1 Introduction

Wireless Sensor Networks (WSN) have evolved as the necessary and potential method of facilitating pervasive communication to various numbers of real time applications [1]. The main issue that needs to be addressed in WSN is to determine the ideal methodology that optimizes the energy of the tiny sensor nodes [2]. In this context, Clustering is considered as the classical mechanism that ensures reliability and energy effective transmission of data between the cluster head and the sensor nodes [3]. In this clustering process, the entire geographical area is partitioned into small regions and a single designated node called the Cluster Head is assigned to each of the divided sectors for energy optimization [4]. This cluster head selection process plays the anchor role in the efficient transmission of data. Thus, the cluster head needs to be selected after each and every finite rounds for facilitating the optimal performance of the network in effective data transmission [5]. Further, the cluster head count within the network and node count per cluster is fixed or variable depending on the applied network environment. This cluster heads are responsible for forwarding the data to the base station or reliable in establishing the second level of hierarchy in the network [6]. But, the process of cluster head selection suffers from the limitations that are related to the incurring of additional overhead during the process of Cluster Head selection and unreliable allocation of the cluster creation process. The aforementioned limitations are responsible for reducing the lifetime of the network [7]. A number of researchers focused on the determination of significant methods that aids in resolving the drawbacks that emerges during the process of cluster head selection [8]. The investigated methods propounded by the researchers include a number of dimensions that improves the method of cluster head selection and network maintenance [9]. This paper also highlights on some of the significant contributions of the researcher towards the cluster head selection and contributes a meta-heuristic optimization scheme for effective cluster head selection in WSN.

Furthermore, meta-heuristic optimization scheme for cluster head selection is essential when the search for determining the optimal cluster head is exhaustive. The meta-heuristic optimization schemes are proving to be effective and efficient when they cover the entire solution space which contains a global optimal point of convergence and when they are capable of generating novel and enhanced solutions. In addition, the meta-heuristic optimization schemes should also possess the capability of escaping from the local optimal point of solution convergence [10]. In the existing literature, there are meta-heuristic optimization schemes like Ant colony optimization, Artificial Bee Colony optimization and Particle swarm optimization algorithms for focusing on the exploration and exploitation of the search space during the process of cluster head selection. But, these optimization algorithms fail to maintain the tradeoff between the degree of exploration and exploitation in the process of cluster head selection. In this paper, an attempt has been made to improve the searching capability of Artificial Bee Colony optimization Algorithm by incorporating the method of Grenade Explosion and Cauchy Operator so as to enhance the degree of exploration and exploitation in the process of cluster head selection in WSN.

The major reasons for the remarkable performance of the proposed IABCOCT scheme over the existing cluster head selection schemes are derived as follows:

  1. (a)

    The rapid convergence rate of the traditional ABC algorithm falling into the local optimal is prevented by utilizing the Grenade Explosion Factor that dynamically adapts the degree of exploitation depending on the growth of the search space.

  2. (b)

    The global exploration possibility of the existing classical ABC algorithm is enhanced through the utilization of the Cauchy Operator.

  3. (c)

    The utilization of Grenade Explosion Factor and Cauchy Operator enables the option of dynamically moving one region to another for searching and prevents the possibility of restricting the search to a specific region which is considered as the core drawback of the traditional ABC algorithm.

  4. (d)

    The proposed IABCOCT scheme also incorporates high degree of computation efficiency during the process of searching compared to the lower efficiency of classical ABC-based cluster head selection.

The subsequent sections of the paper are organized as follows. Section 2 presents the details of some of the predominant meta-heuristic-based cluster head selection mechanism existing in the literature with their pros and cons. Section 3 details on the network model used for the implementation of the IABCOCT scheme. Section 4 highlights on the steps involved during the implementation of the proposed IABCOCT scheme. Section 5 describes the results and their inferences derived from the simulation experiments conducted for exploring the potential of the proposed IABCOCT-based cluster head selection. Section 6 concludes the paper by emphasizing the predominant contributions enabled by the proposed IABCOCT-based cluster head selection scheme.

2 Related Work

In this section, some of the predominant cluster head selection techniques propounded in the literature are discussed with their merits and limitations.

