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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

One of the most critical issues of Wireless Sensor Networks (WSNs) is the deployment of a limited number of sensors in order to achieve maximum coverage on a terrain. The optimal sensor deployment which enables one to minimize the consumed energy, communication time and manpower for the maintenance of the network has attracted interest with the increased number of studies conducted on the subject in the last decade. Most of the studies in the literature today are proposed for two dimensional (2D) surfaces; however, real world sensor deployments often arise on three dimensional (3D) environments. In this paper, a guided wavelet transform (WT) based deployment strategy (WTDS) for 3D terrains, in which the sensor movements are carried out within the mutation phase of the genetic algorithms (GAs) is proposed. The proposed algorithm aims to maximize the Quality of Coverage (QoC) of a WSN via deploying a limited number of sensors on a 3D surface by utilizing a probabilistic sensing model and the Bresenham's line of sight (LOS) algorithm. In addition, the method followed in this paper is novel to the literature and the performance of the proposed algorithm is compared with the Delaunay Triangulation (DT) method as well as a standard genetic algorithm based method and the results reveal that the proposed method is a more powerful and more successful method for sensor deployment on 3D terrains.

Optimal sensor deployment on 3D terrains is the problem of placing the sensors at the most appropriate spots in order to maximize coverage of a wireless sensor network (WSN). WSNs have a key role in today's data acquisition networks where the sensors of a WSN are deployed on environments for detection and surveillance purposes. The sensors can vary from fire detectors, seismographs, cameras to vital sign sensors on soldiers in a battlefield and data gathered from the sensors is usually sank into a base station which is connected to a network backbone [

Sensor deployment can either be stochastic or deterministic. In a stochastic deployment method, sensors are randomly deployed with a normal distribution scheme. However this is far from being effective because random deployment may cause sensors to be centralized or to be blocked by terrain features causing non line of sight (LOS) sensor spots. Hence this will ultimately decrease the probability of detection and sensing in the environment. With a deterministic method, sensors are deployed according to a predefined constraint such as; predetermined priority-regions on a field are equipped with more sensors in order to maximize the QoC. However, when the number of sensors is limited there will be coverage holes. Although both methods have their own advantages and disadvantages, they both fail to provide solutions to the problem of determination of the location coordinates of a predefined number of sensors which maximizes the coverage within a predefined 3D terrain. This is a kind of an NP-hard Minimum Set Cover (MSC) problem where the decision space grows exponentially with wider terrains. For example, within a map size of 1,024 × 1,024 pixels, there are 2^{20} possible sensor locations. With 128 sensors, there are [2^{20} (2^{20}-1) (2^{20}-2)….. (2^{20}-127)] possible sensor deployment schemes. Thus, the huge decision space necessitates a heuristic search algorithm.

As a search algorithm, an elitist and a steady state genetic algorithm (GA) have been utilized to track the optimal placement schemes of sensors on a 3D region. The GA is an optimization technique which is based on an adaptive mechanism of biological systems [

In this paper, first two deployment strategies are investigated

Moreover, most of the sensor deployment algorithms in the literature deal with two-dimensional (2D) zones and do not propose strategies to handle coverage in three-dimensional domains, which is more realistic and a requirement for both civilian and military applications. The deployment of sensors to achieve desired QoC levels is basically more challenging on 3D terrains compared to 2D terrains. In 3D environments, a LOS algorithm is needed in order to determine whether a point on the terrain is blocked by any obstacle or not, thus the complexity of the problem increases. In this paper, Bresenham's LOS algorithm has been employed owing to its faster computation, in the sense that it does not require interpolation calculations and requires less number of calculation points [

The paper is organized as follows: In Section 2, related work on sensor deployment methods which are developed for 3D terrains is reviewed. In Section 3, some preliminaries and problem model are presented and in Section 4, the proposed algorithm is explained and performance evaluations are presented. The paper is concluded in Section 5.

The studies on sensor deployment, especially for 3D terrains, usually take into account that the number of the sensors is constant. With a given number of sensors, the goal is to achieve maximum sensor coverage, thus maximum network utilization, minimum energy consumption or both.

Wang

There are various deterministic sensor deployment examples in the literature. One of the most successful deployment methods is to place each sensor in the middle of a Delaunay triangulation or the middle of Voronoi polygons of sensor coordinates [

Moreover, there are various heuristic deployment strategies in the literature. For example, in [

In this paper, in order to mitigate the coverage holes after the initial deployment of a number of sensors, a wavelet transformation based mutation operator is utilized, which effectively gives better coverage results. Also, as stated above, most of the studies on sensor deployment problem take into account 2D terrains which is not sufficiently accurate for outdoor applications whereas in this study different types of 3D terrains ranging from rough and undulating ones to smooth ones are considered. Also according to the literature mentioned above, we apply more real-world-like input factors such as sensor coverage capabilities, terrain and sensor features,

The primary objective of this study is to maximize the overall QoC of a WSN when deploying a specific number of sensors on a 3D surface. Some GA approaches are empirically tested for the search of an optimal deployment scheme. By starting with the same initial population the search performance of an S-GA and an SS-GA have been evaluated. In this section, firstly the problem model and preliminaries are given, secondly the results for two widely used deployment methods are shown and lastly the proposed deployment algorithm is presented.

