Efficient approaches to optimize energy consumption in 3D wireless video sensor network under the coverage and connectivity constraints

Two advanced approaches (PA_1, and PA_2) based on a realistic 3D model of video sensor nodes (VSNs) deployed randomly over a 2D target area are proposed to minimize energy consumption in the network maintaining area coverage and connectivity. The reduction of the number of active VSNs decreases energy consumption but at the same time reduces the area coverage and connectivity. These conflicting issues are resolved and an optimal solution is obtained by using an integer linear programming-based approach (PA_1). But PA_1 is not tractable for large instances as the problem is NP-Hard. Hence, a heuristic approach (PA_2) based on an advanced genetic algorithm is also proposed in the present work for obtaining a near-optimal solution. Simulation studies are carried out to compare the performance of PA_1 and PA_2 with the other three state-of-the-art approaches (APP_5, APP_6, and ET_3). Among the three existing approaches, APP_6/(ET_3) is the best in energy consumption/(area coverage). It is observed that for the same simulation environment, both PA_1 and PA_2 guarantee higher network services, by reducing energy consumption by 40.85% and 33.34% respectively compared to the best existing approach APP_6; and as well as by increasing area coverage by 0.94% than the best existing approach ET_3 for the node density 150 on the target area of size 75x75 square meter. Between PA_1 and PA_2, PA_2 generates a suboptimal solution and PA_1 substantiates its superiority by reducing energy consumption by 11.26% than PA_2 without losing area coverage for the same simulation environment.


Introduction
A set of video sensor nodes (VSNs) furnished with miniature video cameras called CMOS [1,2] cameras forms a wireless video sensor network (WVSN). Such sensors possess the function of capturing video and images and are extensively utilized in various applications like surveillance work, monitoring in the affected area with natural disasters, tracking, environment monitoring, etc. Operational by limited battery power, WVSN exhibits its challenging attitude in the profile of energy consumption as in almost all the cases the battery is not rechargeable, nor it is replaceable. Such VSNs can exhaust energy rapidly owing to constant sensing and transmission of video data. It lowers both monitoring quality and network lifetime.
The WVSN generally operates in an unfriendly environment, which requires VSNs to be deployed randomly with high density to ensure the smooth working of the application even if a few VSNs fail. But such densely deployed VSNs generate huge overlapping of coverage in the target area. The scheduling schemes of [1][2][3][4][5][6][7][8][9] utilize such overlapping coverage to cover the sensing area/region of a VSN and to shut such VSNs off for lowering the number of active VSNs which results in the reduction of energy consumption in the target area, without losing the percentage of initial area coverage by the VSNs significantly (termed as coverage constraint). But, the minimization (optimization) of the number of active VSNs (or, minimization of energy consumption by the active VSNs) is not addressed in [1][2][3][4][5][6][7][8][9]. Moreover, the connectivity among VSNs and between VSN and the base station (BS) (termed as connectivity constraints) are not addressed in [1][2][3][4][5][6][7][8][9]. The issue of minimizing the number of active VSNs (or energy consumption in the target area) while satisfying coverage constraint and also connectivity constraints is addressed by proposing new approaches (PA 1, PA 2) in this work. Both approaches use the 3D coverage model of VSNs.
PA 1 uses a single-objective optimization technique Integer Linear Program (ILP) for a system of linear constraints, with the objective to minimize the total number of active 3D VSNs for a particular random distribution of 3D VSNs. ILP generates the optimal solution but is intractable for large instances as the problem is NP-Hard [10]. PA 2, a heuristic approach based on the Advanced Genetic Algorithm (AGA) [11,12] solves the same problem to produce the near-optimal solution, which runs in polynomial time and provides the solution for a large problem size.