A modified Ant Colony-based cluster head selection approach was proposed over the traditional LEACH scheme in order to improve its cluster head selection process [11]. This modified Ant Colony-based cluster head selection uses residual energy parameter as the significant factor for significantly improving the potential of the LEACH algorithm towards effective cluster head selection. This modified Ant Colony-based cluster head selection approach was proved to minimize the rate of energy consumptions by incorporating three phases. In the first phase, cluster members are enforced to transmit data to the cluster heads. Then the cluster heads disseminate the data to the leader in the second phase. In the final phase, the leader disseminates the date to the base station. Then, another enhanced modified Ant Colony-based cluster head selection approach was also proposed for improving the effectiveness of the existing LEACH algorithm in order to enhance the network lifetime and energy efficiency [12]. In this enhanced ACO scheme, the efforts incurred in the minimization of the duplicated data sent by the sensor nodes are highly prevented. This enhanced ACO scheme was proved to be optimal in ensuring energy efficiency and network lifetime by optimizing the search process that is improved in terms of exploration and exploration degree. This ACO technique used multiple levels of energy utilized for cluster head selection process such that the cumulative energy of the sensor network is not exhausted unnecessarily.

Further, a Genetic Algorithm (GA)-based cluster head selection scheme was contributed to enhance the network lifetime and energy efficiency [13]. This Genetic algorithm-based cluster head selection scheme partitions the networks into a finite number of clusters and then the cluster head selection is achieved using the intra and inter cluster investigation derived based on their possessed residual energy. This GA method eliminates the possible number of direct interactions between the source and destination in order to restore energy to the maximum level. This GA scheme of the cluster head selection was found to be ideal in terms of fault tolerance, time complexity and computational overhead. A Particle Swarm Optimization Algorithm (PSOA) was proposed based on effective quantification of fitness value and particle encoding for effective determination of cluster heads [14]. This PSOA approach uses reliable factors like sink distance, residual energy, intra-cluster distance and residual energy of the sensor nodes for cluster head selection. This PSOA scheme uses the methodology of cluster formation that depends on the computation of the weight function that improves the probability of the non cluster sensor nodes in joining the cluster head in the rapid rate. This PSOA approach was also proved to improve the rate of energy conservation and network lifetime.

Furthermore, a hybrid cluster head selection mechanism was proposed by integrating the operations of GA and Harmony Search (HS) [15]. This GA–HS scheme improved the rate of energy conservation by dividing the network through the implementation of the evolutionary approaches that optimize the process of cluster head selection. This potential GA–HS scheme used information related to the position of the nodes and residual energy of the sensor nodes for better selection of the cluster heads. This GA–HS scheme was also proved to improve the energy effectiveness of the network and network lifetime, but fails to maintain appropriate synchronization between the sensor nodes of the network. Then, an integrated PSO and Tabu Search (IPSO–TS) inspired cluster head selection approach was proposed for enhancing the count of clusters formed during data communication in order to optimize the energy possessed in the network [16]. This approach IPSO–TS was proved to eliminate the issue of worst local optimal point of solution convergence. IPSO–TS also balances the rate of exploration and exploitation to the maximum degree, but they do not perform well when the sensor nodes are more flexible movement and hence they exhaust huge degree of energy without any purpose. IPSO–TS scheme was also confirmed to reduce packet loss rate and mean delay.

An Enhanced Particle Swarm Optimization Technique (EPSOCT) was proposed [17] for reducing the rate of energy consumptions. This EPSOCT approach selects the cluster head based on PSO that estimates the distance between the sink node and the cluster members, residual energy for better determination. This EPSOCT approach was also proved to improve the expected rate of the network compared to the IPSO–TA, GA–HS and PSOA approach reviewed in the literature. But, EPSOCT approach incurs high computational complexity that impacts the process of selecting cluster heads in the sensor networks. Then, the Hierarchical Clustering-based Cluster Head Election (HCCHE) was also proposed for minimizing the rate of energy consumptions during the process of cluster head selection [18]. The HCCHE-based cluster head selection approach used k-means algorithm for extending the lifespan of the sensor networks. In HCCHE, initially the LEACH algorithm was used for determining the primitive cluster head, then Euclidean Distance is calculated when the nodes need to join the cluster head and finally the cluster center is determined based on the centroid of the clusters formed in the network in order to select the appropriate cluster head for effective data transmission. HCCHE-based cluster head selection approach was proved to enhance the rate of energy consumptions. But, HCCHE is identified to degrade lifetime and energy when the distance between the base station and the cluster members are less.

