MOFPL: Multi-objective fractional particle lion algorithm for the energy aware routing in the WSN

Pervasive and Mobile Computing 58 (2019) 101029

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Pervasive and Mobile Computing journal homepage: www.elsevier.com/locate/pmc

MOFPL: Multi-objective fractional particle lion algorithm for the energy aware routing in the WSN Reeta Bhardwaj

∗,1

, Dinesh Kumar 1

Daviet Jalandhar, India

article

info

Article history: Received 19 December 2018 Received in revised form 20 May 2019 Accepted 31 May 2019 Available online 4 June 2019 Keywords: WSN Energy aware routing Multi-objective fitness function Optimal routing path Normalized network energy

a b s t r a c t Wireless Sensor Networks (WSN) has wider applications in the fields of the healthcare, military, and the weather monitoring. The efficient design of the WSN requires better energy optimization techniques, since the nodes in the WSN are battery operated. The traditional energy aware routing mechanisms neglect the delay, and the traffic rate of the WSN while improving the energy constraints in the node. This work overcomes these challenges by introducing a multi-objective energy aware routing protocol. This paper proposes the multi-objective fitness function based on the energy, delay, traffic rate, distance, and the cluster density. The energy-aware routing is done based on the proposed Multi-objective fractional particle lion algorithm (MOFPL). The proposed MOFPL algorithm finds the optimal cluster head from various cluster head nodes in the WSN. Then the optimal routing path is established based on the proposed multiobjective function. The proposed MOFPL algorithm has 5, 8, 10 alive nodes at the iteration round of 2000 for the WSN with 50, 75, and 100 nodes, respectively. Also, the proposed MOFPL algorithm has achieved higher normalized network energy of 0.05877 and 0.06022 for the WSN with 50 and 100 nodes, respectively. © 2019 Published by Elsevier B.V.

1. Introduction A Wireless sensor network (WSN) [1–4] contains a collection of sensors connected to the wireless medium. The WSN model is powered by the base station which acts as an access point for the series of the sensor devices in the network. The WSN finds application in the various fields, such as weather monitoring, meteorological data collection, and field surveillance [5]. The advancement in the WSN has resulted in the impact in the real-time applications, such as military, science, industry, commerce, transportation, and health-care. The efficiency of the WSN directly depends on the quality of the sensors present in it. The sensors in the WSN need to have better precision, accuracy, and robustness to noise [6]. The sensors [7–9] in the WSN are affected due to the various noise factors from the internal and the external environments. The noise of the surrounding hardware components in the WSN also affects the performance of the sensor nodes. The sensor nodes in the WSN are separated with the large distance. The communication between the sensors nodes is achieved with the wireless channel with low power. The base station effectively collects the data from the sensors and generates the necessary query for the each node [10–19]. The term routing defines the way of sending the packets between the sensor nodes and the base station of the WSN through the wireless communication medium. The main challenge during the routing of the nodes is the consideration ∗ Corresponding author. E-mail address: [email protected] (R. Bhardwaj). 1 Assistant professor. https://doi.org/10.1016/j.pmcj.2019.05.010 1574-1192/© 2019 Published by Elsevier B.V.

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of the energy of the each sensor nodes in the WSN. The lifetime of the WSN network directly depends on the energy of the each sensor nodes [20]. Thus, the routing protocol needs to ensure better network lifetime of the WSN through the efficient routing of the nodes. The energy in the nodes of the WSN is reduced due to the transmission and the reception of the message packets. The routing protocols used for the routing of the nodes can be categorized based on the network parameters, such as participation of the each node in the WSN, various clustering models, mode of working of the nodes, and the network topology. The design of the routing protocol for the WSN directly depends on the factors, such as energy consumption, node deployment, scalability, connectivity, coverage, security [21]. The routing protocols for the WSN are mainly categorized as the single path routing and the multipath routing protocols. The nodes deliver the packets from the source node to the destination node via the intermediate nodes in the WSN. The packet delivery to the sink/destination node via the multiple hops in the WSN depends on the energy efficiency and the load balancing of the network. The routing protocols try to find the tradeoff between the delay, energy cost, and load balancing factors of the WSN for the efficient routing [22]. The nodes present in the WSN are battery powered, and batteries of the sensor nodes are costly. Hence, the routing protocols should provide increased throughput with the efficient reduction in the end-to-end delay of the network. The single path routing protocols analyze the paths for reaching the sink node from the source node and thus, selects only one path for routing, whereas, the multipath routing protocol analyzes the possible paths in the WSN and selects more than one path for the routing. The single path routing suffers from the disadvantage when the environment has more noise factors. The multipath routing protocols [23] handle the load of the network more efficiently since the availability of the routing path is more. The multipath routing increases the bandwidth and the reliability of the WSN [24]. Energy aware routing protocols with optimization algorithms [25–28] have been utilized to increase the life time of the sensor network. Now a day, most of the researchers have studied biological species like ant as an analogy provided for natural representation for optimization problem. Ant colony optimization algorithm simulating manors of ant colony have been applied in various optimization problems, such as wireless sensor network routing [29]. Also, other optimization algorithms, such as Genetic Algorithm (GA), Particle Swarm Optimization (PSO) are used for multi-path routing. This paper proposes the energy aware routing model for the WSN. The proposed multi-objective fractional particle lion algorithm (MOFPL) algorithm finds the optimal routing path through the optimization process. The proposed MOFPL combines the existing fractional theory (FT) and the PSO along with the lion optimization algorithm (LOA). The proposed model performs the routing with the use of the defined fitness function. The nodes in the WSN communicate with the base station via the cluster head nodes. The cluster head nodes in the WSN are selected based on the multiple objectives, such as cluster distance, energy of the nodes in the WSN, delay, traffic rate and density. These multiple objectives are used with the fitness function to find the optimal cluster head. The proposed MOFPL performs the routing based on the fitness function. The major contributions of the proposed work are enlisted as follows:

• The major contribution of this paper is the design of the MOFPL algorithm to find the optimal cluster head node in the WSN to perform the energy aware routing.