A single base station (BS) is set up by the side of the target area both in PA 1 and PA 2 and the location of the BS in the target area is supplied to all the VSNs before their deployment. The BS is connected to WVSN via some VSNs that are inside the communication range of the BS. Each VSN in both approaches executes the neighbor discovery phase, registration phase, and duty cycling phase sequentially in the target area. In the neighbor discovery phase, each VSN identifies the position and also orientation of its neighbor VSNs by exchanging messages among themselves. It then inserts such neighbor information in a neighbor table both in PA 1 and PA 2. In the phase of registration, each VSN in both PA 1 and PA 2 transmits its position and orientation for itself to the BS. The BS inserts such type of information into a table named a base table (BT). During the duty cycling phase, the BS in PA 1/(PA 2) executes a centralized algorithm. The centralized algorithm is ILP/(AGA) based for PA 1/(PA 2). The BS identifies an optimal/(near-optimal) number of active VSNs and sends a sleep message to all the identified VSNs for shutting them off. Such VSNs then enter sleep mode.
The qualitative and quantitative performance of PA 1 and PA 2 are studied. The qualitative performance is assessed considering communication, storage, and computation overhead. The quantitative performance is studied during simulation by noting the variation of the number of active 3D VSNs (Act VSN), total energy consumption by the set of active VSNs (E T ot ), total residual energy (E Res ), percentage of area coverage by the set of active VSNs (Per CoV) and network lifetime with the density of VSNs in the target area. The qualitative and quantitative performance of PA 1 and PA 2 are compared with the three existing approaches, APP 5 [14], APP 6 [14], and ET 3 (upgraded 3D version of [13]). ET 3 is evolved by replacing 2D VSNs with 3D VSNs. In all the approaches PA 1, PA 2/(APP 5, APP 6, ET 3) each VSN executes the neighbor discovery phase, registration phase, and duty cycling phase/(scheduling phase) sequentially. In the scheduling phase of (APP 5, APP 6), each VSN has to undergo two sub-phases -backup set computation and duty cycling [14]. Each VSN has to undergo two sub-phases -redundancy judgment and duty cycling in the scheduling phase of ET 3 [13]. The neighbor discovery phase and the registration phase are the same for PA 1, PA 2, APP 5, and APP 6 as the same coverage model (3D coverage model) of VSN has been used in all the approaches. ET 3 differs from APP 5 and APP 6 in the registration phase and the scheduling phase while in the neighbor discovery phase, they are the same. The duty cycling phase/(subphase) of PA 1, PA 2/(APP 5 and APP 6) is handled in a centralized manner. In ET 3 a hybrid (combination of distributed and centralized) duty cycling technique based on grids is adopted.
It has been observed during simulation that the number of VSNs which are going into sleep mode is optimum (maximum) in PA 1 and hence, PA 1 performs much better with respect to energy consumption compared to PA 2, APP 5, APP 6, and ET 3. Both PA 1 and PA 2 work with the objective to minimize energy consumption while considering connectivity and coverage constraints. Both PA 1 and PA 2 reduce communication overhead compared to APP 5, APP 6, and ET 3.
The most important contributions of this paper are as provided below: • A practical coverage model of VSNs is explained by adopting 3D VSNs which are projected on a 2D plane surface. • Then, the ILP-based optimization technique (PA 1) has been applied for getting an optimal value of the objective function which is the number of active 3D VSNs, i.e., energy consumption subject to connectivity and coverage constraints. Coverage constraint assumes the value of area coverage to remain constant after the deployment of sensor nodes in the target area. • The heuristic approach (PA 2) based on the optimization technique (AGA) is proposed for getting nearoptimal values of the number of active 3D VSNs (or, energy consumption by all the active VSNs in the target area), subject to connectivity as well as coverage constraints.
In this paper, related works are provided in Section 2.
The coverage model, network model, energy consumption model, and some definitions are discussed in Section 3. Section 4 explains the proposed work. Section 5 examines the qualitative performance of PA 1, PA 2, and the existing works APP 5, APP 6, and ET 3. Section 6 demonstrates the simulation experiments, quantitative performance evaluation, experimental analysis, and summary of observation. Finally, Section 7 draws the conclusion of the paper and suggests the future scope followed by references.

