical issues in different protocols. The main constraint of these sensor nodes is their battery energy which

H. Mostafaei (B) Department of Computer Engineering, Urmia Branch, Islamic Azad University, Urmia, Iran e-mail: [email protected] M. Shojafar Department of Information Engineering, Electronics (DIET), Sapienza University of Rome, Rome, Italy e-mail: [email protected]

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limits network lifetime. Therefore, energy efficiency is in design of network protocols is one way to prolong network lifetime. The coverage problem is a fundamental one in WSNs used in environment monitoring and surveillance purposes. The coverage concept is subject to a wide range of interpretations due to the variety of sensors and applications. Generally, coverage has a direct effect on the network performance and can be considered as the measure of the quality of service in WSNs [1]. In this paper, we focus on monitoring targets with a WSN. One of the most common methods for a reduction in energy consumption in sensor networks and increasing network lifetime is to schedule sensor nodes into subsets so that each covers all targets in the deployed network. Then, each subset can be active in different time periods to monitor scattered targets. Meanwhile all other subsets can switch to low energy consumption modes in order to save their energy for their own time periods. Fundamentally, there are two methods to divide sensor nodes into subsets called disjointed set cover and maximum set cover. In disjointed set cover, each node in subset can only be activated for one round which consumes its full energy in activated time. But, in maximum set cover problem each node in different subset could get activated more than once. The coverage requirements are diverse for different applications. There may have some other constraints depending on the assumptions and objectives of the problem. For example, it might be required that the sensor nodes in each sensor cover be also able to form a connected network to the sink. The lifetime maximization problem is much simplified if connectivity is not considered as a constraint. One scenario for not considering connectivity among nodes might be like this. The sensor field is far away from us, and an aircraft as the sink flies over the sensor field to collect the sensors’ data. All active nodes send their sensed data directly to the sink, and they consume almost the same amount of energy for sending the data. In such an example, the energy consumption model is simple. All active sensor nodes consume the same amount of energy per time unit; and all sleep sensor nodes do not consume any energy. However, depending on the coverage requirements, this lifetime maximization problem can be as hard as an NP-complete problem. In this work we proposed an Imperialist Competitive Algorithm (ICA) based approach to find maximum set cover in deployed network and used ICA approach to extend the network lifetime. We assume that the number of deployed sensor nodes is more than it’s required. Therefore we schedule proper (active or idle) nodes to monitor deployed targets. The main contributions of this paper are as following: • We propose an energy-efficient scheduling mechanism for cover set problem in WSNs. • A new cover set formation approach is introduced to monitor all deployed targets. • The proposed algorithm has better performances than traditional algorithms. The rest of the paper is organized as follows. In Sect. 2, we present related works in the field of target coverage energy efficiency problem. Section 3 briefly describes the target coverage problem. ICA as a basic strategy used in the proposed method will be discussed in Sect. 4. In Sect. 5, the proposed method is presented. Section 6 presents the simulation results, and Sect. 7 concludes the paper. 2 Related Work Coverage problem has different definitions and specifications according to the recent researches on wireless sensor networks. Zhu et al. [2] provided a good survey on various