• Firstly, the paper defines the multi-objective fitness function based on the various features of the nodes, such as the distance between the nodes, delay, cluster density, traffic rate, and energy of the nodes.

• Secondly, this paper performs the routing through the proposed MOFPL algorithm. The proposed MOFPL algorithm is the modification of the LOA with the existing models, fractional theory and the PSO. The rest of the paper is organized as follows: Section 1 presents the introductory part of the energy aware routing and the various algorithms for the routing process. Section 2 reviews the literature works and the various challenges in the energy aware routing. Section 3 provides the description of the network and the radio models of the WSN. Section 4 briefs the design and the development of the proposed MOFPL algorithm and the multi-objective fitness function. Section 5 discusses the simulation results of the proposed model and the comparative analysis. Section 6 concludes the paper. 2. Motivation 2.1. Literature survey In this section, various research papers based on the energy aware wireless system with various techniques and methodologies has been discussed. R. Mohanasundaram and P. S. Periasamy [30] have proposed the Hybrid particle swarm optimization algorithm for detecting the fire event. The proposed algorithm integrates the FCM clustering to find the positions of the k storage nodes in the WSN. This paper proposes the FCM clustering based on data storage (CBDS) algorithm for routing the nodes to reduce the energy consumption. The data rate of the WSN used in the simulation is small, and hence the query and the storage are smaller. Kumar and Kumar [31] have proposed the multiobjective fractional artificial bee colony for the clustering of the nodes in the WSN network. Objectives such as energy consumption, distance traveled and delays of the WSN network are considered for efficient query processing. But, the algorithm has a trap at the local optimal solution. Yan et al. [32] have proposed the Degree-Energy-Based Local Random Routing algorithm for the efficient routing of the WSN. The proposed approach performs the routing of the WSN by considering the energy consumption and lifetime

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efficiency of the sensors present in the WSN. The proposed model performs the routing by considering the five different structural topologies under the degree-energy-awareness principle. The multiple costs like distance and energy are not considered as routing criteria. Han et al. [33] have proposed the General Self-Organized Tree-Based Energy-Balance routing protocol (GSTEB) algorithm for the routing of the WSN. The proposed model builds the routing model by selecting the parents of the nodes by considering the neighbor node information and the node itself. Mohammad Hammoudeh and Robert Newman [20] have proposed the cluster-based Route Optimization and Loadbalancing (ROL) protocol for the routing of the nodes in the WSN. The proposed model makes use of the various QoS metrics to ensure the efficiency of the WSN. They have proposed Nutrient-flow-based Distributed Clustering (NDC) algorithm for the load balancing of the network. The proposed method ensures better network lifetime and better end-toend delay. Gurbinder Singh Brar et al. [24] have proposed the directional transmission based energy aware routing protocol (PDORP). The proposed model finds the optimal path within the WSN with the use of the Genetic Algorithm (GA) and Bacterial Foraging Optimization (BFO) algorithms. They have used the computation model to analyze the performance of the proposed protocol. Wang Ke et al. [22] have proposed the energy-aware hierarchical cluster-based (NEAHC) routing protocol for minimizing the energy consumption of the nodes in the WSN. The proposed model ensures reduction of the total energy consumption of the network and optimum usage of the energy by the nodes. The proposed model finds the relay node in the WSN through the nonlinear programming problem. They have found the optimum solution with the use of the defined convex function. Yanjun Yao et al. [34] have proposed the Energy-efficient Delay-aware Lifetime-balancing data collection protocol for the open vehicle routing (OVR) problems occurring in the WSN. The proposed model is more heuristic in nature, and hence the model has more robustness and less computational overhead. The proposed model does not violate the packet delay constraints of the WSN nodes. Haojun Huang et al. [35] introduced an energy-aware dual-path geographic routing (EDGR) protocol for better route recovery from routing holes. EDGR used the residual energy, location information, and the characteristics of energy consumption to make routing decisions. The EDGR was applicable to resource-constrained WSNs with routing holes. Also, it had lower energy consumption and smaller delivery delay. Deepak Sharma and Amol P Bhondekar [36] developed a Traffic and Energy Aware Routing (TEAR) approach to increase the stability period. TEAR outperformed the legacy algorithms, such as DEEC, SEP, and LEACH, in terms of stability period. The performance of the TEAR gets reduced in the absence of traffic heterogeneity. Muhammad Faheem et al. [37] introduced an energy efficient cluster formation algorithm, named Active Node Cluster Formation (ANCF) and a lightweight sensing mechanism, named Active Node Sensing Algorithm (ANSA). Also, they introduced an Active Node Routing Algorithm (ANRA) to overcome the complex intra and inter cluster routing problems. These methods outperformed the other routing methods in terms of congestion management, data redundancy, end-toend delay, and energy efficiency. These methods have reduced performance in more complicated sparse heterogeneous scenarios. M. Faheem and V. C. Gungor [38] introduced a dynamic clustering based energy efficient and quality-of-service (QoS)-aware routing protocol (EQRP), based on bird mating optimization (BMO). This method improved the network reliability and decreases the excessive packets retransmissions. This method was not applicable for robust data delivery. M. Faheem [39] et al. developed a bio-inspired self-optimized butterfly mating optimization-based data gathering routing technique, named Self-optimized Intelligent routing protocol (SIRP) for WSNs-based SG applications. This method achieved its defined goals rather than the existing routing schemes. 2.2. Challenges The energy-aware wireless sensor network system has the following challenges:

• The communication between the nodes in the WSN depends on the power, capacity, and the memory size. The lifetime of the WSN depends on the energy remaining on the each node of the network [10].

