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Wiring and re-configurability of systems are two major problems with wired sensor network. Thus Wireless Sensor networks (WSN) have attracted great interests due to its extendable capability. The limitation with WSN is their limited source of energy (as they are composed by battery supplied nodes), issue of the coverage constraint and the reliability of network. In most of the current designs due to simplicity, sensors nodes are randomly or uniformly distributed. But a planned node deployment strategy provides great benefit over random or uniform node deployment. In this paper, we consider a general WSN with node transmitting information to the sink using shortest connecting path. The best sensor node deployment depends upon the trade-off between the four main objectives: coverage area, lifetime of the network, energy utilization of the network and the reliability of the network. Thus we optimize these four objectives in the placement of sensor nodes. Floyd-Warshall algorithm has been used for the construction of the spanning tree. A sorted (r, theta) representation of the problem has been used by the Genetic algorithm that provides better optimization. The algorithm also accounts for total number of sensors placed in the set region. Experimental results show that we have been effectively able to optimize the objectives in a finite time.


From the last few years there is a growth in the interest of the WSN designers in the field of efficient sensor node deployment to sense, gather and process the data. Efficient deployment of sensor node has a great impact on the energy consumption in the nodes. The areas of application of sensor networks vary from military use to environmental monitoring (measuring temperature, humidity, soil moisture and solar radiation etc.) and from wildlife to disaster management.

According to the available literature [1, 2, 3] based on a survey on deployment of the sensor nodes, the problem seems to be still open. Among many other challenges, in this paper we gave a solution of a basic and practical problem that how we should deploy these sensor nodes. In most of the current designs due to simplicity, sensors nodes are randomly or uniformly distributed. But random or uniform distribution of sensor nodes is not well as this will lead to the Sink routing-hole problem. Sink routing-hole problem:

In WSN, sensor nodes transmit the data to the sink via multiple hops. Thus a node that is nearer to the sink usually has to transmit more data than those nodes that are farther to the sink (as it has to forward the data sense by the farther nodes as well as transmit the data sense by itself). This leads the failure of nodes closer the sink at the very beginning because of more energy consumption. This raises the issue of connectivity between the nodes in the network [4].

Whenever WSN designers design WSN they have to think about some considerations that one has to take into account. The first one is the number of sensor nodes one can afford to cover the area since wireless

sensors are still expensive. The other constraints are the energy utilization of network, life time of the WSN and reliability of network which depends on the power used by the nodes to transmit their data to the given distance. Thus we suggest a genetic algorithm based method to optimize the sensor network layout. There are two ways to optimize the sensor network layout:

  1. Find the minimum number of sensor nodes to achieve coverage, maximum utilization of network energy, reliability, and a good life time.
  2. For a0 fix number of sensor nodes, find out a set of points and the power levels which give the best trade-off between Coverage area, lifetime of the network, energy utilization of the network, and the reliability of the network.

In our work, we use the combination of these strategies. We first start with second approach and then incorporate the first approach in it.

This paper is organized as follows. In Section (2), we give a review of some related work. Problem and objective function for the optimal deployment is given in Section (3). In Section (4), we discuss the GA based solution to this multi-objective optimization (MOO) problem. The simulation and the results are shown in Section (5). At the last in section (6), conclusion of our work and future work is given.

2. Related Work:

The work done in this field can be categorized into two broad fields: Coverage area optimization for sensors nodes and increasing the lifetime of sensor nodes and network.

Existing sensing coverage algorithms do not consider the impact of differential loss of energy. They may be work well initially, but will lose their functionality very soon. Sensing coverage algorithms can be categorized as: location-dependent [5, 6 and 7] and location-free approaches [8 and 9]

Wang et al and Sankar et al [10 and 11] focused on the management of data transfer by considering some optimization purposes. Switching off their transceivers and transfer them to sleep mode, most of the existing power-conservation schemes [12, 13 and 14] attempt to conserve energy of idle nodes.

Tarik Yardibi et al [15] developed the distributed adaptive sleep scheduling algorithm (DASSA) for WSNs with partial coverage. DASSA does not require location information of sensors while maintaining connectivity and satisfying a user defined coverage target. In DASSA, nodes use the residual energy levels and feedback from the sink for scheduling the activity of their neighbors.