In order to make fair comparisons and evaluate the performance of the deployment methods, the algorithms are run with the same parameters such as the interested terrain, the sensor types, coverage calculation algorithm, LOS algorithm, initial population

The sensor deployment is a challenging task, in the sense that different terrains (and also sub-regions of a terrain) may exhibit coverage holes after an initial deployment scheme. In this study, three different 3D terrain types are used,

The problem takes into account a terrain which is denoted as _{n}_{n}_{s}_{i}_{s}_{e}_{s}_{e}_{s}_{e}_{s}_{e}^{®} notation). As it can be seen in _{i}_{s}_{s}_{e}_{s}_{e}

The sensing model utilized in this study is a probabilistic model which allows a realistic modeling of sensor coverage probability [_{r}_{r}_{r}_{r}_{r}_{r}_{r}_{r}_{r}_{r}^{β})_{r}_{r}

The sensing probability _{q}(s,p)

The overall map of sensing probabilities of each location constitutes the so-called QoC matrix. The values of

Wavelets, which are used for representing data or other functions, group data into various frequency components to work on each component separately at each scale. Compared to traditional transformation methods, wavelet analysis has advantages in analyzing physical situations, especially when the signal contains discontinuities and sharp spikes [

Two-dimensional implementation of the discrete wavelet transform (DWT) is commonly used in image-processing applications. The DWT provide spatial (or temporal) and frequency information (

Any two dimensional signal _{φ}_{0}, _{0}_{j0,m,n} are the scaling functions;
_{0} and ^{i}_{j,m,n}_{φ}_{0},^{i}_{ψ}_{φ}_{0},

In this study, the overall QoC is regarded as a measure of signal level provided by the neighboring sensors in each location (pixel). In order to determine the coverage holes in a sub-region we take the DWT of the sub-QoC matrix. The minimum value in the resulting approximation matrix of the wavelet transform gives the least energy bearing pixel point which corresponds to an area in the sub-region. This fact is used to relocate the sensor by moving it towards the least covered region.

In random deployment, N sensors are scattered onto random coordinates of the terrain and the correspondent QoC is evaluated with the probabilistic sensing model. At each iteration, the coverage value and the sensor positions are recorded. This scheme is repeated several times and the QoC value is determined by taking the average. Although a Gaussian distribution can enable equally distributed sensors in a region, random deployment is far from being an optimal solution.

The second deployment method which is evaluated in this paper is the Delaunay Triangulation (DT) based approach. The DT-Score algorithm proposed in [

In

The GA is proven to be a robust and optimal search technique for various applications since it was first proposed by Holland [

An alternative to a traditional S-GA approach is to use a SS-GA approach, where there is only one new (the fittest) child inserted into the new population at any generation. The idea is to iteratively produce a new child (or two), calculate their fitness, and then reintroduce them directly into the population itself, killing off some preexisting individuals to make room for them. The SS-GA has two important features. First, it uses less memory than S-GA because there is only one population at a time. Second, it is fairly exploitative compared to a traditional approach: the parents stay around in the population, potentially for a very long time. This problem can also be tackled with applying an appropriate mutation scheme.

In this study, it is shown that S-GA and SS-GA methods produce better and more satisfying sensor deployment schemes. For both methods, integer representations of sensor pixel positions are used. As shown in

The fitness function evaluates how well each parent (deployment of N sensors) covers the terrain. In other words, while each sensor has predefined coverage parameters, each sensor has an amount of coverage within a circle in its periphery. As stated in Section 3.1, if the sensed pixel p, is within the sensing range, _{r}_{r}_{r}_{r}_{r}^{β})_{r}_{r}_{q}(s,p)

In this study we have utilized the

In this method, a random crossover index _{c}

The mutation operator in our study is based on moving a sensor to a new pixel position within its sub-region. Two deployment strategies arise in our study: a simple deployment strategy (SDS) (random walk mutation) and a WT based deployment strategy (WTDS) (guided walk mutation). The SDS is straightforward that if the sensor is to be mutated, it is put to a randomly new pixel position that is within its periphery. The decision that a sensor will be mutated is given with a comparison of a constant _{m}_{m}_{m}

In WTDS, the next position of the sensor is determined with the help of WT. When a sensor is to be mutated, each sensor is moved to a new pixel position which bears an attractive force to change the current position of the sensor within the sub-region. The attractive force is estimated in two different ways,

In

As stated above, in order to maximize the quality of coverage within a given terrain and a constant number of sensors, numerous versions of GAs are examined in order to find optimal sensor deployment schemes. We have come experimentally to the decision that S-GA and SS-GA methods with a population size of 20 raise more effective solutions than any other GA methods. Roulette wheel selection and an elitist approach are followed in order to sustain the best population of individuals.