• The energy aware routing in the WSN directly depends on the routing algorithm used in work. In the literature [40], the routing scheme used has reduced performance when the solution reaches the local optimum value.

• The WSN with the dynamic topology requires the subsequent altering of the information present in the nodes. Thus the features, such as scalability, reliability, energy efficiency and resource management act as major design criteria for the energy based routing. 3. System model 3.1. Network model of WSN Fig. 1 represents the network model of the WSN. Consider the WSN has N number of sensor nodes. Each node in the WSN is separated with large distance. The sensor nodes in the WSN communicate with each other through the prescribed radio range. The term Si represents the sensor nodes in the WSN. The value of i ranges between 1 ≤ i ≤ N. The dimension of the WSN network is indicated as (P , Q ) in meters. The sensor nodes in the WSN communicate with each other through the wireless medium. The nodes send the sensor readings to the base station. The base station in the WSN is indicated by

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Fig. 1. Network model.

the term B. The location of the base station in the WSN is represented as {0.5Pi , 0.5Qi }. The location of the base station in the WSN is chosen with the help of the optimal local minimum value. The location of the each sensor node in the WSN is represented as {Pi , Qi }. When every node sends their information to the base station node, congestion occurs in the WSN. The nodes send the sensor readings to the cluster head. The cluster head nodes communicate with the base station. The cluster head nodes in the WSN are represented by the term Hj . The WSN contains A number of cluster head nodes. The term j varies between 1 ≤ j ≤ A. A total number of the normal nodes in the WSN is the difference in the total number of sensor nodes and the total number of cluster head nodes i.e. (N − A). The normal sensor nodes in the WSN communicate with the base station through its corresponding cluster heads. The selection of the cluster head in the cluster is the optimization problem. 3.2. Radio model of WSN For the efficient routing of the WSN, the energy of the nodes acts as major design criteria. Each node in the WSN is battery powered. The sensor nodes maintain a routing table. During the routing process, the information in the routing table is subjected to random changes. Hence, the energy of the nodes gets reduced. Consider Cinitial as the initial energy on the node Si . At the initial phase, the energy of the node remains to be high. After the routing process, the energy of the nodes is reduced. The energy of the nodes cannot be rechargeable. Sending and receiving packets between the sensor nodes reduces the energy. The energy remaining in the each node of the WSN can be modeled using the radio model. The WSN contains both the transmitter node and the receiver node. The transmitter and the receiver have the radio electronics and the power amplifier. For every transmission and reception of the data packets in the WSN, the energy of the nodes gets dissipated. When the distance between the sensor node and the cluster head node is greater than the initial distance linitial , then the energy dissipation of the node Si is given as,

4



Cdissipation (Si ) = Celec ∗ m + Camp ∗ m + Si − Hj 

(1)

where, m is the size of the packet. Hj is the cluster head nodes in the WSN, and Si represents the sensor nodes in the WSN. When the distance between the sensor node and the cluster head node is less than the initial distance linitial , then the energy dissipation of the node Si is given as,



2

Cdissipation (Si ) = Celec ∗ m + Cfs ∗ m + Si − Hj 

(2)

R. Bhardwaj and D. Kumar / Pervasive and Mobile Computing 58 (2019) 101029

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where, the term Cfs indicates the sensitivity of the receiver node. The energy dissipation due to the initial distance between the node and the cluster head is given by Eq. (3).

√ Cl initial =

Cfs

(3)

Camp

where, the term Celec indicates the electronic energy of the WSN, the term Cfs indicates the sensitivity of the receiver node, and the term Camp indicates the noise figure of the amplifier. The electronic energy Celec defines the energy dissipated in the node due to the factors, such as coding, spreading, modulation, filtering, and amplification. The Eq. (4) defines the electronic energy of the network. Celec = CTX + CDA

(4)

where, the term CTX indicates the transmitter energy and the term CDA indicate the data aggregation energy. The energy dissipation at the cluster head occurs due to the data transmission to the base station and the due to the receiving of data from the sensor nodes. The Eq. (5) indicates the energy dissipated at the cluster head. Cdissipation (Hj ) = Celec ∗ m

(5)

The data on the network is further transmitted and received by the nodes. This reduces the remaining energy on the nodes. The energy equation of the sensor nodes and the cluster head are updated with Eqs. (6) and (7). Ct +1 (Si ) = Ct (Si ) − Cdissipation (Si )

(6)

Ct +1 (Hj ) = Ct (Hj ) − Cdissipation (Hj )