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coverage and connectivity issues in wireless sensor networks. This problem in WSN can be classified in three main types which are target (point) coverage, area coverage, and barrier coverage. First, the point (target) coverage subject is to monitor a set of deployed targets in networks. Targets are either stationary or fixed. Second, the objective of area coverage is to monitor deployed area in networks. Mostafaei et al. [3,4] proposed a learning automata based approach to prolong network lifetime in wireless sensor networks in which each node in network is equipped with learning automata and helps nodes to select a proper state of either active or asleep. Third, the barrier coverage subject is to detect penetrated path by intruders into networks. For energy efficient monitoring of barriers in WSNs, a learning automata based method has been proposed in [5]. In [6] authors built a barrier sensor with minimum cost in sensor networks. They provided a distributed algorithm to solve minimum-cost barrier coverage problem in asynchronous wireless sensor networks. A distributed learning automata based algorithm for stochastic barrier coverage problem is proposed in [7]. The goal of dynamic point coverage in WSN is to detect some moving target points in the area of the network using as few sensor nodes as possible. One way to deal with this problem is to schedule sensor nodes in such a way that a node is activated only at the times the target point is in its sensing region. In [8] authors proposed a scheduling algorithm based on learning automata to deal with the problem of dynamic point coverage. They used learning automata to select best nodes to cover dynamic targets. In their proposed algorithm, each node in the network is equipped with a set of learning automata. The learning automata residing in each node try to learn the maximum sleep duration for the node in such a way that the detection rate of target points by the node does not degrade dramatically. This is done using the information obtained about the movement patterns of target points while passing throughout the sensing region of the nodes. In [9] authors considered target coverage problem and they proposed a sub-set based method to divide sensor nodes into different cover sets as each cover set can cover all targets in network. The objective of their method is maximizing the number of cover sets. Authors in [10] proposed a learning automata based algorithm to find maximum disjointed set cover. They used learning automata to find a better state (active or sleep) of each node in any given time in network. Mostafaei et al. [11] devised a learning automata based algorithm to solve maximum lifetime problem in WSNs. They used the characteristics of learning automata to schedule sensor nodes into different cover sets and extend network lifetime. In [12] authors devised a novel and efficient coverage algorithm which can produce both kinds of disjoint cover sets, i.e. cover sets with no common sensor nodes, as well as non-disjoint cover sets. While searching for the best sensor to include in a cover set, their approach used a cost function that takes into account the monitoring capabilities of a sensor, its association with poorly monitored targets, and also the sensor’s remaining battery life. Mohamadi et al. [13] proposed four learning automata-based algorithms to solve target coverage problem in Directional Sensor Networks(DSNs). They designed several pruning rules to improve the performance of these algorithms. In [14], authors presented a hybrid approximation approach for complete minimum-cost target coverage problem in wireless sensor networks. They used a combination of LProunding and set cover selection methods to propose their method. Gu et al. proposed a column generation based algorithm to find near optimal solution to address target coverage in wireless sensor networks in [6]. They offered an approach that can guarantee at least (1−ε) of optimal network lifetime. Authors in [15] consider a target covering sensor with users’ satisfied probability. They introduce a failure probability into the target coverage problem to improve and control the system reliability. They modeled the solution as α-Reliable Maximum Sensor Covers (α-

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RMSC) problem and proposed a heuristic greedy method to find maximum number of αReliable sensor covers. Their algorithm can control the failure rate of whole system which is a critical aspect in many applications of wireless sensor networks such as military surveillance and environment monitoring systems. Gil and Han [16] have proposed two greedy algorithms to maximize the number of cover sets while managing the critical targets. The first one uses greedy approach and the second one uses genetic algorithm to find the solution for this problem. The proposed algorithms can find a solution faster compared to the other heuristic algorithms, but it may fail to find an optimal solution due to its local search. Authors [17] used the advantage of optimization capability of memetic algorithms to extend network lifetime. The latter requires an upper bound on the number of covers which cannot be easily obtained. Connected target coverage (CTC) is another type of target coverage problem. The objective in this problem is to monitor all deployed targets in the network in which each selected sensor node should connected to to other and sink node in the network. Zhao and Gurusamy [18] considered CTC problem in wireless sensor networks for special state in which each scheduled sensor node in network can communicate with each other and sink node directly or through multihop communication in network. They studied the problem with two observation scenarios depending on whether a sensor can distinguish the targets in its sensing area or not. They modeled this problem as maximum cover tree problem and proposed a greedy method to solve this problem and developed a low-cost heuristic algorithm which can be implemented in a distributed fashion for both scenarios. Yen et al. [19] proposed an efficient method to guarantee coverage and connectivity in wireless sensor networks. They used a different deployment method to guarantee coverage and preserve connectivity. Gupta et al. [20] introduced another type of target coverage called connected cover set. In this case, each subset selected sensor node can communicate with any other sensor node directly or via multihop communication in the network. In [8,21–23] some coverage-preserving scheduling algorithms were discussed. Tian and Georganas [23] devised an algorithm in which each node in the network autonomously and periodically makes decisions on whether a node turns itself on or off only based on its local working neighbor information. To preserve sensing coverage, a node will turn off when other active neighbors can help it to cover its whole working area. Authors [22] presented optimal coverage-preserving scheme (OCoPS) that extends the well-known Central Angle Method in order to identify fully sponsored nodes. OCoPS comprises an extended Central Angle Method to resolve the off-duty conflict problem under different network densities, and an energy-aware wake-up scheme that solves coverage hole problems in off-duty schemes. A coverage-adaptive random sensor scheduling [21] also presented to meet the desired sensing coverage specified by the users. However, the above algorithms pay little attention to network connectivity. Nan et al. [24] studied the sleep/wake scheduling problem in WSNs and proposed a new coverage-guaranteed distributed sleep/wake scheduling (CDSWS) to improve network performance. They presented this mechanism with the purpose of prolonging network lifetime while guaranteeing network coverage. They divided sensor nodes into clusters based on sensing coverage metrics and allowed more than one sensor node in each cluster to stay active simultaneously via a dynamic node selection approach. Furthermore, a dynamic refusal scheme is proposed to overcome the deadlock problem during cluster merging process. The objective of this paper is to propose an ICA based scheduling algorithm in order to solve the target coverage problem while concerning the extension of the network lifetime.

