Augmented Node Placement Model in -WSN Through Multiobjective Approach

In Wireless Sensor Network (WSN), coverage and connectivity are the vital challenges in the target-based region. The linear objective is to find the positions to cover the complete target nodes and connectivity between each sensor for data forwarding towards the base station given a grid with target points and a potential sensor placement position. In this paper, a multiobjective problem on target-based WSN (t-WSN) is derived, which minimizes the number of deployed nodes, and maximizes the cost of coverage and sensing range. An Evolutionary-basedNon-Dominated SortingGenetic Algorithm-II (NSGA-II) is incorporated to tackle this multiobjective problem efficiently. Multiobjective problems are intended to solve different objectives of a problem simultaneously. Bio-inspired algorithms address the NP-hard problem most effectively in recent years. In NSGA-II, the Non-Dominated sorting preserves the better solution in different objectives simultaneously using dominance relation. In the diversity maintenance phase, density estimation and crowd comparison are the two components that balance the exploration and exploitation phase of the algorithm. Performance of NSGA-II on this multiobjective problem is evaluated in terms of performance indicators Overall Non-dominated Vector Generation (ONGV) and Spacing (SP). The simulation results show the proposed method performs outperforms the existing algorithms in different aspects of the model.

This paper addresses k-coverage m-connected augmented node deployment model in WSN as a multiobjective problem where Non-dominated sorting Genetic Algorithm-II is used to optimize it. The problem is described in this section. Given k target regions and P available positions for node deployment, the objective is to cover k targets using m sensor nodes where m ⊆ P. As it is given in Fig. 1, Let T = {λ 1 , λ 2 , . . . , λ 10 } be the available target regions to be sensed using S = {s 1 , s 2 , . . . , s m } deployed nodes. As per Fig. 1 number of sensor nodes in S is six out of 10 available positions of P. Target λ 2 is covered by a Deployed sensor s 1 since the target is within the sensing range of the deployed sensor s 2 which is deployed in the available position p 2 and the deployed node can transfer the data to a base station through the available positions p 3 and p 4 . By allocating the sensor nodes concerning its coverage and connectivity range, the minimum objective number of deployed nodes to cover all targets are efficiently achieved. This problem is considered an NP-complete problem [5]. Achieving optimization in this problem is highly preferable since exact methods take more high time complexity when compared to the optimization approach.

Related Work
In the past few decades, research contributions on optimizing WSN problems using heuristic and metaheuristics are higher than earlier research exposure [5][6][7][8][9]. In this literature, coverage and connectivity related algorithms are described with their predominant features.
A detailed Survey has been recorded on different methods for effective node placement in WSN by [10]. In [5] a contradictory set of objectives are taken for effective node placement in WSN, namely energy cost, sensible area, and network reliability. The flaws in their approach are the inadequate coverage of complete targets in the given region. The use of meta-heuristics failed to achieve this particular issue which made the algorithm an ineffective one. A new approach for solving the WSN issue is dividing a region into a disjoint sub-region and imposed active and passive mode of operations in it by [11]. The proposed methodology of Cardie was later redefined in [5] to enhance the lifetime of the network by imposing redundant nodes. Irrespective of coverage and connectivity, this approach achieves better results along with improved disjoint sets.  Research on the optimization of resource allocation algorithm in WSN is discussed by [12]. The lifetime of network and connectivity are the objectives considered in this paper, which takes the sensor positions and transmission power level as their attributes to solve the problem. MOEA/D is used to solve the given problem to achieve the objectives with fewer deployed sensor nodes. Coverage was not handled in this paper. Author Harizan et al. [13] proposed an NSGA-II with modified dominance has been proposed for the scheduling problem. The multiple parameters as coverage, connectivity and residual energy of the sensor nodes are considered. A probabilistic sensing model (PSM) and harmony search algorithm (HSA) approach are used in the same type of problem in WSN to achieve the balance between the network coverage performance and the network cost [14].
In 2012, a multi coverage based WSN problem is handled in [15], three different coverage, namely simple coverage, k and Q coverage. For the optimization process, an exhaustive cover set defining process is used in this approach. For the inclusion of connectivity in the proposed algorithm, an M-connected approach is included for optimization. The algorithm's time complexity is higher since the algorithm flow included each node one by one and check for all possible combinations in the set for adaptive placement of nodes.
A simulation-based approach for effective node placement is proposed by [16], where several available positions to place the sensor nodes are given. Without colliding the connectivity between sensor nodes, the nodes should be placed with the minimal number-another approach based on GA proposed in [17] as relay sensor node placement algorithm. This paper's defined objective is to efficiently place the nodes in the given positions, thus minimizing the number of sensors without colliding its connectivity between relay nodes. Using GA, another approach for attacking coverage problem in WSN is proposed to enhance its lifetime. In this approach, sensing targets are not used for simulation. Only the sensors nodes are placed to cover the simulation region without any targets in it. In our proposed method, this problem is addressed. Another GA based approach for addressing the same issue as our proposed method has been made in [4]. However, this method reproduces offspring so that it becomes invalid, and a solution repair process is needed here. In our proposed algorithm, a multiobjective optimization algorithm NSGA-II is used to address this issue and Pareto set solutions.