Related work
A distributed approach of the duty cycling technique is proposed in [2][3][4][5][6][7][8][9]. Each VSN produces two activity messages, specifying its active/inactive status, and sends those two messages to its neighbors. The VSN sends one activity message to its neighbors when it is a deciding factor of whether to slip into sleep mode or stay active. It sends the other activity message to its neighbors after deciding to stay active or go into sleep mode. A huge message loss is caused during such transmission and reception, as no order is maintained. In [1], two duty cycling approaches (APP 1 and APP 2) are proposed. A mingling of a small percentage (40%) of static active/inactive VSN (AIVSN) and a large percentage (60%) of static all-time active VSN (ATVSN) are deployed in a random manner in the target area both in APP 1 and APP 2. It is a significant development over the duty cycling approach as revealed in [2] and in other approaches [3][4][5][6][7][8][9]. Only AIVSNs in APP 1 and APP 2 take part in the duty cycling approach. This brings down collision among messages and as a result, more VSNs enter sleep mode. But, both in APP 1 and APP 2 only AIVSNs (40% of total VSNs) are permitted to enter the sleep mode. Besides, all the approaches consider 2D modeling of the sensing region/Field of View (FoV) of VSN. But, the 2D modeling of FoV does not indicate a realistic model for camera coverage. A novel scheduling algorithm among sensor nodes is suggested in [13]. The scheduling algorithm in [13] is based on the redundancy among Wireless Sensor Nodes (WSNs). It is a hybrid algorithm (i.e., mingling of centralized and distributed) and grid-based for shutting off WSNs. But heuristics in [13] have used the 2D Omnidirectional sensing model of WSNs, not a practical camera coverage model. Two centralized approaches (APP 5 and APP 6) having an advanced duty cycling technique are suggested in [14]. These two approaches are successful in lowering the number of active VSNs, and total energy consumption by the active VSNs more compared to the existing approaches (EX 1, EX 2, EX 3). EX 1, EX 2 and EX 3 are the upgraded 3D version of [1], [2] and [13] respectively as revealed in [14]. Consequently, the loss of coverage by the active VSNs is also more in [14] compared to EX 1, EX 2, and EX 3. But, the scheduling schemes in [1-9, 13, 14] are able to reduce the number of active VSNs and in turn energy consumption at the cost of a reduction in the percentage of coverage. They fail to produce an optimized (minimized) value of the number of active VSNs and energy consumption without losing area coverage. In order to gather images having visual correlation efficiently, a scheduling framework based on differential coding has been proposed [15]. This framework is composed of two components which include Maximum Lifetime Scheduling and Min-Max Degree Hub Location. The proposed scheduling scheme based on differential coding can effectively enhance the energy efficiency of camera sensors and the network throughput. But, the problem of Maximum Lifetime Scheduling is an NP-Hard problem. In [16] two problems have been dealt with. One problem deals with camera scheduling, i.e., the selection of a set of cameras among available possibilities for allowing the required coverage at each instant of time. The second problem addresses energy allocation, i.e., how the total available energy is distributed among the camera sensor nodes. The problem of energy allocation is constructed as a min-max optimization problem that targets maximizing the coverage duration for the most critical region of the target area, where the availability of energy is the minimum. But the min-max optimization problem is an NP-Hard problem that can only be solved for the problem of small size. In [17] a real-time dynamic scheduling algorithm has been proposed based on priority for wireless multimedia sensor networks. The scheme in [17] does not possess any scheduling mechanism at the application level among VSNs and consequently, all VSNs stay in active mode. In [18] a scheduling algorithm based on priority has been suggested to increase the network lifetime. A mixture of static and movable VSNs has been used in [18]. As some VSNs are movable, it results in a huge waste of energy. In [19] an optimal point of partitioning with intelligence between the central BS and the sensor node has been selected. Outcomes in [19] suggest that sending zipped images after segmentation increases the lifetime of the sensor node. But, there still remains a huge wastage of energy and data redundancy because all VSNs stay active both in [17,19] in the target area. A two-phase algorithm is proposed in [20]. The Binary Integer Programming-based algorithm is able to solve the problem of optimal camera placement for a placement space greater than that of the recent study. This study helps to solve the problem in three-dimensional space which is a more realistic scenario. A binary particle swarm optimization (BPSO)-based algorithm is proposed in [21] for solving a planned placement problem of a homogeneous camera sensor network. But both [20,21] deal with the deployment of VSNs in a planned way in the target area. In the post-disaster scenario, the planned deployment of camera sensors is not possible. Many works like [22][23][24][25] deal with target coverage where sensor nodes  are to cover a few target points instead of the whole area of the target. But in a post-disaster scenario, the whole area needs to be monitored. A PSO collaborative evolution-based sleep scheduling mechanism for WSN is proposed in [23]. A hierarchical structure prevails between the ordinary nodes and the backbone nodes [23]. But such a hierarchical structure is unsuitable in the post-disaster scenario where the random deployment of sensor nodes is the only possibility. A PSO-based sleep scheduling algorithm is proposed in [26]. The method used in [26] is able to bring down the number of active WSNs and energy consumption ensuring an adequate percentage of coverage. An improved immune fuzzy genetic algorithm (IIFGA) is suggested in [27] to remove redundancy among WSNs and to select a set of working WSNs without lowering the quality of the coverage much. Both [26,27] lower the number of active WSNs in the target area though they are unable to produce an optimal (minimum) value of the number of active WSNs. Besides, the coverage model of 2D WSNs is used in [22][23][24][25][26][27]. Being Omnidirectional (circular), the coverage model of 2D WSN is very simple, but it cannot be implemented in reality. Both the approaches (PA 1 and PA 2) which utilize the 3D coverage model of VSN are a more realistic model of camera coverage than the 2D coverage model of VSN as considered in [1][2][3][4][5][6][7][8] and 2D Omnidirectional coverage model of WSN as considered in [13,[22][23][24][25][26][27]. Besides, the proposed approaches (PA 1 and PA 2) provide optimal and near-optimal values for the number of active VSNs and energy consumption respectively unlike [1-9, 13, 14, 17]. PA 2 can run in polynomial time unlike [15,16]. All the VSNs do not stay active in the target area as present in [17,19]. Both the approaches (PA 1 and PA 2) shut off VSNs to optimize (minimize) the number of active VSNs and energy consumption in the duty cycling phase without losing coverage and hence, the same quantity of video data is collected with less data redundancy unlike in [17,19]. Unlike [18], the usage of static VSNs further minimizes energy consumption owing to the mobility of VSNs. The deployment of 3D VSNs in a random manner in the target area unlike [20,21] is suitable when it is difficult for the human being to reach first the target area. Unlike [22][23][24][25], in the present work, the whole area needs to be monitored and the motivation of the present work is to minimize the number of 3D active VSNs without losing initial area coverage which is the percentage of coverage when all VSNs were active. The approach PA 1/(PA 2) of the work proposed in this paper is able to minimize the number of active VSNs under the coverage and connectivity constraints unlike [26,27] while PA 1/(PA 2) provides an optimal/(near-optimal) solution.
The list of acronyms used in this paper is displayed in Table 1. Proposed works and several very current related works are summed up in Table 2.