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The proposed scheduling mechanism attempts to construct a maximum number of cover sets each of which are able to monitor all the targets. The proposed algorithms can construct the cover sets in both disjoint and non-disjoint forms.

3 Problem Statement In this study, to state the set cover problem in WSNs, we investigate the following scenario. The sensor field is composed of a set of fixed-location targets that should be monitored continuously, a number of randomly-deployed sensor nodes, and a sink node. We consider maximum set cover problem in which scattered nodes in networks divide into sub sets that are called set covers. The constructed set covers by any approach need not be disjoint. It means that each node in the network can be in more than one set cover. We assume that all nodes in the network have the same amount of initial energy and have the same energy consumption rate in the active state. The lifetime of a single sensor is assumed as one time unit if it is activated all the time. The initial assumptions that are made when setting up the network are as following: • All deployed sensor nodes are homogeneous in terms of sensing range, communication range, and initial energy. • If the Euclidean distance between a sensor node and a target is less than the sensing radius of a node, the node can monitor this target • We suppose that the number of sensor nodes deployed in monitored area is greater than it is required for monitoring target information. In the proposed method, the following notations is taken; • • • • • • • • • •

A signifies sensor network of N sensor nodes T denotes fixed targets which are randomly deployed A L × L depicts the rectangular area . S shows a set of sensor nodes {S1 , S2 , . . . , Sn } M represents the number of targets. T is a set of targets {t1 , t2 , . . . , tm } Wi denotes the lifetime of sensor Si tm symbolizes mth target, 1 ≤ m ≤ M. Si is the ith sensor, 1 ≤ i ≤ N . And λ is the time that each set cover is active

We also assume that all sensor nodes in the network has equal sensing radius and can switch between active and sleep modes. Also, we suppose that the number of sensor nodes deployed in monitored area is greater than it is required to monitor target information. We like to schedule the activity state of the sensor nodes to save their energies and improve the network lifetime. The main problem here is how to organize sensors into several cover sets so that each cover set could monitor all the targets and consequently maximize the network lifetime. In this paper, organizing the sensors refers to specifying the mode of the sensors as either active or passive. Theorem 1 Disjoint set cover problem is NP-complete [9].

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4 Imperialist Competitive Algorithm Meta-heuristic algorithms during recent three decades have been one of the most important groups for solving combinatorial optimization problems. These algorithms such as memetic algorithm, simulated annealing, particle swarm optimization and ant colony optimization have been successfully applied to many difficult optimization problems including TSP, vehicle routing problem, quadratic assignment problem, job scheduling problem, etc. The ICA is one of the meta-heuristic algorithms that have been receiving much attention by researchers and scientists recently. Atashpaz Gargari introduced the ICA approach that uses socio-political evolution of human as a source of inspiration for developing a powerful optimization strategy [25]. This algorithm considers the imperialism as a level of human social evolution, and by mathematically modeling this complicated political and historical process, harnesses it as a tool for evolutionary optimization. The ICA is a new computational method that is used to solve optimization problems in different fields such as computer science, control systems, etc. Like other evolutionary algorithms, it starts with an initial population which is called country and is divided into two types of colonies and imperialists which together form empires. Imperialistic competition among these empires forms in this algorithm. Through this competition, empires with weak powers collapse and powerful ones take possession of their colonies. Imperialistic competition converges to a state in which there exists only one empire and colonies have the same cost function value as the imperialist. The pseudo code of ICA approach is as follows: 1. 2. 3. 4. 5. 6. 7. 8. 9.

Select some random points on the function and initialize the empires. Move the colonies toward their relevant imperialist (Assimilation). Randomly change the position of some colonies (Revolution). If there is a colony in an empire which has lower cost than the imperialist, exchange the positions of that colony and the imperialist. Unite the similar empires. Compute the total cost of all empires. Pick the weakest colony (colonies) from the weakest empires and give it (them) to one of the empires (Imperialistic competition). Eliminate the powerless empires. If stop conditions satisfied, stop, if not go to 2.