Moreover, in order to evaluate the performance of the proposed mutation method, it is compared with a simple deployment strategy (SDS). In SDS, the mutation is realized by assigning a sensor to a new random pixel position within its periphery (1 to 5 pixels). On the other hand with the proposed WT based deployment strategy (WTDS), the sensor to be mutated is guided to a new pixel position which is determined by finding the least energy levels in its sub-region or in its surrounding region. Ultimately, the performances of six different methods which are listed in

In

After detecting that a fully elitist GA approach results in convergence problems, a steady state approach is pursued both with SDS and WTDS based mutations where at each iteration, only the best child replaces the worst parent in the population. As shown in

In our application, we have taken the sensor height from the ground, S_{h}_{r}

As stated in Section 1 and Section 2, the optimal sensor deployment problem has NP-Hard complexity which necessitates heuristic approaches to be used. Although there are interesting and successful deployment methods, the Simulated Annealing [

In this study we utilized different types of GAs and determined the coverage holes with WT which is a novel technique for this application. A drawback in our approach is that, the coverage and LOS calculations for 3D environments are more complex and computational time increases for larger terrains. Also our work aims to deploy stationary sensors. Evaluation of our method for dynamic environments and mobile sensors is an open issue. In addition, bio-inspired models have proven to be useful for solving deployment problems [

The deployment of limited number of sensors on 3D terrains to achieve maximum sensor coverage is a non-trivial task and studies of deploying in 2D environments are extensive, but methods for 3D environments are scarce. In the scope of this paper, we have focused on searching for optimal solutions with GAs. A wavelet transform-based guided walk mutation algorithm has been proposed in order to maximize the QoC levels. The performance results reveal that the proposed algorithms outperform the random deployment, the DT based deployment and the standard GA deploymentapproaches. Among the two approaches proposed for the mutation phase, the one which does not restrict more than one sensor deployment in a sub-region provides better QoC.

This study represents a novel and robust sensor deployment approach on 3D terrains for static sensors. Finding optimal solutions of sensor coverage for the sensors that can be placed at different heights on a mobile platform and equipped with communication facilities will be the next step.

The authors would like to thank the anonymous reviewers for their invaluable suggestions, especially for their contributions to the proposed mutation approaches.

Examples of terrain types used in this study. (

The terrain, sub-regions, and pixel coordinate notations.

Determination of LOS between a sensor and a phenomena.

The analysis filterbank for 2D fast wavelet transform for one-level decomposition.

Voronoi regions and corresponding Delaunay triangulation.

QoC results for random deployment strategy and Delaunay triangulation strategy.

Individual representation of sensor deployment.

Process of WTDS with guided walk mutation (

Comparison of the proposed methods (

Final deployment results of WTDS-SGA method (

Summary of parameters.

Map length | 64 | |

Number of sensors | 64 | |

_{r} |
Sensing range | 6 |

_{r} |
Uncertainty sensing range | 1 |

Environmental characteristics | 0.8 and 0.4 | |

_{c} |
Crossover point | 14 to 54 |

_{m} |
Mutation probability | 0.1 |

_{size} |
Population size | 20 |

_{h} |
Sensor Height | on Surface |

Evaluated GA methods.

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SDS-GA | Simple sensor deployment strategy with a standard genetic algorithm approach | 20 children born in each generation. 20 best are selected for the next population. Mutations are totally random. |

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WTDS1-GA | Wavelet transformation based sensor deployment strategy with a standard genetic algorithm approach | 20 children born in each generation. 20 best are selected for the next population. Mutations are WT guided. The location of a mutated sensor is in its current sub-region. |

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WTDS2-GA | Wavelet transformation based sensor deployment strategy with a standard genetic algorithm approach | 20 children born in each generation. 20 best are selected for the next population. Mutations are WT guided. The new sensor location may move to another sub-region after the mutation. |

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SDS-SGA | Simple sensor deployment strategy with a steady state genetic algorithm approach | 20 children born in each generation. Best child replaces worst parent. |

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WTDS1-SGA | Wavelet transformation based sensor deployment strategy with a steady state genetic algorithm approach | 20 children born in each generation. Best child replaces worst parent. |

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WTDS2-SGA | Wavelet transformation based sensor deployment strategy with a steady state genetic algorithm approach | 20 children born in each generation. Best child replaces worst parent. |