Coverage model and network model
PA 1, PA 2, APP 5, APP 6, ET 3 follow the same coverage and network model as in [14].   [14] respectively) show the FoV of the VSN v when it is projected on the target area, which is a 2D plane surface. When a large number of 3D VSNs are deployed to monitor a 2D target area, their trapezoidal sensing regions over the target area overlap with each other as shown in Fig. 2. Additionally, the BS represents the target area (A) by some uniform random points to make the coverage problem computationally manageable. Fig. 1 a 3D Directional sensing model (source [14]). b The projected trapezoidal area on the target 2D plane (source [14]). c Details of 3D directional sensing model (source [14])

Energy consumption model
The energy consumption model of PA 1 and PA 2 is the same as described in [14].

Calculation of energy consumption (E Tot )
E T ot is the total energy consumption by Act VSN in Joule during the simulation time 0 to t s. E T ot is calculated for only Act VSN. Let E va be the total energy consumption by the VSN v during the simulation time 0 to t s. Therefore, as stated by the model for energy consumption described in [14], E T ot is calculated at simulation time t s using Eq. 1 assuming that all VSNs are deployed at t=0.

Definition 1
The mathematical structure of the general ILP formulation of a single-objective optimization problem is as follows: • F represents the objective function to be optimized • (decs 1 , decs 2 , .....decs n ) are the n decision variables and decs n is the n th decision variable • Furthermore, the problem is subjected to J number of inequality/equality constraints. G j is the j th constraint • Additionally, each decision variable has an upper and/or lower bound associated with it, e.g., 1st decision variable (decs 1 ) has an upper and/or lower bound (decs 1 (U) and/or decs 1 (L) ), 2nd decision variable (decs 2 ) has an upper and/or lower bound (decs 2 (U) and/or decs 2 (L) ), and so on. decs 1 Definition 2 Optimization of the objective function, either minimization or maximization. Definition 5 A solution that satisfies the set of constraints and variable bounds is called a feasible solution. All feasible solutions form a feasible decision space.

Definition 6
An optimal solution is a feasible solution that optimizes the objective function. The optimal solution produces the optimal value of the objective function.

Present work
Both approaches (PA 1, PA 2) are elaborated on in this section. The three phases, neighbor discovery phase, registration phase and duty cycling phase are executed by each VSN in the target area sequentially. PA 1 and PA 2 differ in the duty cycling phase. Figure 3 briefs the flow of execution of the proposed approaches. The neighbor discovery phase and the registration phase of PA 1 and PA 2 are the same and described in Section 1. In the registration phase, each VSN in the target area selects a route from itself to the BS using GPSR routing protocol with tunable MAC [28] which is utilized in multi-hop-based routing.

Duty cycling phase
The BS in both approaches executes a centralized algorithm for duty cycling, coverage and connectivity control (DCC). DCC 1 /(DCC 2 ) are the DCC algorithm for PA 1/(PA 2). Both in DCC 1 and DCC 2 , the objective function (Obj F which minimizes Act VSN) depends on decision variables which are the status of VSNs. The BS formulates singleobjective optimization for the objective function and constraints in the ILP format before the execution of both DCC 1 and DCC 2 as shown below.
Min Obj F(Status 1 , Status 2 , ...... Status T N ) Subject to the following two constraints:  to be satisfied. The value of Act VSN min is calculated by considering =0.3 using Eq. 5 [29].
Here R c is the communication range, λ is the number of 3D VSNs per unit area and is a constant whose value lies between 0 and 0.5. Now, λ is calculated by considering =0.3 using Eq. 4 for a given R c and A, Act VSN min is calculated as (λ*A), i.e., The corresponding E T ot is measured using Eq. 1. in Joule during the simulation time 0 to t s.