Multiobjective Optimization
This section comprises the prescribed definition of the multiobjective optimization problem [18] and Pareto dominance operators, which helps to understand the proposed work better.
Given a problem with solution set P = [C 1 , C 2 , . . . , C n ] with n individuals where each individual C i = G i,1 , G i,2 , . . . , G i,j , . . . , G i,m with m decision variables intents to find a vec- From the solution space given in this definition P = [C 1 , C 2 , . . . , C n ], an individual C 1 = G 1,1 , G 1,2 , . . . , G 1,m is said to dominate C 2 = G 2,1 , G 2,2 , . . . , G 2,m iff f i C 1 ≤ f i C 2 ∀i k and f i C 1 < f i C 2 ∃i k and this can be represented as C 1 ≺ C 2 . Two individuals said to be nondominated to each other if neither C 1 ≺ C 2 nor C 2 ≺ C 1 and this can be represented as C 1 C 2 . Fig. 2 shows an example for dominated and non-dominated solutions. Let us consider a multiobjective problem that consists of two objectives f 1 ( ) and f 2 ( ). Three individuals C 1 , C 2 and C 3 are plotted in Fig. 1 based on their objective values. From the given definition, we can claim that individual C 1 dominates individual C 2 and C 3 and this can be represented as C 1 ≺ C 2 , C 3 . And individual C 2 and C 3 are non-dominated to each other since it satisfies the given definition of the non-dominated solution set and this can be represented as C 2 C 3 .

Problem Formulation
In this section the the formulation of t-WSN problem is defined with an example along with the objectives.

Network Model
Let us assume that the simulation region for target-based WSN is of the two-dimensional region. Our model positions the positions to deploy the sensor nodes randomly based on the available targets. The target points and sensor nodes are static for some available positions. In our proposed model, the available position to sense targets are given with a different range, as shown in Tab. 1. Similarly, communication between nodes are given as coverage range which is listed in same Tab. 1.

Problem Definition
Let us define the notations that are used to create the system model. 5. R sen represents sensor node sensing range.
6. d λ i , s j represents the distance between the target point λ i to Deployed Sensor s j 7. Cov (λ i ) denotes the sensor nodes that cover the target points λ i . This can be represented as: 8. Tcov (s i ) denotes the target points that are covered by s i . This can be represented as:  9. Comm (s i ) denotes the sensor nodes that are covered by s j . This can be represented as: Boolean representation is used to define whether the target i is covered by node j. Points 7-9 is represented as follows: where k represents the target and m represents sensor nodes.

Objectives
There are three objectives of coverage, and connected problem are considered in this paper. The objectives are defined as follows: 1. Minimize the number of Deployed Nodes: The first objective is defined to minimize the number of deployed sensor nodes from the available positions h. It can be formulated as 2. Maximize the cost of coverage: It can be represented as: where Maximize the cost of connection: Mathematical representation can be stated as: where

Non-Dominated Sorting Genetic Algorithm II on Coverage-Connected Problem
This section holds a four-folded algorithm for optimizing coverage-connected problem using NSGA II [19]. In this section, a discussion on the Non-dominated sorting method followed by preservation of diversity will be explained in the second fold, and reproduction operators are discussed. In the final fold, a complete algorithm for solving the coverage-connected problem using NSGA-II is described. NSGA-II is chosen to solve m−connected k−coverge problem over other multiobjective optimization techniques due to its following advantages.The advantages are listed as follows: Non-Dominated sorting techniques are utilized to enhance the solution search towards pareto-optimal solutions. The use of crowding distance improvises the diversity of search. The usage of Elitist technique preserves the optimal solution in every iteration [20].

Non-Dominated Sorting and Density Estimation
Non-dominated sorting is the process of sorting the individuals based on its domination set. It is a rank-based selection method to accentuate the Pareto front individuals to improve the algorithm's search capability. A detailed description of Non-Dominated sorting is given in Algorithm 1. This algorithm is considered as a function to be called by NSGA-II in Algorithm 3.