A Competitive Clustering Technique (CCT) [19] was proposed for resolving the issues that emerge due to the energy heterogeneity of the sensor nodes in the network. CCT approach computes the competition radius based the estimated residual energy of the sensor nodes for effective cluster head selection. This CCT scheme belongs to the category of uneven clustering that extends the cluster-heads’ lifespan by reducing energy consumptions at the nodes that are very close to the sink. The CCT approach also utilized an integrated transmission mode in facilitating selection of successive next hop routing that are determined based on inter distances existing between the cluster head and cluster members.

The aforementioned limitations of the reviewed cluster head selection schemes form the foundation behind the formulation of the proposed IABCOCT technique.

3 Network Model Used for Implementing IABCOCT Scheme

In this implementation of the proposed IABCOCT technique, a free space model is considered as the base network model in which the receiver and the transmitter sections are separated by ‘d’ distance. The receiver and the transmitting sections of this utilized network model comprise of related receiving electronics and transmitting electronic embedded with the transmission amplifier since the information exchange in the network is always achieved in terms of bits. In this network model, the specific collection of sensor is considered to be randomly distributed in the rectangular area. [20]. The considerations of this network model related to the characteristic features of the sensor network are: (i) The sensor nodes in the network are assumed to be quasi-stationary mode, (ii) Each and every sensor nodes are unaware of their location, (iii) The characteristic features of the set of sensor nodes distributed in the network are homogenous in nature, (iv) The energy consumptions of the sensor nodes are considered to non uniform in nature as it is directly influenced by the distance between the cluster head and the base station of the network, (v) the sensor nodes are considered to be self organizing in nature and hence they are not monitored after the deployment and (vi) Each and every sensor nodes are considered to possess a fixed amount of power levels derived based on Eqs. (1)–(3).

$$E_{N(TX)} = I_{A} * E_{CONS} + I_{A} * \varepsilon_{fs} * d_{s}^{2} \quad{\text{if}}\,d_{s} \le d_{s(0)}$$
(1)
$$E_{N(TX)} = I_{A} * E_{CONS} + I_{A} * \varepsilon_{thres} * d_{s}^{2} \quad{\text{if}}\,d_{s} > d_{s(0)}$$
(2)

and

$$I_{A} E_{N(RX)} = I_{A} * E_{CONS}$$
(3)

where \(I_{A}\) is the amount of data being sent, \(E_{CONS}\) is the amount of energy consumed for transmitting single bit of data, \(\varepsilon_{fs}\) is the coefficient of amplification embedded in the transmission amplifier in the free space model when the inter-distance is less than the distance of threshold during the transmission of single bit of data and \(\varepsilon_{thress}\) is the coefficient of amplification embedded in the transmission amplifier in the free space model when the inter-distance is greater than the distance of threshold during the transmission of single bit of data.

In the considered implementation environment, \(TSN\) number of sensor nodes are randomly distributed in the field with the optimal area of \(L * N\) square meters. In order to optimize the process of selecting cluster heads and to determine the optimal ‘\(c\)’ cluster heads, the fitness value of the objective function in this proposed IABCOCT scheme is derived using the function derived by Hoang et al. [21]. Thus the fitness value of the proposed IABCOCT-based cluster head selection scheme is determined using Eq. (4)

$$FPP(SN_{i} ) = \delta * g_{1} + (1 - \delta )g_{2}$$
(4)

where \(g_{1}\) and \(g_{2}\) are derived using Eqs. (5) and (6) respectively

$$g_{1} = Max_{J} \left( {\mathop {\sum {\frac{{D_{Max} (INODE_{i} .CH_{j} )}}{{\left\| {NNC_{j} } \right\|}}} }\limits_{{_{j} }} } \right)$$
(5)

and

$$g_{2} = \frac{{\sum\nolimits_{i = 1}^{TSN} {Energy(SN_{i} )} }}{{\sum\nolimits_{k = 1}^{C} {Energy(C_{k} )} }}$$
(6)

where \(g_{1}\) and \(g_{2}\) denotes the maximum Euclidean distance between the nodes of the clusters to its corresponding cluster heads and degree of initial energy possessed by the lively nodes of the sensor network with \(\delta\) as the factor of scaling (the integrated contribution of \(g_{1}\) and \(g_{2}\) in the objective function \(FPP(SN_{i} )\)) that ranges between 0 and 1.