P er CoV = (CoV Randpoints/T ot Randpoints)
* 100% where CoV Randpoints is the total number of random points covered by all VSNs in the proposed area of size A and Tot Randpoints is the total number of random points created by the base station. Let n v be the number of random points covered by the FoV of v th VSN then Illustrative example Let for a given value of A and Rc, Act VSN min is computed as 2 using Eqs. 4 and 5.
Act VSN min basically ensures connectivity in the network. Let us consider also that the desired threshold coverage value (Th coverage ) is 50%. Let 100010010 denote a particular solution that consists of the status of VSNs in the network. 1/(0) in the solution indicates the activeness/(inactiveness) of the particular VSN in the network. Act VSN is 3 in this solution. Let Per CoV by the active VSNs be 60% which is computed by using Eq. 7. It is clear from this solution that Act VSN > Act VSN min and Per CoV > Th coverage . Therefore, this solution (in which coverage and connectivity constraints are satisfied) is a feasible one. There may exist many feasible solutions to the problem. Out of these solutions, the solution which provides the least value of Act VSN is accepted as the desired solution which minimizes energy consumption in the networks while maintaining the coverage and connectivity constraints.

DCC 1
The BS minimizes (Obj F). The corresponding ILP format of the proposed single-objective optimization is discussed in Section 4.1 The BS solves this single-objective optimization problem as stated below.
Step 1: DCC 1 calls a Python-based package (PuLP) [30] which calls a solver (a program), a coin-or branch cut (CBC) to solve the above single-objective ILP problem for getting an optimal solution and optimal value of the objective function, (Obj F) corresponding to the optimal solution.
Step 2: The BS stores this optimal solution as a set of values for the status of VSNs in a list, L opt . Each value in L opt is either 0 (for inactive VSN) or 1 (for active VSN). L opt stores such values for all the VSNs in the network (T N) and hence, the size of L opt (Size L opt ) is T N bits. The value Status v is in the v th location of L opt . The BS uses a counter to count the number of 1 in L opt and the count value of this counter is the optimal value of Act VSN (Act VSN opt ). For example, Fig. 4 shows L opt for T N = 10. The number of logic 1 in L opt is 6 and hence the optimal value of the objective function (Obj F) is 6, i.e., Act VSN opt = 6. The BS computes the optimal value of E T ot (Energy T ot opt ) using the value of Act VSN opt and Eq. 1.
Step 3: The BS determines the identification of active VSNs using the position of logic 1 in L opt . The BS searches the BT to find the records corresponding to the identification of the active VSNs as obtained from L opt , reads position and orientation from these records to generate FoV of these active VSNs. The BS counts the number of random points in the target area that are inside the FoV of active VSNs as CoV Randpoints using Eq. 7, uses Eq. 6 to compute the value of Per CoV using the value of Tot Randpoints and CoV Randpoints. Per CoV should not be less than Init CoV when Obj F is equal to Act VSN opt . Init CoV should also be greater than Th coverage so that WVSN may remain functional. The BS stores Act VSN opt as the optimal value of the objective functions Obj F and Energy T ot opt in two separate variables.

Step 4: The BS determines the identification of inactive
VSNs using the position of logic 0 in L opt . The BS searches the BT to find the records corresponding to the identification of the inactive VSNs as obtained from L opt , reads the position from these records and sends sleep messages to these inactive VSNs. The BS also updates these records in the BT by replacing the value of "isVSNActive" Boolean variable from 1 to 0.

DCC 2
DCC 2 utilizes AGA [12] based single-objective optimization technique to minimize Obj F subject to connectivity constraint and coverage constraint. AGA is a special category of genetic algorithm (GA) that has characteristics like self-adaptive crossover and mutation operation, scale reproduction etc [12]. AGA adaptively varies the mutation and crossover probability following different conditions of solutions to prevent premature convergence, preserve the solution diversity, to enhance the speed of calculation and the algorithm precision while searching for the optimum value of the objective function. In DCC 2 , each solution (also known as a chromosome) belonging to a population of size N P is of length T N. The value of Status v is in the v th location in the solution. All the solutions in the population are encoded in binary format as the status of each VSN is a binary variable. It is called the genetic representation of a solution. The general format of the genetic representation of a solution is shown in Fig. 5.

DCC 2 is divided into two parts
Part 1 finds the near-optimal solution and near-optimal value of Obj F and Part 2 finds shutting off the maximum number of VSNs in the target area.

Part 1:
To find the near-optimal solution, Procedure GA OPT( ) is executed. Part 2: Shutting off the maximum number of VSNs on the target area Step 2.1: The BS determines the identification of inactive VSNs using the position of logic 0 in L opt . The BS searches the BT to find the records corresponding to the identification of the inactive VSNs as obtained from L opt , reads position from these records and sends sleep messages to these inactive VSNs. The BS also updates these records in the BT by replacing the value of the "isVSNActive" Boolean variable from 1 to 0.