(7)

where, the term Ct +1 (Si ) indicates the updated energy at the sensor node Si , the term Ct (Si ) indicates the energy of the node at the time t, and the term Cdissipation (Si ) indicates the dissipated energy of the sensor node. The term Ct +1 (Hj ) indicates the updated energy at the cluster head Hj , the term Ct (Hj ) indicates the energy of the cluster head at the time t, and the term Cdissipation (Hj ) indicates the dissipated energy of the cluster head. 4. Construction of the proposed MOFPL algorithm for finding the optimal cluster head node In this paper, the optimal routing path for the energy aware routing of the WSN is calculated. Fig. 2 shows the block diagram of the WSN architecture with the proposed MOFPL algorithm. The proposed MOFPL algorithm performs the routing of the nodes with the use of the particle swarm optimization (PSO) [30], fractional theory (FT) [31] and the lion optimization algorithm (LOA) [41] algorithms. The fitness of the each node is calculated based on the proposed multiobjective fitness function. Various objectives, such as delay, distance, the energy of the nodes, density within the cluster, and the traffic rate are considered for the fitness evaluation. The proposed algorithm finds the optimal cluster head from various cluster head nodes and thus, provides the optimal routing path between the sensor nodes. 4.1. Solution encoding The solution encoding for the selection of the cluster heads among the sensor nodes in the WSN is given in Fig. 3. The WSN contains N sensor nodes communicating with the base station through their cluster heads. There are A cluster heads within the WSN. Each node in the WSN is represented by the term Si and the term Hj indicates the cluster head. The jth cluster in the WSN contains Xj nodes. From the Xj nodes of the jth cluster, any one of the nodes is selected as the cluster head. The cluster head node of the jth cluster is represented as Hj . The selection of the cluster head from the various sensor nodes depend on the fitness function. Normally, the cluster head node has better robustness than the other nodes. The solution encoding for the WSN has the size of 1 × N. 4.2. Multi-objective Fitness function In this paper, the selection of the cluster head nodes from the sensor nodes in the WSN depends on the proposed Multi-objective Fitness function. This paper proposes the maximization fitness function based on the various objectives, such as delay, distance, the energy of the nodes, density within the cluster, and the traffic rate of the nodes. To select the sensor node as the cluster head, each node satisfies the fitness function providing the maximum value. The Eq. (8) expresses the proposed Multi-objective Fitness function.

{[ Fitness = max

1−

D(t) Dnorm

]

[ + 1−

M(t) X ∗A∗N

]

} + [C (t)] + [1 − T (t)] + [1 − Z (t)]

(8)

where, the term D(t) indicates the delay of the sensor nodes in the WSN, the term Dnorm indicates the normalized delay of the WSN. The term M(t) indicates the distance between the sensor nodes and the cluster head nodes, X indicates the total number of nodes in the cluster, A indicates the total number of the cluster heads in the WSN, the term N indicates the

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Fig. 2. Energy aware routing model of WSN with the proposed MOFPL algorithm.

Fig. 3. Solution encoding.

total number of nodes in the WSN. The term C (t) indicates the energy of the cluster head nodes. The term T (t) indicates the traffic rate of the nodes present in the cluster. The term Z (t) indicates the density of the clusters in the WSN. The multi-objectives in the fitness function is explained as follows, Delay: Delay of the WSN defines the sum of the delay present in each node of the WSN. To select the node as the cluster head, the delay should be as low as possible. The delay of the node directly depends on the expected transmission count (ETC) of the node, propagation delay of the node, and the transmission delay of the network. The Eq. (9) expresses the delay of the nodes in the WSN. Delay,

D(t) =

N ∑

Ji (t)(α + βi )

(9)

i=1

where, the term Ji (t) indicates the ETC of the ith node of the WSN at the time t. The term α indicates the transmission delay of the network, and the term βi indicates the propagation delay of the ith node of the WSN. The ETC of the node depends on the forward delivery packet ratio and the received delivery packet ratio of the node at a time t. The Eq. (10)

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expresses the ETC of the ith node of the WSN. Ji (t) =

1

(10)

Fi (t) ∗ Ri (t)

where, the term Fi (t) indicates the forward delivery packet ratio of the ith node at time t, and the term Ri (t) indicates the received delivery packet ratio of the ith node at time t Distance: The second objective of the fitness function is the distance between the nodes and the cluster heads. For the effective communication, the distance between the sensor nodes and the cluster heads should be low. The Eq. (11) expresses the distance between the nodes and the cluster head. Dis tan ce,

M(t) =

A N ∑ ∑   Si − Hj  ;

∨j ∈ i

(11)

j=1 i=1

In the above equation, nodes belonging to the jth cluster are taken for the distance measure. Energy: The energy of the nodes should be high to select the node as the cluster head. The energy of the cluster heads in the WSN is expressed by Eq. (12). Energy,

C (t) =

A 1∑

A

Ct +1 (Hj )

(12)

j=1

where, the term Ct +1 (Hj ) indicates the updated energy of the cluster head and the value is obtained from Eq. (7). Density: The density of the nodes within the cluster should be low for better communication between the nodes. The increase in density within the cluster increases the congestion and the packet drop. The density of the node defines the ratio of the number of nodes within the cluster to the total number of nodes in the WSN. The Eq. (13) expresses the density of the cluster in the WSN. Density,

Z (t) =

A 1 ∑⏐ ⏐ ⏐Xj ⏐ N

(13)

j=1

⏐ ⏐

where, the term ⏐Xj ⏐ indicates the nodes in the jth cluster. Traffic rate: The final objective required for the derivation of the fitness function is the traffic rate of the cluster. The traffic rate has the minimum value for the better communication process. The Eq. (14) expresses the traffic rate of the cluster. Traffic rate,

T (t) =

N ∑ i=1

Li (t) max Li (t)

(14)

where, the term Li (t) indicates the flow rate of the ith node. 4.3. Construction of the proposed MOFPL algorithm The proposed MOFPL algorithm finds the optimal routing path for the routing process. The algorithm finds the optimal cluster head among the various cluster heads in the WSN. The existing LOA [41] algorithm uses three lions to solve the optimization problem. They are a male lion, a female lion, and the nomadic lion. Selection of the optimal cluster head from the various cluster head nodes acts as the optimization problem. The three lions used in the proposed MOFPL algorithm represent the cluster head nodes. The optimization process ensures the elimination of the nomadic cluster head nodes from the routing area. The proposed MOFPL algorithm ensures the following criteria,

• The male lion has the better fitness in the optimization problem. • The proposed MOFPL finds the optimal cluster head from the various cluster head of the WSN through the multi-objective fitness function.