4 Improved Grenade Explosion and Cauchy Operator Integrated Artificial Bee Colony Optimization Scheme for Cluster Head Selection (IABCOCT)

The proposed IABCOCT approach uses the meritorious features of the Artificial Bee Colony (ABC) Optimization Algorithm and Grenade explosion and Cauchy Operator for achieving better exploitation and exploration rate during the process of cluster head selection. In the proposed IABCOCT-based cluster head selection scheme, the traditional drawback of ABC algorithm that results in rapid trapping into the local optimal point of cluster head selection is prevented by the Grenade Explosion-Based Exploitation Parameter (GEBEP). Further, the global scope of the search process in the optimal cluster head selection is improved through the utilization of Cauchy Operator. In this IABCOCT approach, the particles (sensors) are allowed to move from one region to the other region by updating its velocity and position parameters at the end of each round in implementation. The potential operation of this proposed IABCOCT approach is divided into number of rounds in which the cluster heads are responsible for collecting the data from the interacting cluster members in order to transfer the aggregated data to the Base Station (BS).

The forthcoming sections describe the steps followed during the implementation of the proposed IABCOCT Scheme.

4.1 Determination of Probability for Objective Function Using the Fitness Value in ABC

The wireless sensor network is created with appropriate energy embedded in each and every node as mentioned in Table 1. Then, the traditional ABC mechanism is facilitated since the inspiring characteristic features of honey bee colony is confirmed to be effective and efficient in determining the premier quality of food sources based on their inbuilt natural dimensional investigation capability. Thus, proposed the IABCOCT scheme plays the significant role in optimizing the process of cluster head selection by utilizing the benefits of attributes derived from the intelligent honey bee foraging behavior. The employee, onlooker and scout bee phase are incorporated in the proposed IABCOCT scheme for determining initial feasible cluster head nodes from different clusters of the network, In the first phase, the information related to the velocity and position of the sensor nodes is collected and shared by the employee bee agents. This employee bee is responsible for generating the feasible number of solutions are computed based on the computation of Probability in Fitness Value of Objective Function \(P(FPP(SN_{i} ))\) that forms the base for cluster head election. Then, the sensor nodes that have the maximum probability of being selected as the cluster head for data transfer can be determined (exploited) in the onlooker bee phase based on the computed \(P(FPP(SN_{i} ))\) value of employee bee phase. The sensor nodes that are found to potent in playing the role of cluster head in the network is identified (explored) in the scout bee phase based on the energy factor quantified in the preceding phases. This process of searching the optimal cluster head in the sensor network is continued until a predetermined number of iterations and threshold.

Table 1 IABCOCT—simulation parameters
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At this juncture, Let ‘n’ be the number of the generated solution vectors that represents the random collection of sensor nodes that has the maximum possibility of being selected as an cluster head of each cluster in order to enhance the lifetime of the network quantified based on incorporated energy. Each generated solution vector \(S_{V(i)} = (S_{V(1)} ,S_{V(2)} , \ldots ,S_{V(n)} )\) is the multi-dimensional vector that represents the possibility of each sensor nodes to be detected as cluster head for each cluster based on a multiple number of parameters like residual energy, inter nodal distance and the distance between the sensor node from the base station, etc. This solution vector is updated at the end of each round in implementation based on the three incorporated phases of classical ABC algorithmic approach until it reaches the predefined minimum number of rounds which is initially considered for the cluster head selection process. In this context, the set of sensor nodes of the network is considered for cluster head selection when it complies with the optimal fitness value \(FIT(S_{V(i)} )\) defined in Eqs. (7) and (8) derived from the individual fitness value derived from Eq. (4)

$$FIT(S_{V(i)} ) = \frac{1}{{1 + FPP(SN_{i} )}},FPP(SN_{i} ) \ge 0$$
(7)
$$FIT(S_{V(i)} ) = 1 + abs.(FPP(SN_{i} )),FPP(SN_{i} ) < 0$$
(8)