Post duty cycling scenario
A maximum number of VSNs enter into sleep mode after the execution of DCC 1 /(DCC 2 ) by the BS. Now, the BS computes T N, number of VSNs in sleep mode (say max ) and Act VSN opt (=(T Nmax )) from L opt for the target area. The BS also calculates Per CoV by Act VSN opt in the target area from the BT. In the case of (Per CoV < Th coverage ), the BS stops gathering data from WVSN since WVSN is no more operational now. Suppose VSN v is in active mode and (Per CoV ≥ Th coverage ), the VSN v begins monitoring the target area. Owing to the continuous dissipation of energy, VSN v dies after a certain time. Its energy having been reduced to the value, a little more than Algorithm 1 GA OPT(N P , Gen Max , p mu , p cr ). zero, the VSN v transmits and routes (utilizing GPSR) dead messages [14] to its neighbors and the BS respectively. The size of the dead message (Size D) is 17 bits [14]. The BS searches the BT using the id of the VSN v after receiving the dead message from it, updating the values, isVSNActive [14] and isVSNDead [14] to 0 and 1 respectively for VSN v. VSN v 1 (a neighbor VSN of the VSN v say) becomes active when it receives a dead message from the VSN v. These phenomena will happen for all dead VSNs and consequently, the sleeping VSNs belonging to max become active. The BS now searches for records of sleeping VSNs (belonging to the set max ) in the BT with the observation of values of "isVSNActive" and "isVSNDead" set as 0 and 0 respectively. VSNs being active now, the BS updates the values of "isVSNActive" and isVSNDead to 1 and 0 respectively.  [14] 231.33 kilobytes 64.35 megabytes APP 6 [14] 231.33 kilobytes 64.35 megabytes ET 3 [14] 241.54 kilobytes 0.22 megabytes All the sleeping VSNs (∈ max ) being active, the BS again calculates Per CoV by max (=(T N -Act VSN opt )) number of VSNs. The BS will stop collecting data from WVSN at this point if Per CoV is less than Th coverage . Otherwise, Act VSN (∈ max ) will go on monitoring the target area till they die owing to energy deficiency.

Qualitative performance
The evaluation of the qualitative performance is carried out with respect to communication overhead (CM OV), computation overhead (CP OV), and storage overhead (ST OV) for the two schemes (PA 1 and PA 2). The existing approach, ET 3 corresponds to EX 3 of [14]. The CM OV, CP OV, and ST OV of APP 5, APP 6, and ET 3 are already evaluated in [14] and are shown in Tables 3 and 4. In the worst case, each VSN in the target area for PA 1 and PA 2 has (T N-1) number of neighbor VSNs. The overheads are studied in the worst case in the target area.
CM OV: CM OV of PA 1 and PA 2 is the summation of the communication overhead in the neighbor discovery phase (CM OV 1 ), registration phase (CM OV 2 ) and duty cycling phase (CM OV 3 ).
CM OV 1 : In PA 1 and PA 2 each VSN sends a packet of size Size Rec NT bits [14] to its (T N-1) number of neighbors. Therefore, CM OV 1 in PA 1 and PA 2 is (Size Rec NT*T N*(T N-1)) bits  [14] 471.62 kilobytes 92.05 megabytes APP 6 [14] 471.62 kilobytes 92.05 megabytes ET 3 [14] 492.58 kilobytes 0.45 megabytes CM OV 2 : In PA 1 and PA 2 each VSN routes a packet of size Size Rec NT bits [14] to the BS. So CM OV 2 in PA 1 and PA 2 is (Size Rec NT*T N) bits CM OV 3  ST OV 2 : In PA 1 and PA 2, the BS stores T N number of records in the BT. Each record has (Tot Param+2) number of parameters [14] of size (Size Rec NT+2) bits [14]. So, ST OV 2 in PA 1 and PA 2 is (Size Rec NT+2)*T N bits.
ST OV 3 : The BS stores the optimal solution in L opt after the execution of DCC 1 in PA 1 and DCC 2 in PA 2. Size L opt is T N bits, i.e., (1/8)*T N bytes. The BS stores (Act VSN opt , Energy T ot opt ) in two separate variables both in PA 1 and PA 2. The data type of the variable which holds the value of Act VSN opt is int. The data type of the variable which holds the value of Energy T ot opt is float. Therefore, the total size needed to hold Act VSN opt and Energy T ot opt is (2+4) bytes, i.e., 6 bytes. So, ST OV 3  CP OV is the highest in PA 1 (exponential) and the lowest in ET 3. CP OV of APP 5 and APP 6 are the same. CP OV of ET 3 is lesser than that of APP 5, APP 6. CP OV of PA 2 cannot be compared with PA 1, APP 5, APP 6, and ET 3 as CP OV of PA 2 depends on two other variables, Gen MAX and N P apart from T N unlike CP OV of the rest of the approaches.
CM OV and ST OV for the five schemes are calculated and shown in Tables 3 and 4 respectively when T N is 70 and 100.
It is observed from Tables 3 and 4 that CM OV is the least and the same for PA 1 and PA 2. CM OV is the highest in ET 3. CM OV is less in APP 5 and APP 6 than in ET 3. It is also observed from Tables 3 and 4 that ST OV is the least in PA 1 and PA 2, the highest in APP 5 and APP 6, and less in ET 3 than in APP 5 and APP 6.

