Optimized localization of sensor nodes in 3D WSNs using modiﬁed learning enthusiasm-based teaching learning based optimization algorithm

Localization in wireless sensor networks (WSNs) is used to determine the coordinates of the sensor nodes deployed in the sensing ﬁeld. It is the process that determines the location of the target nodes relative to the location of deployed anchor nodes. These anchor nodes are deployed at known locations having GPS installed in them. However, mostly in all 3D applications, the area under observation may have a complexity in the sensing environment. In this work, a modiﬁed learning enthusiasm-based teaching learning based optimization algorithm (LebTLBO) is proposed to deal with the 3D localization problem using single anchor and moving target nodes in anisotropic network with DOI 0.01. LebTLBO is a metaheuristic inspired by the classroom teaching and learning method of teaching learning based optimization algorithm. An improved LebTLBO algorithm aims to achieve enhanced performance by balancing the exploration and exploitation capabilities of conventional LebTLBO to improve its global performance. On the CEC2019 benchmark functions, the suggested technique is assessed, and computational ﬁndings show that it provides promising outcomes over other competitive algorithms. Also, mLebTLBO out-performs well in terms of localization error in 3D environment. The proposed technique is useful to cope up in case of rescue operations.


INTRODUCTION
The advancement in wireless technology inspired many researchers to work in the field of wireless sensor networks (WSNs). In these networks, the nodes deployed in the region of interest can sense, measure, and communicate with other nodes to share the useful information among each other [1,2]. There are numerous applications of WSNs such as forest fire detection, military applications, air pollution control, safety surveillance etc. in which sensor nodes might be placed randomly or at predefined locations [3,4]. WSNs are categorized into structured and unstructured types. A network that consists of lesser or fewer nodes is referred to as structured WSN.
There are certain challenges in unstructured WSNs, such as retaining the network and making the node connectivity with each other.
non-uniform pattern of radiation, and degree of irregularity (DOI)). The challenges to be addressed in mobility-based scenarios are networking, coverage, and energy usage. An effective localization of the target node is one of the key challenges in dynamic WSNs. In space, atmosphere and underwater applications, where network height is most required, the assumptions made for 2D are violated. Nodes are often distributed randomly in three-dimensional space for these types of applications.
In this paper, we introduced the concept of deploying single anchor and assuming this node virtually in six distinct directions for targeting the unknown nodes using a modified learning enthusiasm-based teaching learning based optimization (LebTLBO) algorithm. As these target nodes drop under the range of anchor node, then at 60 degrees angles the virtual anchors are projected in six distinct directions with same range inside the circle, anchor node itself and three virtual nodes are nominated (as minimum four SNs are required to estimate 3D positions) of unknown nodes.
In this paper, the mLebTLBO algorithm is proposed to evaluate the performance of the localization problem of 3D WSNs with various meta-heuristics. The main problem with teaching learning based optimization (TLBO) is that all learners have the same opportunity to acquire knowledge in the teacher or learner phase. In reality, learners are distinct in actual, and they have a distinct passion for learning. When studying, learners with elevated learning excitement are more focused; therefore, they have a great opportunity to gain understanding from others. On the other hand, learners with low learning enthusiasm have relatively little chance of learning from others. This research, motivated by this behaviour, will bring to the TLBO the notion of the mechanism of learning enthusiasm to suggest a novel strategy called LebTLBO [12].
LebTLBO's optimization method can be considered as the continuous conversion of its search space. The search space is hard to contain the optimum solution when it drops into the local optimum. Therefore, guiding the present solution space approximation to the optimum solution space is very important.
It has been found that the proper balance between the diversification and intensification process is missing in LebTLBO and more research is needed to achieve the balance. Furthermore, a probability that defines the degree of exploration and exploitation is a very important factor and no proper study was done to find this parameter. However, the algorithm is very effective in exploring the search space; it takes a lot to improve its exploitative tendencies. Motivated by these, we developed a new improved version of LebTLBO in the current work that has good properties for exploration and exploitation. To achieve these goals, a new variant was introduced to achieve the abovesaid balance. The concept inspired by Grey wolf optimization [13] is implemented in a bid to improve LebTLBO's worldwide search capability (i.e. exploration capability). LebTLBO uses the present best solution in the local stage and random alternatives to improve local search. The local neighbourhood search (LNS) model [14] is introduced to improve the local search capability to enhance convergence characteristics. LNS's primary concept is to use the finest solution discovered in a tiny neighbourhood of the present solution to update the present solution. To validate the proposed algorithm in solving some extremely difficult data sets, benchmark problems are applied to CEC 2019 and comparative analysis is provided in relation with well-known algorithms.
The paper is structured as follows: In Section 2 literature review on 3D localization in WSNs is presented. Section 3 discusses the LebTLBO and suggests the LebTLBO variant in detail. Section 4 performs the performance assessment and thorough analysis of mLebTLBO. Section 5 presents single anchor deployment structure in 3D WSN. Section 6 deals with results and discussions. Conclusion and future scope are discussed in section 7.