Further, the probability of the objective function derived from the optimal fitness value for selecting the superior solution vector of the feasible solution vectors generated based on the exploitation degree attributed by the onlooker bee phase of classical ABC is presented in Eq. (9)

$$P(FIT(S_{V(i)} ) = \frac{{FIT(S_{V(i)} )}}{{\sum\nolimits_{n - 1}^{NS} {FIT(S_{V(i)} )} }}$$
(9)

Once the superior solution vector of the generated feasible solution vectors is identified, each individual solution related to the superior solution vector is investigated for cluster head selection by including a reference velocity factor. Thus the new fitness probability value for each individual solution related to the superior solution vector is estimated based on Eq. (10)

$$N(S_{V(i)} ) = S_{V(ij)} + \psi_{(ij)} (S_{V(ij)} - S_{V(kj)} )$$
(10)

where \(\psi_{(ij)}\) and \(k\) refers to the reference velocity factor and random number chosen based on the possible number of solutions that are equally compatible to be determined as cluster head in the deployed sensor network with the randomly chosen searching dimensions i and j ranging between − 1 and + 1 respectively. Furthermore, the Greedy selection [22] approach is imposed over each individual solution of the determined superior solution vector for reassuring the reliability of each them to be selected as the cluster head in order to improve the lifetime of the network. Thus, if \(S_{V(i)}\) is the estimated reliable solution, then the scout bee phase of ABC explores this reliable solution for determining its optimality based on Eq. (11)

$$S_{V(ij)} = S_{V(MIN,j)} + random(S_{V(MAX,j)} - S_{V(MIN,j)} )$$
(11)

where \(S_{V(MIN,j)}\) and \(S_{V(MAX,j)}\) denotes the minimum and maximum limits fixed for exploring the possibility of the estimated reliable solution (0.2 and 0.6 are used as the minimum and maximum limits) in the proposed IABCOCT scheme.

4.2 Onlooker Bees-Based Exploitation Mechanism Using Grenade Explosion Factor

In the proposed IABCOCT scheme, the onlooker bee phase is responsible for electing an optimal sensor node based on the computation of the Fitness Probability Factor \(FPP(SN_{i} )\). This Fitness Probability Factor iteratively identifies the set of sensor nodes (solutions) that has the maximum possibility of being selected as the optimal cluster head. Thus the Fitness Probability Factor determined for each generated solution vector \(S_{V(i)}\) is helpful for exploiting each and every solution from the generated solution vectors based on the Exploitation Factor \(E_{F(ij)}\). This Exploitation Factor \(E_{F(ij)}\) is determined from \(S_{V(i)}\) by modifying a single potential parameter based on the satisfaction of the constraint \(E_{F(ij)} \ne S_{V(ij)} * E_{F(ij)}\). This potential change in \(E_{F(ij)}\) from each solution set \(S_{V(i)}\) is always facilitated from the randomly selected position points of the newly estimated set of sensor nodes that has the possibility of being selected as cluster head. Further, the parameter j is the influential deviating factor that appropriately determines the difference between the position, velocity, energy and other related factors of the sensor nodes to the randomly chosen position of the optimal cluster head in terms of the same attributes as facilitated through the traditional ABC technique. Furthermore, the choice of j parameter in ABC alone cannot ensure optimal selection of cluster heads since they possess the limitations of slow convergence and possibility of being caught into the local optimal point during the process of searching cluster heads in the sensor network. Thus Grenade Explosion Factor (GEF) [23] is used for resolving the issue of j parameter for two principal reasons, They are (a) they utilize a set of significant benchmark functions and randomly generated multi-modal functions for detecting better optimal solutions in cluster head selection and (b) They have a maximum probability of converging the solution onto a global minimum searching process. Hence, the Grenade Explosion Factor is used in the onlooker bee phase of an IABCOCT technique for achieving the maximum degree of exploitation during the process of cluster head selection.