Quantitative performance
Both PA 1 and PA 2 are simulated using OMNET++ Castalia simulator [31]. WVSN−v4 framework [32] which supports the modeling of video sensor coverage contains a simulation model of WVSN. A particular VSN possessing a larger processing capability is supposed to be the BS both in PA 1 and PA 2. The BS utilizes pulp [30] and pymoo [33] (both are python-based packages) to get an optimal solution and a near-optimal solution respectively in the duty cycling  [14]. Hence, the basic simulation environment, simulation environment for energy consumption, tunable MAC parameters, and GPSR protocol parameters as in [14] are summarized in Tables 5 1 , 6, 7, and 8 respectively. Tables 5, 6, 7, and  8 correspond to Tables 5, 6, 7, and 8 in [14] respectively. Table 9 summarizes the parameters used in DCC 2 .

Simulation metric
The quantitative performance of PA 1 and PA 2 is studied based on Act VSN, E T ot (in Joule), E Res (in Joule), Per CoV (in percentage), network lifetime (in seconds) and R T (in seconds) in the target area. R T is the execution time (in seconds) of PA 1, PA 2 excluding the execution time of the neighbor discovery phase and registration phase. The quantitative performance of PA 2 is also studied based on Act VSN for studying the convergence of GA OPT to the optimum value of Act VSN, i.e., Act VSN opt .
With the increase in the total number of deployed VSNs in the target area (node density) Act VSN increases and as a result of which E T ot , Per CoV, E Res and network lifetime also increase. Therefore, the variation of Act VSN, E T ot , E Res , Per CoV and network lifetime is studied with the variation of the node density during simulation. With the increase in node density, R T increases as a result of which network lifetime also increases. Therefore, the variation of R T is studied with the variation of the node density during simulation. The increase in the total number of function evaluations (Function Evaluation) defined as the product of population size and the number of generations in GA OPT decreases Act VSN if GA OPT converges to the optimum value of Act VSN, i.e., Act VSN opt . Therefore, 1 Horizontal Offset Angle α will be 18 • in [14]

Simulation results and performance evaluation
Five simulation experiments are conducted to compare the performance of PA 1 and PA 2 with APP 5, APP 6, ET 3 and Init Ran. The sixth simulation experiment is conducted to compare the performance of PA 1 and PA 2 with APP 5, APP 6 and ET 3. The seventh simulation experiment is also conducted during the simulation of PA 2 for studying the convergence of GA OPT to Act VSN opt . All the simulation experiments except the fifth, sixth and seventh simulation experiments have been conducted for the duration (0-700) s. The fifth simulation experiment is conducted for (0-1500) s.

Act VSN versus node density
The first simulation experiment is conducted for observing the variation of Act VSN with node density. The plot of

Network lifetime versus node density
The fifth simulation experiment is conducted for observing the variation of network lifetime with node density. The plot of network lifetime vs. node density for Init Ran, PA 1, PA 2, APP 5, APP 6 and ET 3 is shown in Fig. 10.
Observation from Fig. 10 Network lifetime is the least in Init Ran and ET 3 (770 s) and the highest in PA 1 and PA 2 (1500 s) for all node density. It is lesser in APP 6 than in PA 1 and PA 2 for the node density less than equal to 80. It is lesser in APP 5 than in PA 1, PA 2 and APP 6 for all node densities except node densities 120 and 150. The nature of graphs in Fig. 8 explains the nature of graphs in Fig. 10.

Comparison among PA 1, PA 2, APP 5, APP 6 and ET 3 with respect to R T
The sixth simulation experiment is conducted for observing the variation of R T with node density. Tables 10 and 11