• The routing path between the sensor nodes and the optimal cluster is established. • The selection of the optimal cluster head is made by calculating the fitness of the each node in the WSN with the use of the PSO and the FT algorithms. Various steps in the proposed MOFPL algorithm is explained as follows, Step 1: Pride generation The initial step in the formation MOFPL algorithm is the pride generation. The sensor nodes in the cluster act as the pride of the cluster head node. The term Y U indicates the male lion, the term Y V indicates the female lion, and the term Y W 1 indicates the nomadic lions in the WSN. Y W 1 and Y W 2 are the two nomadic lions, in which Y W 1 is initialized in pride

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generation and Y W 2 is initialized in territorial defense. The various elements of the male lion Y U , female lion Y V , and nomadic lion Y W are expressed as follows, Y U (p) = Y U (1), Y U (2), . . . . . . Y U (P) ;

p = 1, 2, . . . , P

(15)

Y (p) = Y (1), Y (2), . . . . . . Y (P) ;

p = 1, 2, . . . , P

(16)

{

V

{

}

V

V

V

}

Y (p) = Y (1), Y (2), . . . . . . Y (P) ; W

{

W

W

W

}

p = 1, 2, . . . , P

(17)

where, P indicates the population size. Step 2: Proposed multi-objective Fitness evaluation The proposed MOFPL algorithm finds the fitness of the each node through Eq. (8). A threshold is defined for the selection of the cluster head node among the sensor nodes. The fitness of the each lion in the optimization process is calculated as the maximization problem. Step 3: Fertility evaluation based on the PSO and the FT algorithm The next step in the proposed MOFPL algorithm is fertility evaluation. In this step, the fertility of the male lion and the female lion is calculated. The proposed MOFPL algorithm avoids the convergence of the algorithm at the local optima. The fertility evaluation of the male and the female lion depends on the fitness of each lion. In fertility evaluation, the following factors are considered: updated female lion, reference fitness, Laggardness rate, sterility rate, female update count and female generation count. The algorithm chooses a reference fitness value f thres for the evaluation process. When the fitness of the male lion node is greater than the reference fitness, the laggardness rate is updated. Otherwise, the fitness of the male lion is chosen as the reference fitness, and the value of the laggardness rate is reset. The fertility evaluation of the female lion is given as, YqV

{ =

YpV ; if

}

q=p

(18)

other w ise

YqV ;

YpV = min Yqmax , max(Ypmin , ∇ p)

⌊

⌋

(19)

where, the terms YqV , and YpV indicates the qth and the pth vector elements of the female lion Y V . Eq. (19) is the bounding condition, as defined in [41]. The term p indicates the random integer between the values 0 to P. The term ∇ p indicates the female lion update function. The Eq. (20) expresses the formulas for the female lion update function ∇ p.

[ ] ∇ p = YpV (t) + (0.1a2 − 0.05)(YpU (t) − a1 YpV (t))

(20)

where, a1 and a2 ranges between 0 and 1. The proposed MOFPL algorithm enhances the female lion update function ∇ p with the use of the several conditions. The existing LOA algorithm updates the ∇ p by considering the values of the current iteration only. When the value of the Yqmax is greater than the max(Ypmin , ∇ p) and the value of Ypmin is less than the ∇ p, then the vector element YpV changes as follows and represented by Eq. (21). YpV (t) = ∇ p

(21) YpV (t)

where, ∇ p indicates the female lion update function. The value of the is updated for the next iteration. The Eq. (21) expresses the pth vector element of the female lion takes the value of the female update function when the value of the Yqmax is greater than the max(Ypmin , ∇ p) and the value of Ypmin is less than the ∇ p. The update equation of the LOA [41] is represented as follows, YpV (t + 1) = YpV (t) + (0.1a2 − 0.05)(YpU (t) − a1 YpV (t))

[

]

(22)

where, YpV (t + 1) indicates the next iterative value for the pth vector element of the female lion. The FT can be used to consider the values from the previous iteration. The inclusion of the FT algorithm in updating process improves the accuracy of the fertility evaluation. According to the FT Eq. (22) is modified. YpV (t + 1) − YpV (t) = (0.1a2 − 0.05)(YpU (t) − a1 YpV (t))

[

]

(23) η

In the above equation, the term in the RHS can be replaced with the differential function D . Where the value of the

η ranges between 0 and 2. The Eq. (23) is modified as follows, [ ] Dη (YpV (t + 1)) = (0.1a2 − 0.05)(YpU (t) − a1 YpV (t))

(24)

The Eq. (24) is expanded using the FT model and it is expressed as follows, YpV (t + 1) = ηYpV (t) +

1

1

ηYpV (t − 1) + η(η − 1)YpV (t − 2)+ 6 [ ] 1 V η(η − 1)(η − 2)Yp (t − 3) + (0.1a2 − 0.05)(YpU (t) − a1 YpV (t))

24

2

(25)

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Multiply Eq. (25) with (−1) on the both sides. The above equation is modified as follows, 1

