Wireless Sensor Networks Optimization by using 2 ...

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Wireless Sensor Networks Optimization by using 2-Stage Algorithm based on Imperialist Competitive Algorithm (2S-ICA) Hamid R. Lashgarian Azad1, Seyed N. Shetab Boushehri2 Abstract—Wireless sensor networks (WSN) have become progressively popular due to their wide range of applications. Wireless Sensor Network is made of numerous tiny sensor nodes that are battery powered. Maximizing the lifetime of wireless sensor network is very important problem. In this paper, we propose two-stage protocol based on imperialist competitive algorithm (2S-ICA) to solve a sensor network optimization problem. Long communication distances between sensors and a sink (or destination) in a sensor network can greatly drain the energy of sensors and reduce the lifetime of a network. By clustering a sensor network into a number of independent clusters using a 2S-ICA, we can greatly minimize the total communication distance, thus prolonging the network lifetime. Comparison results of proposed protocol and LEACH protocol, which is the common to solve WSN problem, show that our protocol has a better performance in term of improving network life and increasing number of transmitted data.

be very power consuming due to the long distances from sensors to the sink. Alternative designs that shorten or minimize the communication distances can prolong network lifetimes. The use of clusters for transferring data to a base station leverages the advantages of small transmit distances for most nodes, requiring only a few nodes to transmit far distances to the base station. Clustering means to divide the network into a number of independent clusters, each of which has a clusterhead that gathers data from all nodes within its cluster. These cluster heads then compress the data and send it directly to the sink. Clustering can greatly decrease communication costs of most nodes because they only need to send data to the nearest cluster head, rather than directly to a base station that may be further away [1] (see Figure2).

Index Terms—Wireless Sensor Network, Imperialist Competitive Algorithm, LEACH protocol, K-means clustering

I. INTRODUCTION Wireless sensor networks are developing quickly and have been widely used in both military and civilian applications such as target tracking, surveillance and security management. Since a sensor is a small, weightless, battery-powered device, it has limited energy. Therefore, energy consumption is a critical issue in sensor networks [1]. We are interested in sensor networks in which a large number of sensors are circumfused to attain a given goal. All data achieved by member sensors must be transmitted to a base station or data collector. The longer the communication distance, the more energy will be consumed during transmission. Figure 1 is an example of direct transmission where each sensor transmits messages directly to the sink. Direct transmission networks are very uncomplicated to design but can

Figure 2: Clustering of network in order to reduce communication costs

In this paper, we assume the sensor network is static. All nodes are assumed to have the capabilities of a cluster head and the ability to regulate their transmission power based on transmission distance. Clustering a network to minimize the total distance is an NP-hard problem [2]. For a given network topology, it is difficult to find the optimal number of cluster-heads and their locations. Consider a 100-node network, to perform a search of all possible solutions requires 100 1 2 C100 + C100 + …+ C100 = 2100 -1

Figure 1: An example of direct transmission 1

Corresponding author, Email: [email protected]

(1)

different combination that is far too large to be controlled by existing computer resources. Imperialist competitive algorithm (ICA) is one of the most powerful evolutionary algorithms. It has been used extensively to solve different kinds of optimization problems. This algorithm is based on social and political process of 2

Assistant Professor of Industrial Engineering Department in Isfahan University of Technology