After dividing all colonies among imperialists and creating the initial empires, these colonies start moving toward their relevant imperialist state which is based on assimilation policy [26,27]. Figure 1 demonstrates the initial empire formation. By applying an assimilation policy in the direction of various optimization axes, imperialists gain the favor of their colonies. The total power of each empire is modeled as the sum of the imperialist power and a percentage of the mean power of its colonies. After the initial formation of empires, imperialistic competition starts among them. Any empire that has no success in the imperialistic competition with nothing to add to its power is eliminated from the competition. So the survival of an empire depends on its power to assimilate competitors’ colonies. As a result, the power of greater empires is gradually increased in imperialistic competitions, and weaker empires will be eliminated. Empires have to make improvements in their colonies in order to increase their power. For this reason, colonies will eventually become like empires from the point of view of power, and we will see a kind of convergence. The stopping condition of the algorithm is

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Fig. 1 Formation of the empire

having a single empire in the world. An ICA approach for independent task scheduling in grid computing proposed in [28]. 5 Proposed Method In this section, we describe our proposed method based on ICA to solve maximum set cover problem in wireless sensor networks. First, we suppose that all sensor nodes in network are the same, and each network can have two node types, namely active node and idle node. We try to select the proper active nodes to monitor the deployed targets in the network area. In the proposed algorithm, active and idle states are assigned to nodes based on ICA approach. We also suppose that all sensor nodes and targets are deployed randomly, and each node has the same sensing range. 5.1 Generation of Initial Population In the proposed approach, each country (whether imperialists or colonies) represents a sensor node. Our solution for cover set problem in the ICA population consists of two components: a scheduling plan and a monitor plan for each sensor node in the network. The first component is the scheduling plan that tries to schedule nodes into cover sets. In scheduling plan, the empire of each colony, based on covered target information of each node, tries to schedule nodes in best cover set with minimum overlap of covered targets by each sensor node. The second component contains the monitor plan for each node in different cover sets. In this plan, active nodes of empire perform target monitoring operations, and other nodes switch to sleep mode to save their energy. The initial population of countries in the ICA approach is generated randomly. Each country is defined as a 1 × n array where n is the number of network targets. The values in each country are covered targets by this node. Figure 2 shows an example solution to the sensor scheduling problem. In this example, three sensor nodes are considered for monitoring targets and S1, S2, and S3 are run to monitor targets T1 to T9. The cost of each country is calculated by the fitness cost function in Eq. (1). Fitness (country) = makespan (country)

(1)

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Fig. 2 An example solution for a problem with three running sensors on nine targets

Fig. 3 Modification that moves colonies toward an imperialist

According to the cost function, the lower a country’s makespan is, the more appropriate the solution it represents for solving the scheduling problem is. At the outset, a number (Ncountry) of countries are produced, and a number (Nimp) of the best members of this population (countries with the least cost function values) are selected as imperialist countries. The remaining Ncol countries are colonies, each of which belongs to an empire. The colonies are divided among the imperialists in proportion to the imperialists’ power. To do this, the normalized cost (Ci) of each imperialist (i) is computed based on the cost of all imperialists through Eq. (2): Cn = max(ci ) − cn ,

(2)

where cn is the cost of the nth imperialist and Cn is its normalised cost. The colonies are distributed among imperialists based on their Euclidian distance. The normalised power of each imperialist is defined by:     Cn   (3) Pn =   N  imp  C  i=1

i

Then, the number of colonies of an empire will be NCn = round(Pn · Ncol )

(4)

where round is a function that yields the closest integer to a decimal number. The initial number of colonies for each imperialist is randomly selected. Given the initial state of the imperialists, the imperialistic competition begins. The evolution process continues until the stopping condition is satisfied. It is obvious that in the division of colonies, more powerful imperialists will have more colonies. 5.2 Colonies Moving Toward (Assimilation) According to the basic ICA, imperialists try to assimilate their colonies and make them similar to themselves, a goal which is obtained by moving their colonies toward themselves. Depending on how a country is represented for solving an optimization problem, the central government can apply an assimilation policy to try to make its colonies similar to itself in various ways. This part of the colonization process in an optimization algorithm models colonies moving toward the imperialist country’s culture. Specifically, an operation is applied to make part of the colonies’ structures the same as the imperialist’s structure. This operation is shown in Fig. 3 and is implemented as follows: 1. Some cells are randomly selected as imperialist. 2. The selected cells are directly copied into the New-Colony array at the same indexes. 3. The remaining cells of the New-Colony array are copied from the Colony array at the same indexes (cells 1, 4, 5, 6, and 7 in the figure).