LITERATURE REVIEW
There are many works related to wireless networks. Yang Liu et al. [15,16] have many works in varied wireless networks, for example, Mobile Ad Hoc Social Networks and Mobile Opportunistic Networks. In contrast to their network, this paper focuses on WSNs that contain many sensor nodes to monitor a physical region. Recently, various localization schemes have been proposed, while most research proposals are dealing with 2D localization problems, where the sensing area is assumed flat. However, mostly in all 3D applications, the area under observation may have a complexity in the sensing environment and large differences in altitude levels. As a result, this problem in WSNs presents new challenges for 3D localization system design.
A 3D localization algorithm based on the received signal strength indicator (RSSI) concept [17], follows parameter matching between each pair of reference node and unlocated node and then evaluating the loss in a wireless signal using various models when there are obstacles (walls) between them. Cheng et al. [18] presented a technique that is applied for underwater localization application for 3D acoustic sensor networks. Chen et al. [19] enhanced the conventional centroid localization algorithm in 2D space to 3D, that uses a greater number of anchor nodes and shows an inverse relationship between localization accuracy and deployed anchor nodes. Besides, the rangefree algorithm DV-HOP is also extended to 3D space by Wang et al. [20]. Shi et al. [21] introduced a 3D localization method for WSN. Their localization approach uses a mobile beacon that transmits ultra-wideband (UWB) signals to determine the exact position. During the reception of these signals, every target node by using the TOA technique determines the distance to the anchor node. Graefenstein et al. [22] suggested a technique that is energy efficient in which the RSSI method is utilized to calculate the approximate distance among the reference and target nodes deployed in the field using a trilateration approach. Sumathi and Srinivasan [23] have suggested a method that requires a single anchor node for localizing the unknown nodes using the RSS method. The least-square approach for locating the fixed target nodes is in this paper. Guo et al. [24] developed a perpendicular intersection (PI) mobile-based approach that does not specifically map RSS distances. The measurement of the node position is carried out using the geometric PI relation. Shi et al. [25] used ultra-wide band, ToA technique to compute node location in a 3D environment. By using this technique, the distance between reference and an unknown node is calculated more efficiently. Wang et al. [26] introduced distance vector-hop based approach for locating sensor nodes. The main reason behind the failure of this algorithm is the complexity and increased cost. Xu et al. [27] introduced another enhanced 3D localization technique that adopted DV-distance with a quasi-Newton optimize method for optimizing the results. By considering localization accuracy and coverage, the authors further tested the effectiveness of the proposed algorithm. Li et al. [28] suggested the 3D WSN localization method based on an irregular RSSI model. To calculate the relation among DOIs and the variability in signal transmission range, the authors proposed this model. Ahmad et al. [29] suggested a parametric loop-division algorithm for 3D localization where the deployed sensors are located in an area surrounded by a group of anchor nodes. In this method, the network shrinks toward the centre accurately and provides accurate localization results.
Gopakumar and Jacob [30] suggested a new and computationally efficient swarm intelligence approach for locating static nodes with easier implementation and low memory requirements. Chuang and Wu [31] use RSS ranging technique for locating sensor nodes efficiently using PSO-based approach. The scheme has a higher success rate in terms of localization. Kulkarni et al. presented a distributed iterative localization algorithm called PSO-iterative [32,33]. For each target node, there exist more than three anchors and PSO is exploited to minimize the localization error. Kumar et al. [34] suggested localization techniques that use the concepts of HPSO and BBO by taking minimal hardware requirement, referred to as range free HPSO and BBO respectively. By using PSO and BBO applications, the edge weights are further optimized. Arora and Singh [35] suggested an optimization algorithm called BOA to optimize the location of unknown sensor nodes. PSO and FA performances in 2D scenarios are compared and contrasted with the performance of BOA. Their approach outperforms in terms of convergence time and location accuracy as compared to other metaheuristic algorithms. Due to the higher accuracy, the range-based methods are commonly used but flip ambiguity is the major drawback of range-based methods.
The method adopted to locate target nodes in 3D environment has the following benefits. issues to a greater extent. c. The problem of flip ambiguity in range-based approaches is also reduced.
In this paper, mLebTLBO has been proposed to deal with the localization concept used in WSNs. The main objective is to explore the efficiency of the mLebTLBO algorithm in 3D WSNs localization problem and to compare the performance with various other algorithms. The basic idea behind mLebTLBO is explained in the next section.