Preserving Diversity
A multiobjective evolutionary algorithm is supposed to hold two properties such as: • Convergence towards Pareto front individuals.
• A diversified search should be done during the run.
In NSGA-II, two methods are used to handle this diversity preservation: density estimation and crowded comparison operator. This method eliminates the process of user-dependent feature.

Crowd Comparison (≺ n )
For selecting an individual, the crowding comparison operator can be used in the crowded population. Crowd comparison operator is used when both the individual obtains the same rank in non-dominated sorting. Each individual C ∈ P consists of attributes, namely 1. Non-dominated Ranking (C rank ) and crowd distance (C d ). C 1 ≺ n C 2 if it falls in two conditions which are: when an individual fall into these two conditions, then the individual with a lower rank will be selected.

Process of NSGA-II on m-Connected k-Coverage
The individuals are represented as chromosomes, and a complete solution set can be represented as population P. Boolean representation is used to represent each individual C. For Reproduction (Offspring), simulated binary crossover and 2-point mutation are used for effective diversification. After initializing the population, the offspring is done with the parent population. Children are produced and appended along with their parents. The detailed flow of NSGA-II is given in Algorithm 3. ← {G i,1 , G i,2 , . . . , G i,j , . . . , , G i The experimental setup for evaluating the proposed algorithm's performance on the k-coverage m-connected problem, NSGA-II, is implemented on the problem using MATLAB version 8.4 in the system configured with Intel Core i7 processor, 3.4 GHz processor speed, and 4 GB RAM. The designed testbed for this paper's described problem, two different grid-based scenarios are generated, namely WSN1 with a 300-m × 300-m grid and WSN2 with a 500-m × 500-m grid. The base station for WSN1 and WSN2 were set in the position coordinates of (300, 150) and (500, 250), respectively. The available positions for sensor nodes and targets are randomly placed in the grid. The parameters are given in Tab. 1.

Performance Metrics
Performance measures using for evaluating the proposed algorithm are F-value, Computation time in seconds. F-value: F-value is the ratio between the number of available positions to the number of deployed sensors in it (a higher value is better). It can be formulated as: Computational Time: Computational time is defined as the algorithm's time to perform its entire run. In this simulation, the computational time is given in seconds.
The simulation results are tabulated in Tab. 2.

Performance Measures Using Multiobjective Performance Indicators
Figs. 3 and 4 are showing the performance of the proposed algorithm in terms of multiobjective solutions, two effective unary indicators are evaluated with Pareto front solutions, namely Overall non-dominated vector generation (ONGV) and Spacing (SP). To evaluate the performance of the proposed algorithm in terms of multiobjective solutions, two effective unary indicators are evaluated with Pareto front solutions, namely Overall non-dominated vector generation (ONGV) [21] and Spacing (SP) [22]. ONGC and SP are formulated as follows:

Result Analysis
For comparison purpose, we simulated other existing algorithms, namely heuristic-based method Greedy Method and GA based method [15][16][17]23] and GA in [1]. Tabs. 2 and 3 comprises the results in terms of efficiency and Pareto front individuals, respectively. From Tab. 2, the results of the proposed algorithm show significant performance in terms of F-value on coverage and connection range (k, m) values (1, 1) and (2, 2). Tab. 3 holds the ONGV and SP metric results, which are performance indicators for evaluating the multiobjective problem. Figs. 5 and 6 shows the performance comparison of deployed sensor nodes for all algorithm with different coverage and connectivity range and the performance comparison of WSN1 and WSN2. From the given results, it is justified that the proposed algorithm's performance outperforms with appropriate performance measures.

Conclusion
In this paper, the NSGA-II optimization algorithm is used to handle the multiobjective coverage connectivity problem in WSN. The described objectives were efficiently handled using NSGA-II to obtain a high number of Pareto front set solutions. The proposed NSGA-II on coverage connectivity was tested with different grid size, communication and sensing range. In terms of F-Value, the proposed method performance with superior values for most of the simulations. Also, in terms of computational time, the proposed algorithm outperforms when compared with the existing algorithms. For justifying the proposed algorithm, five existing techniques were simulated with the same grid, and the values were tabulated in terms of F-Value and Computational time. For comparing the results in terms of multiobjective performance indicators, the final iteration individuals are taken to count with respect to its Euclidian distance.
The future directions of the proposed model can be enhanced by solving more number of objectives. On the other hand, improvising heterogeneous algorithms for solving m-connected kcoverge problem is also an another scope of the research.
Funding Statement: This research has been funded with the support of the project SP2021/45, assigned to VSB-Technical University of Ostrava, the Ministry of Education, Youth and Sports in the Czech Republic.

Conflicts of Interest:
The authors declare that they have no conflicts of interest to report regarding the present study.