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Fig. 4 An example of one revolution operation to resolve sensor scheduling Fig. 5 Exchanging the position of a colony and the imperialist

Fig. 6 The entire empire after position exchange

5.3 Revolution Operation To do revolution operation, two cells are first randomly selected in the colony, and their values are exchanged. This stage (random exchange or revolution operation) is repeated based on a percentage of the total number of deployed targets; this percentage is indicated by the %Revolution parameter. If the new colony is better than the old colony, it replaces the old colony; otherwise, this procedure is repeated. This operation is illustrated in Fig. 4. 5.4 Position Exchanges of Colony and Imperialist Having moved towards the imperialist, a colony may reach a position with lower cost than that of the imperialist. In this case, the colony will become the imperialist in the current empire and vice versa. In the following iterations, colonies in the empire will move to the new imperialist. The colony and imperialist position exchange is shown in Fig. 5. In this figure, the best imperial colony that has a lower cost than that of the imperialist is shaded. Figure 6 shows the entire empire after the exchange. 5.5 Total Power Calculation in an Empire The power of an empire is the power of the imperialist country plus some percentage of the power of all of its colonies. Thus, the total cost T ·Ci of the ith empire is defined as following: T · Ci = cost (imperialisti ) = +ζ mean(cost (colonies of empire))

(5)

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where ζ is a positive real number between 0 and 1. Using a small value for ζ leads to the total cost of an empire being equal to the cost of its central government (imperialist country), while increasing ζ results in an increase in the effect of colonies’ costs on the empire’s total cost 5.6 Imperialistic Competition In the ICA approach, all empires compete to seize more colonies and add to their current colonies. The imperialistic competition gradually causes weaker empires‘ power to decrease and powerful empires‘ power to increase. This competition among imperialists is modeled as follow; the weakest colony of the weakest empire is released from its current imperialist and waits to be possessed by the other empires. During the competing process, each empire will have a likelihood of taking possession of the freed colony based on their total power, that is, empires with more total power will be more likely to possess it. As noted earlier, each empire that fails to increase its power is eliminated in imperialistic competitions. This elimination occurs gradually. Powerless empires lose their colonies (usually one colony at a time) over time, and more powerful empires take possession of those colonies and increase their own power. In each iteration of the algorithm, one or more of the most powerless colonies of an empire are selected, and a competition for possession of these colonies takes place among all empires. Possession of these colonies won’t necessarily go to the most powerful empire, but more powerful empires have greater chances of taking possession. To model the competition among empires for possession of these colonies, each empire’s normalized total cost N · T · Ci is first calculated according to Eq. (6), based on the empire’s total cost T · Ci and Eq. (7), based on the empire’s total cost T · Ci and N · T · Ci = maxj (T · Cj ) − T · Ci

(6)

Empires with lower total costs will have higher normalized total costs. Each empire’s probability Pp i of taking possession (which is proportional to the empire’s power) during the competition for colonies is then calculated through Eq. (7)       N.T.C i   Ppi =   N  imp  j=1 N.T.Cj  and

  P = Pp1 , Pp2 , Pp3 , . . . , P(pNimp)

(7)

(8)

Then, a vector R with the same size as P is created, and its elements are uniformly distributed over random numbers:   R = r1 , r2 , r3 , . . . r(Nimp )

(9)

r1 , r2 , r3 , . . . r(Nimp ) ∈ U(0, 1)

(10)

where

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Then, a vector D is formed by simply subtracting R from P:   D = P − R = D1 , D2 , D3 , . . . D(Nimp )   = Pp1 − r1 , Pp2 − r2 , Pp3 − r3 , . . . , P(pNimp) − r(Nimp)

(11)