Teaching learning-based optimization (TLBO)
A relatively new metaheuristic inspired by the behaviours of the teaching and learning process in a classroom called TLBO [36]. To search good solutions TLBO exploits two creative operators, called the teacher and learning phase.
In the teacher phase, by raising the mean outcome of the classroom (x mean ) towards his/her position x teacher , the teacher attempts to improve the outcomes of other learners (x i ). To preserve stochastic search characteristics, the solution x i uses two randomly generated parameters rand and TF as: are the ith learner's current and previous positions, respectively, TF is a teacher factor, and its value may be either 1 or 2. x i,new is accepted, If it is better than x i,old , otherwise x i,old remains intact.
In the learner phase, to further enhance its efficiency, a learner x i randomly chooses other learner x j (j ≠ i) for interaction and the learning process can be expressed as follows: where f(x) is the fitness function and x j,old is the old position of the jth learner.

Learning enthusiasm based TLBO (LebTLBO)
LebTLBO is a modified version of basic TLBO. Modification in TLBO enhances search capability for an optimum solution. LebTLBO introduced two new modules one is learning enthusiasm-based teacher part and second is learner phase [12]. These are conferred to boost the search potency, to enhance the standard of the poor learners using poor student tutoring phase. In basic TLBO, every learner has the same capability of acquiring knowledge from others [36]. LebTLBO is motivated from a real-world learning enthusiasm mechanism, where every learner has different capabilities and enthusiasm to learn. LebTLBO is motivated by this learning enthusiasm mechanism.
The algorithm in its initial stage consists of a population of NP learners (where the total population is denoted by x), initialized as x max are lower and upper bound respectively. After the population initialization of learners, the fitness of each learner is evaluated. The learner with the highest fitness is termed as teacher x teacher . The details and description of different phases of the LebTLBO algorithm are discussed as follows.
Learning enthusiasm based teacher phase: LebTLBO utilizes a learning enthusiasm based model in that the students with decent evaluations have higher learning excitement, and they have an extensive likelihood of getting the information from the instructor. The students with terrible evaluations have less learning energy and little likelihood of getting the information from the educator.
In this phase, all learners are sorted depending upon their fitness value as follows: Then, the learner's learning enthusiasm value is defined as where LE max is maximum learning enthusiasm and LE min is minimum learning enthusiasm with suggested values of LE max = 1 and LE min ∈ [0.1, 0.5]. The learning enthusiasm curve is plotted in Figure 1. It is well depicted from Figure 2 that the highest learning enthusiasm is shown by the best learner, while lowest learning enthusiasm is displayed by the worst learner.
In the wake of characterizing the learning enthusiasm, depending upon learning enthusiasm value LE i every student is classified into the category of gain or learn from the instructor or not learn from the instructor. For student x i , create an irregular number r i ∈ [0, 1], if r i ≤ LE i , at that point student x i will gain from the educator; else a student x i will disregard generally the learning of the instructor. If student x i can procure the information from the instructor, it refreshes the position utilizing an assorted variety upgraded showing methodology, and the accompanying condition: Learning enthusiasm curve [12] FIGURE 2 Diversity enhanced teaching strategy [12] where r 1 , r 2 and r 3 (r 1 ≠ r 2 ≠ r 3 ≠ i ) are random integers chosen from {1, 2, …, NP}; d ∈{1, 2, …, D}; rand 1 and rand 2 are randomly generated numbers which are uniformly distributed within [0, 1]; and F is a scale factor in [0, 1]. It is well clear from Equation (6) that it may be seen as a hybrid model of TLBO and DE given by

Learning enthusiasm based learner phase
The learning strategy of the learner is also learning enthusiasm based in LebTLBO. Same as with the teaching strategy it includes higher learning enthusiasm for learners with good grades and those learners lie on high probability region for getting knowledge from others and vice versa. Based on the performance of grades all learners are sorted in the case of learning enthusiasm inspired learner phase as defined in Equation (5). A randomly generated number between r i ∈ [0, 1] for learner x i , if r i ≤ LE i , then learner x i will learn from the other learner; otherwise knowledge of the learner will be neglected by the learner x i . If learner x i obtains the knowledge from the teacher, then based on diversity enhanced teaching strategy its position will be updated as where f (x i ) is the objective function, x i,old is the previous position of the ith learner. If x i,new is fitter than x i,old then x i,new is accepted, otherwise x i,old is unchanged.