2 imperialistic competition [3]. In this paper, we propose 2-stage algorithm based on imperialist competitive algorithm (2S-ICA) to determine both the number and location of the cluster-heads that minimizes the communication distance in a sensor network to efficiently reduce energy consumption and maximize the lifetime of the network. The paper is organized as follows: In section 2, wireless sensor network lifetime problem is discussed. In sections 3, imperialist competitive algorithm is described. The following, in sections 4, 2-stage algorithm based on imperialist competitive algorithm (2S-ICA) is shown. In section 5, comparison between 2S-ICA and LEACH protocol is done and Being more efficient of the 2S-ICA is demonstrated. Finally, section 6 includes a summary and the conclusion. II. WIRELESS SENSOR NETWORK A Wireless Sensor Network (WSN) can be defined as a network of small-embedded devices, called sensors, which communicate wirelessly following an adhoc configuration. The tendency to progression in research and development of WSN was initially motivated by military applications such as surveillance of threats on the battleground, mainly because WSN can replace single high-cost sensor assets with large arrays of distributed sensors. There are other interesting fields like house control, building mechanization and medical applications. A number of hospitals and medical centers are investigating the usage of WSN technology in a wide range of applications, including pre-hospital and in-hospital patient monitoring, rehabilitation, and disaster response. WSNs can also be found in environmental monitoring applications such as fire detection in forest and rural areas [4]. The main concern in communication between nodes of WSNs is the energy consumption. In sensor networks, a sensor node is equipped with one or more integrated sensors, embedded processors with limited capability, and short-range radio communication ability. These sensor nodes are powered using batteries with limited capacity. By contain to standard wireless networks, wireless sensor nodes are often deployed in variable environments, making it difficult to change their batteries. Moreover, recharging sensor batteries is complicated and still impossible. These severe constraints have a direct impact on the lifetime of a sensor node. As a result, energy conservation becomes an important area in WSNs to prolong the lifetime of sensor nodes [5]. Therefore, the power

management schemes of wireless sensor networks have attracted high attention in recent years. Much published research has addressed all kinds of issues related to them. In [6], the number of clusters that should be formed for escalating the lifetime of a network with provisions made to include equal number of nodes in each cluster has been minimized. The analysis and simulation results show that with realistic radio model we have achieved better load balance than several existing protocols, like LBEERA, HDS, SHORT, PEGASIS, LEACH and BINARY. A suitable node deployment strategy was adopted for ensuring wireless connectivity between each node. In [7] LEACH Algorithm is presented, which randomly and periodically alternates the role of the cluster head over all existing nodes and ensures that all the nodes run out of their battery almost simultaneously. In this case, very low remained energy is wasted at the expiration time of the system [8]. However, the disadvantage of applying cluster head role rotation is that all the nodes in the network must be able to act as cluster heads, and therefore should have necessary hardware capabilities [9]. This method has some advantage as follows: a cluster head can reduce the number of redundant packets by aggregating data in the cluster [10]. By limiting the domain of the inter-cluster interactions to cluster heads, it maintains communication bandwidth [11]. In addition, this method can minimize the rate of energy consumption in nodes. III. PROPOSED ALGORITHM A. Original ICA ICA starts with an initial population. In this algorithm, any member of the population is called a country. Some of the best countries in the population are selected to be the imperialist states and all the other countries form the colonies of these imperialists. After allocating all colonies among imperialists and generating the initial empires, these colonies start moving toward their relevant imperialist country. This movement is a simple model of assimilation policy that was perused by some imperialist states. The movement of colonies toward their relevant imperialists along with competition among empires and collapse mechanism will hopefully cause all the countries to converge to a state in which there exist just one empire in the world and all the other countries are its colonies. As a result, ICA could be taken into account as a powerful technique [3].

Figure 3: Flowchart of original ICA [3].

3 B. K-means clustering Clustering is one of the unsupervised learning branches where a set of patterns, usually vectors in a multi-dimensional space, are collected into clusters in such a way that patterns in the same cluster are similar in some sense and patterns in different clusters are different in the same sense. K-mean is one of the most popular methods of clustering. The term ‘k-means’ was first used by MacQueen (1967) [12], though the idea goes back to Hugo Steinhaus in 1956 [13]. Lloyd first proposed the standard algorithm in 1957 as a technique for pulse-code modulation, though it was not published until 1982 [14]. The goal of the K-means algorithm is to minimize the total cost function, which is a squared error function. Each cluster is identified by a centroid. The algorithm follows an iterative procedure. Initially, k cluster is created randomly. Next, the centroid of each group (cluster) is computed. After this, a new partition is built by associating each entry point to the cluster whose centroid is closest to it. Finally, the cluster centers are recalculated for the new clusters. The algorithm is executed until convergence is reached. The cost function is calculated as follows: For each data vector, assign the vector to the cluster with the closest centroid vector, where the distance to the centroid is determined using 𝑛 2 𝐹(𝑋, 𝑌) = ∑𝑁 𝑖=1 min ∑𝑗=1(𝑥𝑖,𝑗 − 𝑦𝑖,𝑗 ) , (2)