1

−YpV (t + 1) = −ηYpV (t) − ηYpV (t − 1) − η(η − 1)YpV (t − 2)− 2 6 [ ] 1 η(η − 1)(η − 2)YpV (t − 3) − (0.1a2 − 0.05)(YpU (t) − a1 YpV (t))

(26)

24

In Eq. (26), add the term ηYpV (t + 1) in the RHS and LHS. 1

1

−YpV (t + 1) + ηYpV (t + 1) = −ηYpV (t) + ηYpV (t + 1) − ηYpV (t − 1) − η(η − 1)YpV (t − 2)− 2 6 [ ] 1 η(η − 1)(η − 2)YpV (t − 3) − (0.1a2 − 0.05)(YpU (t) − a1 YpV (t))

(27)

24 Rearranging Eq. (27),

(1 − η)YpV (t + 1) = η(YpV (t + 1) − YpV (t)) −

1

1

ηY V (t − 1) − η(η − 1)YpV (t − 2)− 2 p 6 ] [ 1 η(η − 1)(η − 2)YpV (t − 3) − (0.1a2 − 0.05)(YpU (t) − a1 YpV (t)) 24 ⎡ ⎤ 1 1 V V V V 1 ⎥ ⎢ η(Yp (t + 1) − Yp (t)) − 2 ηYp (t − 1) − 6 η(η − 1)Yp (t − 2)− YpV (t + 1) = ⎣ 1 [ ] ⎦ (1 − η) V U V η(η − 1)(η − 2)Yp (t − 3) − (0.1a2 − 0.05)(Yp (t) − a1 Yp (t))

(28)

(29)

24 The existing LOA algorithms use the crossover and the mutation for the various processes. These processes increase the complexity of the algorithm. Hence, this paper includes the PSO algorithm for updating the fertility evaluation function. According to the PSO, the fertility evaluation of the female lion is further updated by including the velocity factor. The term YpV (t + 1) − YpV (t) indicates the velocity update in the PSO. V (t + 1) = YpV (t + 1) − YpV (t)

(30)

The velocity update in the PSO depends on the velocity of the current value and the pbest() and the gbest() values. The velocity update is expressed by Eq. (31). V (t + 1) = V (t) + w1 ∗ rand() ∗ [pbest(t) − YpV (t)] + w1 ∗ rand() ∗ [YpU (t) − YpV (t)]

(31)

where, V is the velocity. Substituting Eq. (30) in Eq. (29), the fertility evaluation of the female lion can be obtained.

⎤ 1 V 1 V η (V (t + 1)) − η Y (t − 1) − η ( η − 1)Y (t − 2) − p p 1 ⎢ ⎥ 2 6 YpV (t + 1) = ⎣ 1 [ ] ⎦ (1 − η) V U V η(η − 1)(η − 2)Yp (t − 3) − (0.1a2 − 0.05)(Yp (t) − a1 Yp (t)) ⎡

(32)

24

Eq. (32) expresses the fertility evaluation function of the female lion. In the above equation, the term YpV (t + 1) depends on the velocity update function of the female lion and the present and the previous iteration values of the female lion. This reduces the overall complexity of the algorithm. The term also depends on the pth vector element of the male lion YpU (t). Step 4: Mating of the nodes In the next step in the proposed MOFPL algorithm performs the mating. The mating process includes the crossover and the mutation operators to produce the cubs of the lion efficiently. The mating is done as follows, Y cub (r) = Lr ◦ Y U + Lr ◦ Y V

(33)

In Eq. (33), ◦ is the Hadamard product and the term Lr indicates the crossover length of the mask F . The value of the r ranges between the values one and four. The mating of the male lion and the female lion efficiently produces four cub lions Y K (r). Step 5: Cub growth formation The cub growth formation depends on the mutation of the both the male cub Y U_cub and the female cub Y V _cub . The mutation rate for the cub growth formation is less than 0.2. The mutated male cub and the female cub replace the old male cub and the female cub if the fitness value of the respective cubs is higher. Step 6: Territorial defense The territorial defense for the proposed MOFPL algorithm depends on the Nomad coalition, survival fight, pride update, and the nomad update. The Nomad coalition between the two nomad lions Y W 1 and the Y W 2 results in one of the winning nomad lion Y win_W . The survival fight between the lions depends on the winning nomad lion Y win_W . The conditions for the nomad Lion to win the survival fight are indicated by the following equations, fitness(Y win_W ) > fitness(Y U )

(34)

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R. Bhardwaj and D. Kumar / Pervasive and Mobile Computing 58 (2019) 101029

fitness(Y win_W ) > fitness(Y U_cub ) fitness(Y

w in_W

) > fitness(Y

V −cub

(35)

)

(36) w in_W

U

The pride update is done when the male lion Y is defeated by the winning nomad lion Y . The Nomad coalition update is done when the winning nomad lion gets defeated Y win_W . The Eq. (37) expresses the nomad coalition update. The Nomad coalition occurs by replacing one of the nomad lions Y W 1 and the Y W 2 . The Nomad lion is selected if the E W 1 is greater than E. The selection criterion for the first nomad lion is given as, E W 1 = exp

(

b1

)

max[fitness(Y W 1 ), fitness(Y W 2 )]

max(b1 , b2 )

fitness(Y W 1 )

(37)

Where the term b1 and b1 indicates the Euclidean distance between the nomad lions Y W 1 and the Y W 2 and the male lion. Step 7: Territorial takeover The territorial takeover is done by the replacing the old lions with the cub lions if the fitness is satisfied. The replacement of the male lion is done based on the following conditions, Y

U

{ =

Y U_cub ; YU;

if (fitness(Y U ) < fitness(Y U_cub )) else

} (38)