Poor student tutoring phase
This phase is not available in basic TLBO, the main motive behind this phase is to improve the grades of weak students. The same procedure is followed in this phase too based on their grades the learners are arranged in the range of best to worst. The learners are considered as a poor learner if they are in the bottom 10%. This phase will randomly choose learner x T from each poor student x i whose rank lies in the top 50% and the learning is based on the following equation.
The students having bad grades have less probability to update the position in the category of good students whereas students with good grades have relatively more probability to update their position. Poor student tutoring phase plays a keen role in the improving grades of the poor student to good student. This strategy is relevant to a real-time teaching-learning process where poor students always badly require tutorials for their improvement as compared to other good students. The pseudo-code for LebTLBO is given in Algorithm 1 as shown in the Appendix.

The proposed modified LebTLBO
LebTLBO has gained attention among researchers in the recent past due to its linear nature. The revised improved LebTLBO seeks to achieve enhanced performance by improving its basic exploration and exploitation capabilities both. Exploration has been improved by the introduction of search equations inspired from Grey wolf optimization (GWO) [13], exploitation has been enhanced by local neighbourhood search (LNS) driven by the knowledge of the finest solution so far found in the current solution's small neighbourhood [14]. The concept of LNS is discussed as follows:

Local neighbourhood search (LNS)
LebTLBO uses the current solution and local information to improve the search space in the teacher phase. The local neigh- Assume that in the current LebTLBO population X = (X 1 , X 2 , X 3 , . . ., X NP ) , X i (i ∈ [1, NP]) is a vector. The neighbourhood of radius (2r + 1 < NP) is defined for each X i vector; that is, X i neighbourhood consists of X i−r , . . ., X i , . . ., X i+r . For analysis, we assume that according to their indices, the vectors are organized into a ring topology. Figure 3 shows the local neighbourhood model concept. Therefore, the topology of the neighbourhood is static all the time and about the description of the set of vectors. The model for LNS is defined in where X n_opt is the finest solution in the X i neighbourhood and p, q ∈[i − r, i + r] (p≠q≠i), and m, n ∈ rand() are the scaling factors. The new best solution is updated according to Equation (9) in the improved version of LebTLBO, and the updated solution performs the teacher phase.
where L i is the best solution updated by LNS and X t k and X t m are two random solutions for kth and mth learner where k ≠ m and r is a scaling factor, where r ∈rand().

Modified LebTLBO (mLebTLBO)
The learning enthusiasm based teacher phase is improved in the modified LebTLBO to enhance the performance of conventional LebTLBO. This new search equation is strengthened by taking the mean from the set of learners of the first three learners. Such three solutions are created based on the best solution available termed as x teacher . The proposed equations in this respect are where A 1 , A 2 , A 3 and C 1 , C 2 , C 3 belongs to A and C respectively. A and C are given by where a is a linearly decreasing [0, 2] random number with iterations, r 1 and r 2 are two uniformly distributed random numbers. These random numbers allow the search agents to spread at any location within the search space and thus increase the LebTLBO's explorative capabilities. GWO search equations have inspired the basic idea for this change [13]. In GWO, the solution is created by adjusting the parameters to best search agent location. The same definition is used to get new solution ) otherwise (14) To strengthen the exploitation capability of LebTLBO, the local neighbourhood search (LNS) model is introduced as discussed above. In basic LebTLBO, during teacher phase, the learners update their position depending on the local information as well as their own experience.
In this case, the number of iterations is separated into two parts. For the first part of the iterations, the learning enthusiasm based learner phase equation is used, and a new search equation is added for the second half. In the improved version of LebTLBO, the new best solution is updated according to Equation (9), and the teacher phase is performed by the updated solution as where L t i is the best solution updated by LNS and r is a scaling factor, where r ∈rand(). The pseudocode of mLebTLBO is given in Algorithm 2 as shown in the Appendix.