where X denotes the input data vector, Y denotes the centroid vector of cluster, n subscripts the number of features of each centroid vector and (N) the number of data input. Figure 4 shows its flowchart [15].

C. 2-Stage Algorithm based on Imperialist Competitive Algorithm The proposed algorithm has two stages. Stage 1 presents a protocol in which network clustering performs base on Kmeans method and imperialist competitive algorithm. In the stage 2, we evaluate amount of dissipated energy of network. These stages designed as follows: Stage 1 – Clustering of network Step 1: Creation initial empires A) Generate country An initial population of input data is created randomly: 𝑋1 𝑋2 𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 = [ ⋮ ] (3) 𝑋𝑁𝑝𝑜𝑝 𝑋𝑖 = 𝐶𝑜𝑢𝑛𝑡𝑟𝑦𝑖 = [𝐶1 , 𝐶2 , … , 𝐶𝑘 ] , 𝑘 = 1,2, … . , 𝑁𝑛𝑜𝑑𝑒 (4) 𝑅 = 𝑅𝑎𝑛𝑑𝑜𝑚 𝑛𝑢𝑚𝑏𝑒𝑟 𝑠𝑒𝑙𝑒𝑐𝑡 𝑓𝑟𝑜𝑚 [1 𝛼 × 𝑁𝑛𝑜𝑑𝑒 ] (5) 𝐻 = {𝑅 𝑛𝑢𝑚𝑏𝑒𝑟𝑠 𝑟𝑎𝑛𝑑𝑜𝑚𝑙𝑦 𝑠𝑒𝑙𝑒𝑐𝑡 𝑓𝑟𝑜𝑚 [1

(6) 1 𝐶𝑗 = { 0

𝑖𝑓 𝑗 ∈ 𝐻 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

𝑁𝑛𝑜𝑑𝑒 ]}

(7)

where 𝑋𝑖 is one of the country, 𝐶𝑗 is 𝑗𝑡ℎ element for 𝑖 𝑡ℎ country, 𝑁𝑝𝑜𝑝 is the number of population, 𝑁𝑛𝑜𝑑𝑒 is the number of network nodes and 𝛼 is the distribution rate. Sample of population is shown in Figure 5.

𝑋1 = 𝐶𝑜𝑢𝑛𝑡𝑟𝑦1 𝑋2 = 𝐶𝑜𝑢𝑛𝑡𝑟𝑦2 𝐶𝑜𝑢𝑛𝑡𝑟𝑦4

𝑋3 = 𝐶𝑜𝑢𝑛𝑡𝑟𝑦3

𝑋4 =

Figure 5: Sample of population - in each country, dark points represent elements which have 1 value and white points represent elements which has 0 value.

B)

Calculate cost of each country

i.K-mean clustering for each country Use k-means algorithm for each country and replace cluster heads with nearest countries. Therefore, elements of each country are divided to two groups as below: 𝐶𝑜𝑢𝑛𝑡𝑟𝑦𝑖 = [𝐶1 , 𝐶2 , … , 𝐶𝑘 ] = {(𝐶𝐻𝑗 , 𝐶𝑀𝑙 ) | 𝑗 = {𝑘|𝐶𝑘 = 1}, 𝑙 = {𝑘|𝐶𝑘 = 0} } (8)

Figure 4: Flowchart of K-mean clustering.