The replacement of the female lion is done based on the following conditions, YV =

{

Y V _cub ; YV;

if (fitness(Y V ) < fitness(Y V _cub )) else

} (39)

Step 8: Termination This is the final step of the optimization process. When the termination condition is not met, the algorithm gets repeated from the step 3. The termination of the algorithm is done until the maximum iteration Tmax reaches. The flow diagram of the proposed MOFPL algorithm is shown in Fig. 4. 5. Results and discussion This section provides the simulation results of the proposed MOFPL algorithm. The performance of the MOFPL algorithm is compared with the various existing models for the comparative analysis. 5.1. Experimental setup The simulation of the proposed MOFPL algorithm is done on the PC having the Windows 10 OS, 4 GB RAM, and the Intel I3 processor. The entire proposed work is implemented using the Matlab R2015a tool. 5.2. Evaluation metrics The performance metrics such as a number of alive nodes and the normalized network energy evaluate the performance of the proposed MOFPL algorithm. The metrics are explained as follows, Number of alive nodes: The number of alive nodes in the network defines the total number of nodes in the WSN with the energy. The energy of the node depends on Eq. (6). The node with the zero energy is declared as the dead node. Normalized network energy: The normalized network energy is energy of the sensor nodes and the cluster heads. It is given by Eqs. (6) and (7). 5.3. Methods taken for comparison The existing methods, such as LEACH, FABC [31], PSO [30], F-LION [42] are used as the comparative models for the comparative analysis. The existing LEACH, FABC, and PSO models use the same simulation setup as the proposed MOFPL algorithm.

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Fig. 4. Flow chart of the proposed MOFPL algorithm. Table 1 Simulation setup for the WSN. Simulation parameters

Values

Simulation area Simulation time Number of nodes Bit rate Initial energy of the node Sensitivity of the receiver Noise figure of the amplifier Energy required for the transmission Data aggregation energy Nodes communication range Packet size Routing protocol Node Speed

100 m × 100 m 3600 s 50, 75, 100 4000 bit 0.5 10 pJ/bit/m2 0.0013 pJ/bit/m2 50 nJ/bit/m2 10 nJ/bit/signal 250 m 512 bytes OLSR 40 km/hr

5.4. Experimental results Simulation setup Table 1 shows the simulation setup for selecting the optimal cluster head through the proposed MOFPL algorithm. Fig. 5 shows the experimental results of the proposed MOFPL algorithm. The presence of the alive nodes for the each iteration of the MOFPL algorithm is shown in the each figure. The simulation results are shown for the WSN with the 50 nodes. The blue mark in the figure represents the normal node of the WSN. The green mark indicates the cluster head, and the mark X indicates the base station. The magenta color indicates the dead nodes after the simulation. It is evident

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Fig. 5. Simulation results of the Proposed MOFPL at the various iteration rounds.

from the results that the proposed model has an alive nodes at the end of the iteration round and hence the proposed model is more energy aware. 5.5. Performance analysis The performance analysis of the proposed MOFPL algorithm is done by varying the population size of the optimization process. The evaluation metrics analyze the performance of the models for the varying number of nodes. 5.5.1. Performance analysis based on the number of alive nodes Fig. 6a shows the performance analysis of the proposed MOFPL algorithm based on the number of alive nodes in the network. The evaluation is done by varying the iteration round for the various population size. The Fig. 6a.i shows the performance analysis of the proposed MOFPL algorithm in the WSN with 50 nodes. When the WSN contains 50 nodes, the proposed MOFPL algorithm has 50, 38, 5, and five alive nodes for the iteration rounds of 500, 1000, 1500, and 2000 respectively for the population size of 6. The Fig. 6a.ii shows the performance analysis of the proposed MOFPL algorithm in the WSN with 100 nodes. For the population size of 5, the proposed MOFPL algorithm has 100, 56, 10, and ten alive nodes for the iteration rounds of 500, 1000, 1500, and 2000 respectively. When the population size is increased to 15, the proposed MOFPL algorithm has 100, 88, 10, and ten alive nodes for the iteration rounds of 500, 1000, 1500, and 2000 respectively. 5.5.2. Performance analysis based on the normalized network energy Fig. 6b shows the performance analysis of the proposed MOFPL algorithm based on the normalized network energy of the WSN. The evaluation is done by varying the iteration round for the various population sizes. The Fig. 6b.i shows the performance analysis of the proposed MOFPL algorithm in the WSN with 50 nodes. When the WSN contains 50 nodes, the proposed MOFPL algorithm has 0.3472, 0.1474, 0.0678, and 0.0654 normalized network energy for the iteration rounds of 500, 1000, 1500, and 2000 respectively for the population size of 5. The Fig. 6b.ii shows the performance analysis of the proposed MOFPL algorithm in the WSN with 100 nodes. For the population size of 5, the proposed MOFPL algorithm has 0.34168, 0.140619, 0.071565, and 0.06299 normalized network energy for the iteration rounds of 500, 1000, 1500, and 2000 respectively.

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Fig. 6a. Performance analysis of the proposed MOFPL algorithm based on the number of alive nodes.

Fig. 6b. Performance analysis of the proposed MOFPL algorithm based on the Normalized network energy.