STATISTICAL TESTING OF MODIFIED LEARNING ENTHUSIASM-BASED TLBO ALGORITHM
A set of 10 CEC 2019 benchmark functions termed as the "100-Digit Challenge" [37] is selected for the proposed modified LebTLBO evaluation. These are all scalable test functions.
where x n_opt is the best solution in the neighbourhood of x t i , and u, v ∈rand() are the scaling factors. The updated solution performs the teacher phase using LNS is given by Comparison with FPA [38], GWO [13], CS [39], FDO [40], SCA [41], TLBO [36], and LebTLBO [12] is done to check the effectiveness of its proposed variant. For every algorithm, a total of 500 iterations are performed using 30 agents. For all the algorithms under evaluation, the results are described in terms of the best, worst, mean, and std. dev. values for 30 independent runs. mLebTLBO achieves better than competitive algorithms, except in CEC06, CEC07, and CEC10 as shown in Table 1. Figure 4 displays the convergence graph and box plot of various algorithms for the different benchmark functions. It has been found that the mLebTLBO algorithm's results for function CEC01 are better in terms of the best value obtained in comparison to other algorithms. However, for the worst, average, and median values achieved, the results of TLBO are better. Most of the algorithms can find an optimal solution for function CEC02, but it is found that mLebTLBO is better for minimum standard deviation values attained. For the CEC03 function, all the algorithms achieve an almost globally optimal solution; but overall, in terms of minimum standard deviation, mLebTLBO is found to be better than other algorithms. Results of mLebTLBO are better than others in the case of CEC04 and CEC05, in terms of the best, worst, mean, and median fitness performance obtained.
Results of mLebTLBO are better than other algorithms for CEC06, in terms of the best fitness performance obtained. However, for worst, average, median and standard deviation values achieved; the results of CS are better than competitive algorithms. CS algorithm's results for function CEC07 are better in terms of all performance matric. For CEC08 and CEC09 functions, mLebTLBO is found to be better than other algorithms. mLebTLBO's results are competitive and better than others for function CEC10 in terms of the best value obtained. Figure 4 also draws the box-plot of competitive algorithms for CEC2019 benchmark functions. The box-plots here are used to measure algorithm efficiency in terms of fitness values. It can be shown that in most cases the proposed mLebTLBO algorithm is cost-effective in fitness values as their median of fitness values is lower. Therefore, their overall performance is found to be consistent with other algorithms for optimization.

SINGLE ANCHOR NODE DEPLOYMENT IN 3D WSN
In the problem based on 3D localization, we considered a single sensor node whose location is defined prior. Using the knowledge of this anchor, the locations of mobile nodes are identified that are randomly deployed in the sensor field. These nodes are divided into three separate layers with an anchor placed at the top position, and unlocated nodes are placed at the middle and bottom layers are positioned using Parasol projection as shown in Figure 5.
The anchor node transmits a beacon signal that helps the target nodes to identify themselves Figure 6. Once these target nodes drop under the range of their respective anchor, they will listen to beacon first and use this information to retrieve the RSSI information. Then using RSSI information, the Euclidean distance between target and anchor node is calculated. The pseudo code representing parasol and localization using parasol projection are described in Algorithm 3 and 4 as shown in Appendix.
The steps mentioned below are used for locating target nodes in 3D scenario: a. N numbers of target nodes are assumed for this 3D localization problem that are randomly deployed at middle layer and bottom layer of a chaotic cubic structure having three layers. On the topmost layer, a single anchor is deployed. The transmission range for both target and anchor nodes are different (i.e. variation in battery backups, radiation patter, DOI). b. Whenever a moving target node comes under the range of a particular anchor, a target node is said to be localizable. The target nodes maintain a list of their in-range anchors which contains the useful distance information. Along with an anchor node, three other virtual anchors are projected in surrounding of target node to locate itself as (minimum four anchors condition is required to locate target nodes in 3D scenario).
c. Using radio irregularity model, distance between the anchor and target node is calculated based on obtained RSSI [42] using d ∧ i = d i − (D p + F ), as d i is calculated using Equation (17). D p is DOI path loss and F represents fading.
where (x t , y t , z t ) represents the target node position for a 3D scenario. (x, y, z ) represent anchor node's current location for 3D scenario. The centroid (x c , y c , z c ) is calculated using Equation (18) for 3D scenario and is represented in Figure 7.  Figure 8 shows that proposed mLebTLBO is applied for the coordinate determination of target node represented by (x s, y s , z s, ). The objective function used in Equation (19) will minimize distance among the deployed and estimated target node coordinates.
Here,(x e , y e , z e ) represents the estimated target node position, (x i , y i , z i ) represents the location of beacon node i and estimated location of target nodes (M > 4 to compute 3D location) respectively for the 3D scenario. E t , represents error taking place in the process of localization and is calculated using Equation (20) and represented in Figure 9 for 3D scenario.