In this potentially modified onlooker bee phase of IABCOCT technique, the search dimensions are dynamically determined and explored. Then the fitness value of each of the solution is determined based on the number of Grenade Explosion Factor (GEF) that are assigned based on the location of the sensor nodes in the network. In IABCOCT technique, GEF relates the partitioned region of the search space that are defined based on the computation of exploration radius. Hence, the cluster head is exploited based on Eq. (12)

$$S_{V(ij)} = S_{V(ij)}^{1} + sign(RN_{D} )(RN_{D} )^{f} L_{IM}$$
(12)

With \(RN_{D}\), \(E_{RAD}\) and \(L_{IM}\) being the random number which is uniformly distributed, exploration radius and length of impact under constant function \(f = \hbox{max} \left( {\frac{{\log \frac{{RN_{D} }}{{L_{IM} }}}}{{\log E_{RAD} }}} \right)\).

Then, the fitness value of the sensor nodes that can be selected as the cluster head is facilitated using the exploration radius and length of impact using Eqs. (13) and (14)

$$E_{RAD} = \frac{{E_{RAD - INITIAL} }}{{(E_{USED} )^{{\frac{USED - ITER}{MAX - ITER}}} }}$$
(13)

and

$$L_{IM} = (L_{IM - INITIAL} )^{d} (E_{RAD} )^{d - 1}$$
(14)

where ‘d’ is iteratively varied from a higher threshold value to a lower threshold value. Thus the exploration in the optimal selection of cluster heads is achieved in the global and optimal manner through the use of the onlooker bee’s phase of IABCOCT approach.

4.3 Cauchy Operator Based Scout Bees Exploration Phase of IABCOCT Technique

Cauchy operator is incorporated in the Scout Bees Exploration Phase of IABCOCT scheme is similar to the Grenade Exploitation factor used in the onlooker bees step. But the only difference is that, the Grenade Exploitation factor plays a vital role in the exploitation of the search space for estimating the cluster head and the Cauchy operator is responsible for exploring the space for exploration. The Cauchy Operator-based exploration is mainly for facilitating the feasible options for determining search process to be executed in the global space in order to eliminate the possibility of exploration to be trapped into the local optimum point of convergence. This Cauchy Operator is mainly used in IABCOCT approach since the possibility of generating a random number is in high deviation with the origin when compared to the Gaussian operator. In addition, Cauchy Operator facilitates a better and wider search dimension than the compared probability distribution-based operators of the literature used for assigning an exploration dimension [24, 25].

Thus the Cauchy operator used in IABCOCT technique is facilitated by the scout bee phase of IABCOCT technique using Eq. (15)

$$d_{X(k)}^{\exp } = d_{X(k)}^{\exp } P_{CAUCHY(0,1)}$$
(15)

In this context, \(P_{CAUCHY(0,1)}\) is related to the baseline Cauchy distribution function used in the IABCOCT scheme with the distribution function centered at ‘0’ and scaling parameter set to ‘1’. Thus the baseline Cauchy operation of the proposed IABCOCT scheme is derived using Eq. (16)

$$P_{CAUCHY(0,1)} = \frac{1}{{\pi (1 + FPP(SN_{i} )^{2} )}}$$
(16)

This phase of exploitation and exploration are continued until the number of implementation rounds is reached.

5 Simulation Outcomes and Discussions

The network environment for understanding the potential of IABCOCT is designed using Network Simulator (ns-2.34) that implements the proposed optimization technique for the formation of clusters and electing cluster heads for conserving energy of the sensor nodes for extending the life of the network. This simulation is enforced under the deployment of 100 nodes with the terrain area of 250 × 250 square meters. The IABCOCT parameters and the simulation parameters of the network are highlighted in Table 1.

Figures 1 and 2 demonstrates the significance of the proposed IABCOCT scheme analyzed based on the received number of packets and throughput of the network evaluated under the different rounds of cluster head selection.