5.7 Eliminating Powerless Empires As already mentioned, powerless empires are gradually eliminated in the imperialistic competitions, and more powerful empires are given the possession of colonies. In the present algorithm, an empire is eliminated when it loses all of its colonies, and then it becomes an object of competition among the remaining empires. 5.8 Termination Condition The convergence condition proposed in this paper is when the total number of iterations has been completed, or all but one of the empires have fallen. In either case, the imperialistic competition ends. 5.9 The Proposed ICA Procedure for DSC The computational procedure of the proposed ICA based method for cover set problem is described as follows. • Step 1: Initialize parameters of the ICA: Npop, Nimp, and MaxIter. • Step 2: Randomly generate Npop number of countries. Choose Nimp number of best countries as imperialists and determine their colonies according to their power. • Step 3: If the termination criterion is not met, repeat the following steps. • Step 4: Assimilation • Step 5: Imperialistic competition • Step 6: Revolution • Step 7: Elimination of powerless empires Figure 7 demonstrates the flowchart of proposed scheduling mechanism for cover set problem. 5.10 Computing Network Lifetime During target monitoring, each active sensor lifetime will be updated. We represent the activation time of each target monitoring phase is λ, and it shows that in every phase all selected sensors consume λ amount of their residual energy. Once a sensor finishes its time, it is removed from the set of available sensor list. 5.11 Complexity Analysis In this section, we analyse computational complexity of the proposed algorithm theoretically. To do this, we can do as following: let’s assume that E is the number of Imperialists and P represents the number of countries. Time complexity of selecting each imperialist among countries is O(p). Also, we need O(P) ×E to construct an imperialist in the deployed network. Let’s also assume K to be the overall iteration of ICA approach. In this case, overall time complexity of proposed algorithm is K(O(P)+ O(P) ×E). Therefore, with the use of a capital O notation attributes, the overall time complexity of proposed algorithm is O[K(P) × E].

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H. Mostafaei, M. Shojafar Fig. 7 Illustration of ICA flowchart

6 Simulation Results In this section, we conduct a set of simulations to evaluate the performance of the proposed scheduling mechanism, referred to as proposed scheduling mechanism, in comparison to the performance of similar existing methods. In these simulations, a fixed sensor network is assumed in which all sensor nodes are randomly scattered throughout a 500 m × 500 m two dimensional area. A number of fixed targets are also deployed randomly within this area. Sensing ranges of all sensor nodes are assumed to be equal. Parameters of the conducted simulations are as follows: N: Number of sensor nodes; we vary n in the range [10, 400] to study the effect of the node density on the performance of proposed scheduling mechanism. T: Number of targets; we set m to [5, 10, 50] R: Sensing the range of sensor nodes; we vary R in the range of [150, 400] meters. λ: consumed energy of each sensor nodes in each round; we λ set to 1. To evaluate the performance of the proposed scheduling mechanism the following four experimental factors are evaluated. • Number of sensors: this factor is used to investigate whether the proposed scheme solves the DSC problem. We then compare the performance of the ICA based scheme in terms of how much the network lifetime is extended with the different numbers of targets and sensors.

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Maximizing Lifetime of Wireless Sensor Networks Table 1 Simulation parameters for proposed algorithm

Parameter

value

Network Area

500 m × 500 m

Rs

150–400 m

Sensors

10–400

Targets

5–50

β

0.1

ζ

0.1

Prevolution

0.1

• Sensing ranges: this factor is used to investigate the performance of the proposed scheme with regard to the diverse sensing ranges of deployed sensors. In proportion, as we grow the sensing range, the target coverage of sensors increases. • Distribution of sensors with different sensing ranges: when sensors have different sensing ranges, it is important to investigate the effects to find optimal cover sets. This factor is used to investigate the performance of the proposed scheme with the distribution of the number of sensors over different sensing ranges and to analyse how the distribution affects the performance of the two schemes. • Coverage redundancy: according to [10] coverage redundancy can be defined as the following equation:  Coverage Redundancy = γ nr (12) where nr indicates the number of nodes required for monitoring all deployed targets, and γ represents the number of redundant sensor nodes. The optimal value for coverage redundancy is 1. A sensor node is redundant if its targets are monitored by other nodes in the cover set. In order to obtain the number of redundant sensor nodes, we used our remove redundancy pseudo code in [10]. Energy consumption of sensor nodes for communication tasks follows the first order energy model given in [29]. In this model, the energy required for running the transmitter or receiver circuitry is E elec = 50 nJ/bit, and the transmitter amplifier requires E amp = 100 pJ/bit/m2 . The energy required to transmit a data packet of size l bits from node i to node j is given by T i, j = l E elec + l E amp di,2 j , where di, j is the distance between node i and node j. the energy required to receive an l bit packet from any node j is given by Ri = l E elec . Furthermore, for energy consumption of nodes during sleep and idle states, we use the specifications of MEDUSA II sensor node given in [27]; the energy consumed during the sleep and idle modes would be equal to 0.02 and 22 mJ, respectively. The energy required to switch a node from sleep to active mode is assumed to be negligible. All simulations have been implemented using J-Sim simulator. J-Sim is a java based simulator which is implemented on top of a component-based software architecture. Using this component based architecture, new protocols and algorithms can be designed, implemented and tested in the simulator without any changes to the rest of the simulator’s codes [30]. Results are averaged over 20 runs. Table 1 demonstrates the simulation parameters which are used in our simulation. 6.1 Effect of the Number of Sensors In this experiment we study the effect of the number of sensor nodes deployed within the area on the network lifetime. We fix the sensing ranges to 250 m, and sensor nodes from 10 to