RESULTS AND DISCUSSIONS FOR 3D SCENARIO
A novel proposed mLebTLBO is applied for a 3D localization problem using the principle of deploying a single anchor and six virtual anchors presumed to be positioned in six  an anchor node, a parasol projection is formed, and the virtual anchors are assumed for determining 3D locations of target nodes. It is also theoretically possible to deploy more than six virtual anchors, but in this work, we assumed only six virtual anchors in a 3D environment for locating target nodes by selecting only four nearby anchor nodes. Various optimization algorithms are discussed below in the mobility-based scenario. Anchor node is kept fixed for all target nodes, while mobility is applied for all target nodes. The fitness function is calculated using Equation (19). The strategic settings considered for various meta-heuristic optimization algorithms is given in Table 2.
In a mobility-based scenario, various optimization algorithms are evaluated discussed above. The target nodes are deployed randomly at the bottom and middle layers, and the topmost layer is equipped with anchor node. Anchor node is kept fixed while mobility is applied for all target nodes. The fitness function is calculated using the average localization error given in Equation (16). The results of these different optimization algorithms are drawn in Figures 10-14. By using a virtual anchor concept, LoS problem is also minimized to a greater extent. From these results, it is quite clear that mLebTLBO outperforms in the context of other meta-heuristic optimization algorithms and has a faster convergence rate.
In Table 3 the average localization error is calculated for all competitive algorithms and is presented in Figure 15. The average localization error of mLebTLBO is quite less as compared to other competitive algorithms tested for the same scenario.
Algorithmic complexity can be described as the standard notions (big O notation) of computational complexity in time. That is how long a localization algorithm runs before estimating the positions of all the nodes in the network and how much memory (storage) is needed for such calculations. The time complexity of the proposed method is obtained by the following analysis. The method is built on two major components: localization and optimization algorithm.
In localization, the cost of communication is the cost incurred by the network to spread out the information about the hop size between every connected pair of the nodes. In the algorithm, each anchor node out of total anchor nodes 'm' has to inform all the target nodes 'N' of the network about its hop size FIGURE 15 Comparison of meta-heuristic algorithms to estimate localization error value. So, every node informs every other node in the network about the hop size of an anchor node. Repeatedly this controlled flooding takes place the same number of times as that of the number of anchor nodes. Therefore, the communicational cost is O(mN 2 ). Here in our algorithm, only one anchor node is considered, therefore, the overall communicational cost is O(N 2 ).
The computational complexity of mLebTLBO according to the major steps of the algorithm is given by: • For a population size of NP, the computational complexity for initialization is given by O(NP ). • After initialization, the second step is to evaluate the current population and hence the complexity is given by O(NP ). • Ranking the population and finding the current best solution has a complexity given by O(N P 2 ). • In the iterative search, the positions of existing solutions is changed continuously and their fitness is calculated as O(2NP ). • Even in the iterative search, the population is sorted and the best individual is calculated. The complexity for this operation is O(N P 2 ).
Thus, based on the above points, the total run time complexity of the mLebTLBO for G max iterations is given by Overall, the generalized run time complexity of the mLebTLBO for a D-dimensional search space is then given by DG max (O(N P 2 + 2NP )).
Therefore, we can say that the time complexity of localization algorithm using mLebTLBO algorithm is O(N 2 ) + DG max (O(N P 2 + 2NP )).

CONCLUSIONS
The range-based technique along with the proposed mLebTLBO optimization technique was used in this research to obtain 3D target node coordinates using the concept of a single anchor node. The concept of anchor and virtual anchor node forms a parasol projection to locate all target nodes. Whenever the moving targets fall within the anchor node; three virtual anchors and anchor itself operate together to locate the target nodes (as to obtain 3D locations at least 4 nodes are required). There are various applications like logistics, underwater scenario, localization of occurring events in remote and hilly areas, and tracking of workers in the coal mine industry where localization of sensor nodes is essential. The proposed mLebTLBO algorithm performs in comparison with other competitive algorithms to estimate node location precisely. The results achieved show the accuracy of mLebTLBO is higher and it has faster convergence characteristics. One can implement another hybrid optimization approach in the future to achieve better accuracy and faster convergence. Generate a random r i in [0, 1]

22
if r i ≤ LE i 23 Update learner x i according to equation