where 𝐶𝐻𝑗 is 𝑗𝑡ℎ cluster head for 𝑖 𝑡ℎ country, 𝐶𝑀𝑙 is 𝑙 𝑡ℎ cluster member for 𝑗𝑡ℎ cluster. ii.Calculate objective function value The cost function is evaluated for each country as below:

4

𝑁𝐶𝐻 𝐹(𝐶𝑜𝑢𝑛𝑡𝑟𝑦𝑖 ) = ∑𝑗−1 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 (𝐶𝐻𝑗 , 𝐵𝑎𝑠𝑒 𝑆𝑡𝑎𝑡𝑖𝑜𝑛) + 𝑁𝐶𝑀

𝐶𝐻 ∑𝑁 ∑𝑙=1 𝑗 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 (𝐶𝐻𝑗 , 𝐶𝑀𝑙 ) (9) 𝑗=1

where 𝑁𝐶𝐻 is the number of cluster head for 𝑖 𝑡ℎ country, 𝑁𝐶𝑀𝑗 is the number of cluster member for 𝑗𝑡ℎ cluster head. C) Select the imperialist states and Divide colonies among imperialist Countries with minimum cost function are chosen as the imperialist states and the remaining ones form the colonies of these imperialists. After selecting the imperialists, the remaining countries are assigned to the imperialists based on their cost function value, respectively. Step 2: Assimilation 𝐼𝑚𝑝𝑒𝑟𝑖𝑎𝑙𝑖𝑠𝑡𝑖 = [𝐶1 , 𝐶2 , … , 𝐶𝑘 ] = [𝐶𝐻𝑖 𝐶𝑜𝑙𝑜𝑛𝑖𝑒𝑠𝑖𝑗 = [𝐶1 , 𝐶2 , … , 𝐶𝑘 ] = [𝐶𝐻𝑖𝑗

𝐶𝑀𝑖 ] 𝐶𝑀𝑖𝑗 ]

𝑖 = 1 𝑡𝑜 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝐸𝑚𝑝𝑖𝑟𝑒 (12) 𝑗 = 1 𝑡𝑜 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑖𝑡ℎ 𝐸𝑚𝑝𝑖𝑟𝑒 𝑐𝑜𝑙𝑜𝑛𝑖𝑒𝑠

(10) (11)

(13)

𝐶𝐻𝑖 = 𝐶𝑙𝑢𝑠𝑡𝑒𝑟 𝐻𝑒𝑎𝑑𝑠 𝑜𝑓 𝐼𝑚𝑝𝑒𝑟𝑖𝑎𝑙𝑖𝑠𝑡𝑖 (14) 𝐶𝑀𝑖 = 𝐶𝑙𝑢𝑠𝑡𝑒𝑟 𝑀𝑒𝑚𝑏𝑒𝑟𝑠 𝑜𝑓 𝐼𝑚𝑝𝑒𝑟𝑖𝑎𝑙𝑖𝑠𝑡𝑖

(15)

𝐶𝐻𝑖𝑗 = 𝐶𝑙𝑢𝑠𝑡𝑒𝑟 𝐻𝑒𝑎𝑑𝑠 𝑜𝑓 𝐶𝑜𝑙𝑜𝑛𝑖𝑒𝑠𝑖𝑗 (16) 𝐶𝑀𝑖𝑗 = 𝐶𝑙𝑢𝑠𝑡𝑒𝑟 𝑀𝑒𝑚𝑏𝑒𝑟𝑠 𝑜𝑓 𝐶𝑜𝑙𝑜𝑛𝑖𝑒𝑠𝑖𝑗

(17)

For all empires, we carry out two steps as below: 1) Randomly, one of 𝐶𝐻𝑖 select and if index of selected 𝐶𝐻𝑖 is k, then kth of component of all colonies will be equal to one. 2) Randomly, one of 𝐶𝑀𝑖 select and if index of selected 𝐶𝑀𝑖 is k, then kth of component of all colonies will be equal to zero. Step 3: Revolution First, we calculate number of colonies which must be changed according to revolution rate for all empires and generate new colonies equal to the number specified as explained in step 1-A. Then we have to replace new generated colonies with random selection of colonies. At the end of this section, we calculate cost of new colonies as explained in step 1-B. Step 4: Posses Empire As it is mentioned, during the colonies movement toward the imperialist, some of them may get better position to reach the imperialist. Indeed, it will be happened when colonies cost function is less than imperialists.