Experimental analysis
In PA 1, PA 2, APP 5, and APP 6 the collision among messages and consequently loss in messages is reduced by tunable MAC protocol which utilizes CSMA/CA for reducing the message collision. As a result, the BS receives all the messages from VSNs in the registration phase. The BS in PA 1, PA 2/(APP 5, APP 6) sends a sleep message again using tunable MAC protocol for turning off T N-Act VSN opt number of/(a set of) VSNs. This results in the minimization of Act VSN as observed in Fig. 6 and minimization of E T ot as observed in Fig. 7 which leads to the maximization of E Res (as observed in Fig. 8) and in turn network lifetime (as observed from Fig. 10) both in PA 1 and PA 2. This also results in the reduction in Act VSN, E T ot , Per CoV and an increase in E Res , network lifetime in the case of APP 5 (for node density > 100) and APP 6 in comparison to ET 3 as observed from Figs. 6,7,9,8 and 10 respectively. The four BSs operate simultaneously in APP 6. Hence, the BS in APP 6 receives most of the request messages from the VSNs in the target area. This reduces Act VSN, E T ot , Per CoV and enhances E Res , and network lifetime more in APP 6 than in APP 5 and ET 3. The minimization of Act VSN both in PA 1 and PA 2 ( Fig. 6) results in no reduction of Per CoV from Init CoV as observed in Fig. 9. Therefore, Per CoV is the highest in PA 1 and PA 2 and it is the same as Init Ran.
No message-passing takes place in the duty cycling phase of PA 1 and PA 2. Therefore, CM OV of PA 1 and PA 2 is the least as observed in Tables 3 and 4. Act VSN opt in PA 1 is optimal (minimum) and Act VSN opt in PA 2 is near-optimal. Therefore, Act VSN opt and Energy T ot opt in PA 1 are lesser than Act VSN opt and Energy T ot opt in PA 2 as observed from Figs. 6 and 7 respectively. E Res in PA 1 is greater than E Res in PA 2 for the same reason as observed from Fig. 8. PA 2 being based on AGA produces very good results in terms of minimizing Act VSN and E T ot , and maximizing E Res and network lifetime while maintaining Per CoV equal to Init CoV compared to that obtained by using APP 5, APP 6 and ET 3 (as observed from Figs. 6, 7, 8, 9 and 10 (respectively).
The group leader [13] in the grid sends a sleep message to the two VSNs belonging to the q th grid having the highest and second-highest weight respectively in ET 3. The VSNs get the sleep message from the corresponding group leader and broadcast the SAM message [13] to their corresponding neighbors. There is a collision between the sleep messages and the SAM message although sleep messages do not collide with each other across the grids in the target area. This results in a loss of sleep message. The loss of sleep message owing to collision enhances with the enhancement of deployed VSNs in the target area. A huge number of VSNs having the highest or second-highest weight in several grids do not receive sleep messages from their corresponding group leader and consequently, those VSNs remain active although they fulfill the condition of redundant coverage [13,14]. This enhances Act VSN (Fig. 6), E T ot (Fig. 7) and Per CoV (Fig. 9) and decreases E Res (Fig. 8) and network lifetime (Fig. 10) in ET 3 compared to APP 5 (for node density > 100).

Summary of major observation
It is observed that APP 6 produces a better result than that of (APP 5, APP 6, and ET 3) with regard to E T ot . ET 3 shows the best results among these three state-of-the-art works with regard to Per CoV. Act VSN is lesser in PA 1 compared to PA 2. PA 1 and PA 2 are able to reduce E T ot by 40.85% and 33.34% respectively from the existing best approach APP 6 (with respect to E T ot ) for 150 deployed VSNs over the target area. With the reduction in Act VSN, E T ot also decreases but at the expense of reduced Per CoV in APP 5, APP 6, and ET 3. But the reduction in Act VSN does not cause a reduction in Per CoV in PA 1 and PA 2. For the same node density, both PA 1 and PA 2 gain a little amount of Per CoV (i.e., 0.94%) than the existing better approach ET 3 (in terms of Per CoV). Both PA 1 and PA 2 have the same CM OV. Both of them show better results by 0.32%/(4.25%) from (APP 5 & APP 6)/(ET 3) in terms of CM OV for 100 deployed VSNs on the same target area. Finally, PA 1 reveals its superiority concerning reduced E T ot (11.26%) over that of PA 2 without losing Per CoV for 150 deployed VSNs.

Conclusions
In this paper, two advanced approaches, PA 1 and PA 2 have been proposed to minimize the number of active 3D video sensor nodes monitoring the 2D target area without losing area coverage and ensuring network connectivity in the target area with randomly deployed VSNs. The total energy consumption by the video sensor nodes being proportional to the number of active video sensor nodes, PA 1 and PA 2 is designed for minimizing energy consumption. PA 1 produces the optimal value of energy consumption, while PA 2 produces a near-optimal value of energy consumption, subject to coverage and connectivity constraints. APP 5, APP 6, and ET 3 are the existing state-of-the-art approaches with which PA 1 and PA 2 are compared both with regard to energy consumption and area coverage. It is observed that both PA 1 and PA 2 produce much better results while minimizing energy consumption and also maintaining the initial coverage compared to APP 5, APP 6, and ET 3.
A new approach can be developed in the future to address the above-mentioned conflicting issues in the presence of heterogeneous 3D video sensor nodes where all video sensor nodes will have different communication and sensing ranges.
Availability of data The data underlying this article will be shared on reasonable request to the corresponding author.

Declarations
Competing interests The authors declare no competing interests.