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Network Lifetime

14 12 10 8 Proposed Algorithm (M=5) Proposed Algorithm (M=10)

6 4 2

10

20

30

40

50

Number of Sensors Fig. 8 Comparison of network lifetimes according to the number of sensors

50 are used to cover 5 and 10 targets, respectively, and the performance of proposed scheme is evaluated. Figure 8 demonstrates the effect of the number of sensor nodes on the network lifetime of proposed scheduling mechanism schema. It can be seen from this figure that the network lifetime for 5 targets is longer than that for 10 targets. The lifetime is sensitive to the number of targets in this experiment since targets follow a random uniform distribution. Doubling the number of targets barely decreases the network lifetime. Another result is presented in this figure. As we increase the sensing range, longer lifetime is gained proportionately. It should be noted that the increase in the number of sensor nodes can lead to finding more cover sets. 6.2 Effect of Sensing Range In this simulation, we study the performance of the proposed approach according to the changes in sensing ranges of sensor nodes. To do this, we set N to 10, 30, and 50 nodes, and the sensing range of each sensor node varies from 150 to 300 m in 50-m steps. The number of deployed targets are set to 5 targets. The lifetime variation was evaluated with these parameters. Figure 9 demonstrates the effect of sensing ranges on the performance of the proposed scheme. It can be seen from this figure that the network lifetime becomes longer as the sensing ranges increase. This is due to the fact that the great sensing ranges can cover a greater number of targets than low ranges, and thus fewer sensor nodes are used to build cover sets. By finding as many such cover sets as possible, the overall network lifetime can be extended. Therefore, we can see that wide sensing ranges cause the network lifetime to be extended in WSNs. In Fig. 10, we repeated the same simulation for different deployed targets. To do this simulation, we set deployed targets to 10. We compared Fig. 10 with Fig. 9 and observed that even the lifetime of each curve is very close to the others. 6.3 Proposed Scheduling Mechanism Versus Previous Works In this experiment, we compared the results of ICA based approach with those of the existing works like (heuristic Greedy-DSC method) in [9], our LA-based algorithm called LADSC [10], Mohamadi et al. [13], and Zorbas et al. [12]. To do this experiment we set the

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Maximizing Lifetime of Wireless Sensor Networks 25

Network Lifetime

20

Proposed Algorithm (N=50) Proposed Algorithm (N=30) Proposed Algorithm (N=10)

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number of deployed targets to 50 and let the sensing of sensor nodes vary in the range of 200– 400 m with 50-m incremental steps. We also set the number of sensor nodes to 40 to study the effect of the sensing range of nodes on the lifetime of the network in the proposed scheduling mechanism with different sensing ranges. Figure 11 demonstrates the gained results of this experiment. As it can be seen, the network lifetime is higher when the proposed scheduling mechanism is used rather than heuristic Greedy-DSC method or learning automata based disjoint set cover (LADSC) in [10] and [13]. It also has the same result in [12] where it is a near optimal method to find cover sets in the network. This is because, in our ICA based algorithm, the empire of each colony tries to select the best sensor nodes to monitor targets and put redundant nodes to low energy consumption state until selected for the next rounds. The next experiment was carried out to investigate the influence of the number of each sensor nodes on the network lifetime in the proposed scheduling mechanism. To do this experiment again we set the number of deployed targets to 50 and let the number of sensor nodes vary in the range of 20–60 with 10-unit increment in the number of sensor nodes. The gained results of this experiment, which are given in Fig. 12, display that as we increase