Step 5: Check total cost of each empire It is possible to calculate each empire cost which is related to the power of both imperialist and its colonies. It is calculated as follows: 𝑇. 𝐶𝑛 = 𝐹(𝑖𝑚𝑝𝑒𝑟𝑖𝑎𝑙𝑖𝑠𝑡𝑛 ) + 𝛿 𝑚𝑒𝑎𝑛{𝐹(𝑐𝑜𝑙𝑜𝑛𝑖𝑒𝑠 𝑜𝑓 𝑒𝑚𝑝𝑖𝑟𝑒𝑛 )} , 0 < 𝛿 < 1

(18)

𝑇. 𝐶𝑛 is the total cost of 𝑛𝑡ℎ empire. In addition, 𝛿, as an attenuation coefficient, is used to reduce the effect of colonies cost (0 < 𝛿 < 1). Step 6: Do imperialistic competition Imperialistic competition is another strategy utilized in the ICA methodology. All empires try to take the possession of colonies of other empires and control them. The imperialistic competition gradually reduces the power of weaker empires and increases the power of more powerful ones. The imperialistic competition is modeled by just picking some (usually one) of the weakest colonies of the weakest empires and making a competition among all empires to possess these (this) colonies. Based on their total power, in this competition, each of empires will have a likelihood of taking possession of the mentioned colonies [3]. Step 7: Remove weakest empire Powerless empires will collapse in the imperialistic competition and their colonies will be divided among other empires. In modelling collapse mechanism, different criteria can be defined for considering an empire powerless. In most of our implementation, when we assume an empire collapsed, we eliminate it as it loses all of its colonies [3]. Step 8: Check number of empire If there is just one empire, stop it, otherwise return to step 2. Stage 2 – Data transmission process Step 9: Calculate probability of selection as a cluster head for members of each empire Firstly, we have to calculate total destination of each node for each empire as below: 𝑑(𝑁𝑜𝑑𝑒𝑘𝑖 ) = 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 (𝑁𝑜𝑑𝑒𝑘𝑖 , 𝐵𝑎𝑠𝑒 𝑆𝑡𝑎𝑡𝑖𝑜𝑛) + 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑒𝑚𝑝𝑖𝑟𝑒𝑘 𝑚𝑒𝑚𝑏𝑒𝑟 ∑𝑗=1 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 (𝑁𝑜𝑑𝑒𝑘𝑖 , 𝑁𝑜𝑑𝑒𝑘𝑗 )(19) Then we can evaluate probabilities of selection as a cluster head for all nodes as follow: 𝑃𝑟𝑜𝑓𝑐ℎ(𝑁𝑜𝑑𝑒𝑘𝑖 ) = 𝑑(𝑁𝑜𝑑𝑒𝑘𝑖 )/ 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑒𝑚𝑝𝑖𝑟𝑒𝑘 𝑚𝑒𝑚𝑏𝑒𝑟 ∑𝑗=1 𝑑(𝑁𝑜𝑑𝑒𝑘𝑗 )

(20)

Step 10: Election of cluster heads In each empire, a node is elected randomly by considering selection probability of each node.

5 Step 11: Data transmission to base station and calculation energy dissipated for all cluster heads

Number of Alive Nodes

Step 12: Comparison distance node-base station and nodecluster head then data transmission to cluster head or base station (regard to shorter distance) and calculation energy dissipated for all nodes in each empire Step 13: Energy check for all nodes and remove dead nodes. Step 14: If there is no node, stop it, otherwise return to step 10.