Fig. 1
figure 1

IABCOCT—number of packets received based on number of rounds

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Fig. 2
figure 2

IABCOCT—throughput based on number of rounds

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Similarly, Figs. 3, 4, 5 and 6 highlights the performance of the proposed IABCOCT technique investigated using the packet drop, delay, normalized routing overhead and lifetime based on different rounds of cluster head selection.

Fig. 3
figure 3

IABCOCT—packet drops based on number of rounds

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Fig. 4
figure 4

IABCOCT—delay based on number of rounds

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Fig. 5
figure 5

IABCOCT—normalized routing overhead based on number of rounds

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Fig. 6
figure 6

IABCOCT—lifetime based on number of rounds

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Figures 7, 8, 9 and 10 presents the significance of the proposed IABCOCT cluster head selection scheme over the compared EPSOCT, HCCHE and CCT techniques investigated using Relative Energy, Mean energy consumptions, Mean Residual Energy and Cumulative Residual Energy under different rounds of cluster head selection.

Fig. 7
figure 7

IABCOCT—relative energy based on number of rounds

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Fig. 8
figure 8

IABCOCT—mean energy consumptions based on number of rounds

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Fig. 9
figure 9

IABCOCT—mean residual energy based on number of rounds

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Fig. 10
figure 10

IABCOCT—cumulative residual energy based on number of rounds

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Finally, Figs. 11, 12 and 13 emphasizes the potential of the proposed IABCOCT cluster head selection scheme evaluated using Rounds with unequal energy, number of Alive Nodes and Increase in Packet Delivery Ratio identified under the different mortality rate of sensor nodes. The proposed IABCOCT cluster head selection scheme is remarkable than the considered EPSOCT, HCCHE and CCT baseline cluster head selection techniques due to the following reasons, (a) the rate of exploration towards the selection of optimal energy based cluster head is maximized using the Cauchy operator in ABC phase and (b) the degree of exploitation offered by the Grenade Explosion Factor is also maximum during the selection of cluster head. Thus, the rounds of cluster head selection with unequal energy are sustained even when the mortality rate of the sensor nodes is systematically increased. This sustainable characteristic features the proposed IABCOCT cluster head selection scheme further increases the probability of retaining the number of alive nodes in the network for improving the lifetime of the network This increase in the number of alive nodes of network systematically increases the packet delivery rate compared to the benchmarked EPSOCT, HCCHE and CCT baseline cluster head selection techniques. Thus, the number of rounds under unequal energy is sustained by proposing an IABCOCT scheme at an average rate of 13%, 11% and 9% compared to EPSOCT, HCCHE and CCT techniques. Likewise, the number of alive nodes in the network is improved by IABCOCT at an average rate of 10%, 7% and 6% compared to EPSOCT, HCCHE and CCT techniques. In addition, the proposed IABCOCT scheme increases the packet delivery rate by 11%, 8% and 6% compared to the cluster selection approaches used for investigation.

Fig. 11
figure 11

IABCOCT—rounds with unequal energy based on mortality of nodes

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Fig. 12
figure 12

IABCOCT—number of alive nodes identified based on mortality rate of nodes

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Fig. 13
figure 13

IABCOCT—increase in packet delivery ratio identified based on mortality rate

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6 Conclusion

IABCOCT is an integrated attempt that introduces maximum exploitation and exploration in the search field of cluster head election for reducing the energy utilization rate under maximized network life cycle. This IABCOCT applies a centralized approach to the process of clustering and uses a distributed scheme for cluster head election. On demand distance vector protocol is deployed as the multipath routing protocol in IABCOCT as the data sensed by the sensor nodes after aggregation by the cluster heads are relayed to the base station depending on the threshold of routing through direct means or relay nodes. The simulation outcomes of IABCOCT confirms its remarkable performance in reducing the mean residual energy, cumulative residual energy and the mean energy consumption rate to about 23%, 18% and 16% better to EPSOCT, HCCHE and CCT techniques of energy efficient clustering. A Sink node with mobility or multiple number of sink nodes are planned to be used in the future for reducing delay to a significant level that could be incurred during the collection and aggregation of data. This IABCOCT technique can be further investigated with the utilization of variant Ant Colony Optimization techniques with Differential Evolution (DE) strategies for facilitating the energy effectiveness for extending the life cycle of the network.