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the number of the sensor nodes, the network lifetime increases proportionally. This Figure also demonstrates that our proposed algorithm outperforms the LADSC algorithm, greedy algorithm, and algorithm in [13] in terms of prolonging the network lifetime. The gained results from our proposed algorithm is similar to the proposed method in [12]. Comparing the results of these experiments with the algorithms in [9,10,12,13] scheme show that the proposed ICA-based scheme markedly extends the network lifetime. In this experiment, we also study the relationship between the sensor nodes in a large number and the total network lifetime. To this end, the number of sensor nodes was set in a range between 100 and 400 with a 50-unit increment step. Let the number of targets be

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Maximizing Lifetime of Wireless Sensor Networks 250 Algorithm in [11] Proposed Algorithm Algorithm in [12] LADSC Greedy Algorithm

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5, and set sensing range r to 250 m. The results demonstrated in Fig. 13 show that the large networks behave as the small ones do. That is, increasing the number of sensors causes the total network lifetime to increase. 6.4 Coverage Redundancy This experiment tries to compare the coverage redundancy of proposed algorithm with the optimal method in terms of coverage redundancy (which is 1, as stated before). We set the number of nodes in the network to 200 and set the sensing range to 250 m. The number of targets was varied from 10 to 50 with an incremental step of 10. The obtained results of this experiment are shown in Fig. 14. As it can be seen, our protocol has a coverage redundancy

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that is about 1–2 % from the optimal. This indicates that our algorithm is able to compute near-minimal covers. We repeated the same simulation to study the effect of the sensing ranges of the sensor nodes on the coverage redundancy of the network in the proposed scheduling mechanism with different sensing ranges. To do this simulation, we set deployed targets to 20 and the number of nodes in the network to 200. The sensing range of each sensor node was ranged from 150 to 300 with an incremental step of 50. It can be seen from Fig. 15 that our proposed algorithm has a coverage redundancy that is about 4–6 % from the optimal. This fact is because with great sensing range the overlaps between sensor nodes are greater and the coverage redundancy in this state is a little greater than that in the previous experiment. 7 Conclusion In this paper, the set cover problem in wireless sensor networks was investigated with the ultimate aim of extending the network lifetime. We proposed an ICA based approach to solve the problem in WSNs. In the proposed algorithm, network nodes are divided into subsets with the help of ICA. Empire nodes in the deployed network try to help their colonies to schedule their best status in any given time of our simulations. In order to investigate the efficiency of the proposed scheme in terms of extending the network lifetime, several simulation experiments were conducted. Simulation results demonstrated that the proposed algorithm, regardless of the sensor nodes’ density, number of the sensor nodes, and sensing radius of the sensor nodes, outperforms the similar existing methods in terms of the network lifetime. Acknowledgments his assistance.

The authors would like to thank Dr. Jamshid Bagherzadeh from Urmia University for

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Habib Mostafaei received the B.S. degree from the Islamic Azad University Khoy branch, in 2006 and the M.S. degree from the Islamic Azad University Arak branch, in 2009, both in software engineering. He joined the faculty of the Computer Engineering Department at Urmia Azad University in 2009. He is a reviewer for Journal of Network and Computer Applications (JNCA), Computer and Electrical Engineering (COMPELECENG), Wireless Networks (WINE), and Computing (COMP). His research interests include learning systems, sensor networks, soft computing, and cloud computing.

Mohammad Shojafar is currently a Ph.D. student in Information and Communication Engineering at DIET Dept. of the “La Sapienza” University of Rome. He Received his M.sc. in Software Engineering in Qazvin Islamic Azad University, Qazvin, Iran in 2010. Also, he Received his B.Sc. in Computer Engineering-Software major in Iran University Science and Technology, Tehran, Iran in 2006. His current research focuses on wireless communications, distributed computing and mathematical and AI optimization. He is an author/co-author of 30+ peer-reviewed publications (h-index=7) in well-known conferences (e.g., IEEE PIMRC, IEEE ICC, IEEE HIS) and journals in IEEE, Elsevier, IOS Press and Springer Publishers. Since 2013, he is the membership of IEEE Systems Man and Cybernetics Society Technical Committee on Soft Computing and a Distinguished Lecturer of IEEE Computer Society representing Europe. In addition, Mohammad was a Programmer and Analyzer in Exploration Directorate Section at N.I.O.C. in Iran from 2012–2013. Email: [email protected] and follow more information at: www.mshojafar.com.

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