Number of Alive Nodes

120 100

2S-ICA LEACH

80 60 40 20

Rounds

Figure 6: The number of alive nodes in each round for 2S-ICA and LEACH

TABLE I PARAMETER SETTING

60

Value

Initial Countries

60

Initial Imperialistic

7

Network dimensions

(-10,10)×(-10,10)

Initial energy of each node

0.5

Number of Iteration

2000

Base Station Location

(11,0)

Number of Nodes

100

50

Total Energy

Parameters

Total Residual Energy LEACH

40 30 20 10 0

1 92 183 274 365 456 547 638 729 820 911 1002 1093 1184 1275 1366 1457 1548 1639 1730 1821 1912

IV. EXPERIMENTAL RESULTS We have simulated the proposed algorithm using MATLAB and compared it to LEACH protocol. The list of the used simulation parameters and their values are shown in Table 1.

1 107 213 319 425 531 637 743 849 955 1061 1167 1273 1379 1485 1591 1697 1803 1909

0

Rounds Figure 7: Total residual of energy in each round

The performance of the proposed algorithm is evaluated using several tests. For the simulation, we have considered a scenario in which 100 nodes are distributed in the area randomly. Number of alive nodes in 2000 simulation rounds is shown in Figure 6. As can be seen, the death rate of nodes in LEACH algorithm is faster than 2S-ICA algorithm. This is due to the. appropriate selection of cluster heads using the proposed algorithm. In addition, the first dead node is in 1010th and 927th round for 2S-ICA and LEACH respectively. In the second experiment, we compared the sum of residual energy of nodes in the proposed algorithm and LEACH protocol during different rounds. As can be seen in Figure 7, the proposed algorithm consumes less energy impalpably and so, prolongs the network lifetime. To clarify superiority of 2S-ICA, we have calculated number of transmitted pocket data to base station and cluster heads for each round and have shown in figure 8, 9. The total number of transmitted pocket data to cluster heads is 111497 and 111123 in 2S-ICA and LEACH respectively. In addition, the total number of transmitted pocket data to base station is 18822 in 2S-ICA and 12512 in LEACH.

V. CONCLUSION In this paper, we proposed a 2-stage algorithm based on imperialist competitive algorithm. Stage 1 presents a protocol in which network clustering implements base on K-means method and imperialist competitive algorithm. In the stage 2, we assess amount of dissipated energy of network. The proposed algorithm considers different parameters to increase the network lifetime. In order to evaluate proposed algorithm, we simulated our algorithm and compared it to LEACH protocol. The results of the simulations show the effectiveness of the proposed mechanism. 2S-ICA has a better performance than LEACH in term of improving network life and increasing number of transmitted data.

6 Pocket to Cluster Heads in LEACH 120 Number of Transmitted Pocket

100 90 80 70 60 50 40 30 20 10 0

100 80 60 40 20

1 144 287 430 573 716 859 1002 1145 1288 1431 1574 1717 1860

0

1 135 269 403 537 671 805 939 1073 1207 1341 1475 1609 1743 1877

Number of Transmitted Pocket

Pocket to Cluster Heads in 2S-ICA

Rounds

Rounds

Figure 8: The number of transmitted pocket data to cluster heads in each round

Pocket to Base Station in 2S-ICA

Pocket to Base Station in LEACH 25 Number of Transmitted Pocket

12

20

10

15

8 6

10

4 2

1 127 253 379 505 631 757 883 1009 1135 1261 1387 1513 1639 1765 1891

0

Rounds

5 0

1 144 287 430 573 716 859 1002 1145 1288 1431 1574 1717 1860

Number of Transmitted Pocket

14

Rounds

Figure 9: The number of transmitted pocket data to base station in each round

REFERENCES

[1] S. Jin, M. Zhou, and A. S. Wu, “Sensor network optimization using a genetic algorithm,” in Proceedings of the 7th World Multiconference on Systemics, Cybernetics and Informatics, 2003. [2] P. Pardalos and H. Wolkowicz, “Quadratic Assignments and Related Problems”, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Vol. 16,1994. [3] E. Atashpaz, and C. Lucas, “Imperialist competitive algorithm: an algorithm for optimization inspired by imperialistic competition”, IEEE Congress on Evolutionary Computation, pp.4661–4666, 2007. [4] S. Sendra, “Power Saving and Energy Optimization Techniques for Wireless Sensor Networks”, Journal of communications, vol. 6, no. 6, 2011.