5.5.3. Performance analysis based on the fitness Fig. 6c shows the performance analysis of the proposed MOFPL algorithm based on the fitness value. The evaluation is done by varying the iteration round for the various population size. When the WSN has 50 nodes, the proposed MOFPL algorithm has the fitness value of 30.0811, 13.7872, 9.96807, 7.025, and 1.0068 for the iteration values of 0, 500, 1000, 1500, and 2000 respectively. When the WSN has 75 nodes, the proposed MOFPL algorithm has the fitness value of 49.2895, 20.2534, 14.2695, 9.8838, and 1.0103 for the iteration values of 0, 500, 1000, 1500, and 2000 respectively. When the WSN has 100 nodes, the proposed MOFPL algorithm has the fitness value of 58.73055, 27.2615, 19.5357, 13.303, and 1.0117 for the iteration values of 0, 500, 1000, 1500, and 2000 respectively. 5.6. Comparative analysis The comparative analysis of the proposed model is done by measuring the performance of the each comparative models for the each iteration round. Various existing works such as LEACH, FABC, PSO, and F-LION algorithm are used for the comparative analysis. 5.6.1. Comparative analysis based on the number of alive nodes Fig. 7a shows the comparative analysis of the each model based on the number of alive nodes in the WSN. The methods with the maximum number of the alive nodes at the end of the iteration are said to be the better model. Fig. 7a.i shows the comparative analysis for the WSN with 50 nodes. At the iteration round of 1000, the existing LEACH, FABC, PSO, and F-LION models have 22, 19, 9, and 42 alive nodes. At the iteration round of 2000, the existing LEACH, FABC, PSO, and

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Fig. 6c. Performance analysis based on the fitness.

Fig. 7a. Comparative analysis based on the number of alive nodes.

F-LION models have 3, 5, 4, and 5 alive nodes. But, the proposed MOFPL model has 46, 5, and five alive nodes for the iteration rounds of 1000, 1500, and 2000 respectively. Fig. 7a.ii shows the comparative analysis for the WSN with 100 nodes. At the iteration round of 1000, the existing LEACH, FABC, PSO, and F-LION models have 49, 42, 19, 56 alive nodes. At the iteration round of 2000, the existing LEACH, FABC, PSO, and F-LION models have 5, 5, 0, and 10 alive nodes. But, the proposed MOFPL model has 69, 12, and ten alive nodes for the iteration rounds of 1000, 1500, and 2000 respectively. 5.6.2. Comparative analysis based on the normalized network energy Fig. 7b shows the comparative analysis of the each model based on the normalized network energy in the WSN. The methods with the maximum normalized network energy at the end of the iteration is said to be the better model. Fig. 7b.i shows the comparative analysis for the WSN with 50 nodes. At the iteration round of 2000, the existing LEACH, FABC, PSO, and F-LION models have normalized network energy value of 0.01266, 0.034128, 0.01423, and 0.05777. But, the proposed MOFPL model has normalized network energy of 0.05877 for the iteration round of 2000. Fig. 7b.ii shows the comparative analysis for the WSN with 100 nodes. At the iteration round of 2000, the existing LEACH, FABC, PSO, and F-LION models have normalized network energy value of 0.0068, 0.00773, 0, and 0.058011. But, the proposed MOFPL model has normalized network energy of 0.06022 for the iteration round of 2000. 5.7. Discussion Table 2 shows the comparative analysis of the proposed MOFPL algorithm with the existing models. From the table, it is evident that the proposed MOFPL algorithm has achieved better performance regarding the number of alive nodes and the normalized network energy. The proposed algorithm has a higher number of alive nodes at the end of an iteration for the

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Fig. 7b. Comparative analysis based on the normalized network energy. Table 2 Comparative analysis of the proposed MOFPL algorithm. Comparative methods

LEACH FABC PSO F-LION Proposed MOFPL

Iteration rounds

2000 2000 2000 2000 2000

Comparative analysis Number of alive nodes

Normalized network energy

50 nodes

100 nodes

50 nodes

100 nodes

3 5 4 5 5

5 5 0 10 10

0.01266 0.034128 0.01423 0.05777 0.05877

0.0068 0.00773 0 0.058011 0.06022

WSN with different configurations. The proposed MOFPL algorithm has 5, 8, ten alive nodes at the iteration round of 2000 for the WSN with 50 and 100 nodes. The normalized network energy of the proposed model is higher than the existing works at the each iteration round. The proposed MOFPL algorithm has achieved higher normalized network energy of 0.05877 and 0.06022 for the WSN with 50 and 100 nodes. 6. Conclusion This work has introduced an energy aware routing mechanism for the WSN. The paper proposed the MOFPL algorithm based on the PSO, LOA and the fractional theory. The proposed work has utilized the multi-objective fitness function to select the optimal cluster head for the routing purpose. The proposed MOFPL considers various factors such as energy, delay, traffic rate, distance, and the density of the nodes for calculating the fitness function. The simulation of the proposed model is done by varying the population size and the nodes of the WSN. Evolution metrics, such as a number of alive nodes and the normalized network energy calculate the performance of the models. The comparative analysis is done with the existing models such as LEACH, FABC, PSO, and F-LION. The results are varied for the each iteration round. The proposed MOFPL algorithm has 5, 8, and 10 alive nodes at the iteration round of 2000 for the WSN with 50 and 100 nodes. The proposed MOFPL algorithm has achieved higher normalized network energy of 0.05877 and 0.06022 for the WSN with 50 and 100 nodes. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. References [1] A. Boukerche, A. Mostefaoui, M. Melkemi, Efficient and robust serial query processing approach for large-scale wireless sensor network applications, Ad Hoc Netw. 47 (2016) 82–98. [2] Mihaela Miticia, Martijn Onderwater, Maurits de Graafa, Optimal query assignment for wireless sensor networks, Int. J. Electron. Commun. 69 (8) (2015) 1102–1112.

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