[5] A. Boudhir, M. Bouhorma, M. Benahmed, “Energy Optimization Approaches In Wireless Sensor Networks: A Survey”, International Journal of networks and systems, vol 1, No. 1, 2012. [6] J. Banerjee, S. K. Mitra., P. Ghosh,. M. K. Naskar., “An optimized reduced energy consumption algorithm for routing in wireless sensor networks”, Proc. of Advances in Computing and communications in Computer and information science. Vol. 192, No. 2, pp.82-92, 2011. [7] A. Nayebi, H. Sarbazi., “Performance modeling of the LEACH protocol for mobile wireless sensor networks”, Proc. Of Parallel Distribution Computing. Vol. 2, No. 2,pp. 812–821, 2011. [8] W. Allen, K. Lorincz., M. Welsh., O, Marcillo., J. Lees., “ Deploying a Wireless Sensor Network on an Active Volcano”, Proc. of IEEE Internet Computing Vol.10 No. 2, pp. 1825,2006.

7 [9] N. Jafari, S. H. Eshagi., “Reduce Energy Consumption and Increase the Lifetime of Heterogeneous Wireless Sensor Networks: Evolutionary Approach”, International Journal of Advanced Research in Computer Science Vol. 2, No. 5, pp. 112-117, 2011. [10] L. Qing, Q. Zhu., M. Wang., “Design of a distributed energy-efficient clustering algorithm for heterogeneous wireless sensor networks”, Proc. of Computer Communications, Vol. 29 , No. 4,pp. 2230–2237, 2006. [11] H. C. Li, C. C. Chen., “Characteristics of long-term regional seismicity before the 2008 Wen-Chuan, China, earthquake using pattern informatics and genetic algorithms, Natural Hazards and Earth System Sciences”, Nat. Hazards Earth Syst. Sci., 11, 1003–1009, 2011. [12] J. MacQueen, “Some methods for classification and analysis of multivariate observations”, Proc. of the Fifth Berkeley Symp. On Math. Stat. and Prob., vol. 1, pp. 281-296, 1967. [13] F. Lindsten, F. Ohlsson, L. Lennard, "Just Relax and Come Clustering. A Convexification of k-means Clustering", Technical report from Automatic Control at Linköpings universitet (Linköping University), 2011. [14] S. P. Lloyd., "Least squares quantization in PCM". IEEE Transactions on Information Theory 28 (2): 129–137, 1982. [15] A. Jain, N. Murty, P. Flynn, “Data clustering: A review”, ACM Computing Surveys, 31 (3), 264–323, 1999.

Hamid Reza Lashgarian Azad is received MSc degree in Industrial Engineering from Isfahan University of Technology, Isfahan, Iran, in 2011 and his BE in Applied Mathematics from Arak University, Arak, Iran, in 2008. His research interests are in optimization, development and application of evolutionary algorithm, Fuzzy logic, system dynamics, and decision making problems. Seyed Nader Shetab Boushehri received the B.S. degree in electrical engineering and the M.S. degree in systems engineering from Isfahan University of Technology, Isfahan, Iran, in 1986 and 1989 respectively. Also he received the PhD degree in transportation planning from Sharif University of technology, Tehran, Iran in 1997. His research interests are in operation research, urban transportation planning, system dynamics and economics. He is an Assistant Professor of Industrial Engineering Department in Isfahan University of Technology.