Leonardo Barboni et al [16] propose a heuristic algorithm for network deployment for single route. The algorithm predicts number of nodes, nodes distances and nodes output power level in order to give a deployment that reaches maximum battery lifetime and compliant with user specifications for a given distance. A. Bogdanov et al [17] proposed the deployment of sinks in a scenario of multiple sinks. Qingguo Zhang et al [18] proposed a genetic algorithm based localization (GAL). The proposed genetic algorithm adopts two new genetic operators: single-vertex-neighborhood mutation and the descend-based arithmetic crossover. When some node fails or lost from sensing area J. Wu et al and G. Wang et al [19 and 20] suggested relocating mobile sensors to some other appropriate locations. Authors of SOGA propose a reduced-complexity genetic algorithm for optimization of multi-hop sensor networks. The goal of the system is to generate optimal number of sensor clusters with cluster-heads.

3. Problem and Objective functions:

As sensor nodes transmit the data to the sink via multiple hops, Inner node has to transmit data packet sense by itself as well as data packet that arrives from the farther nodes. Suppose is the life time of nodes where N is the number of nodes. We have to maximize min of them.


For that we can choose any power level available for any of node (one node can use only one power level at a time) but we also have to take care that sum of the transmitting ranges (depends upon the power level which we choose) of nodes between source and destination should be greater than distance between source & destination as per the given equation. If a path from source to destination uses n hops then according to the equation

Sum of the transmitting Distance between

Ranges of nodes in the ≥ source &

Route destination

Where is the transmitting range of ith node and are the transmitting range of the nodes that lies on the route to sink.

Deployment of nodes contain array of the location of nodes where sensors are placed. There are some distinct output power levels in each node (say where n is the maximum number of power levels for any node). The transmitting distance (say ) of any node depends upon the output power level which it used. If the distance between the nodes is d and the radio coverage of node is then d must be less than or equal to for communication between the nodes. So distance between any two nodes can take max value . We can achieve best coverage by minimizing the distance between sensors and sink node and maximizing the distance between the sensor nodes.

Consider two circles of radius and centered at A and B respectively. Let C and D be the intersecting points. The circles have been shown in figure 2. The coverage of a single sensor node is given by equation

The overlap area between two circles is given by equation

Equation (5) gives the total area covered by all nodes

Fig.2 Over-lapping coverage area of two nodes

Where angle can be represented in the form of distance d between the two nodes and given by

A generalized version of equation (5) may be used to calculate the total coverage area for multiple intersections. To calculate the coverage area of the sensor nodes we take help of Voronoi diagram[23]. A Voronoi diagram is a special kind of subdivision or decomposition of space determined by distances to a specified discrete set of objects. In the plane, set of points S (Voronoi sites) are given. Each site S has a Voronoi cell V(s) consisting of all points nearer to S than to any other point. All the sites in the plane that are equidistant to the two closest points are called the boundary of Voronoi cell. In our work, we used following steps to calculate the coverage area.

* Each node is considered as a Voronoi site.

* Make the Voronoi diagram: we take intersecting lines between the coverage circles of nodes to make the Voronoi cell.

* Calculate the intersecting area of Voronoi cell with the coverage area of respective node.

* Take the sum of all that areas.

During the lifetime () the sensor node either sense the data or forward it to the next node or sink. Each node when receive or transmit the data uses power from the battery.

(The region between the dark lines represents voronoi cell)

As power is fixed in battery so when battery is discharged the node is considered as dead. Packet/data route from source to destination with use of hops (nodes) between them. Death of any node in the network is considered as a death of network because when a node in a route is dead it can't able to transmit further. So it is possible that data packet chooses path in which a node between source and destination is dead.

If is the energy used by node i for transmitting data packet, (constant) is the energy used for sensing and processing and each node transmit an l-bit message over distance d then

Where is constant of the amount of energy consumed during signal amplification in the amplifier and is constant of the amount of energy consumed when data are converted into radio frequency or from radio frequency and do is constant.

If during the lifetime if node transmitted n number of messages then whole amount of consumed energy duringlifetime of node i is given by equation

Where j is the index of node from the farther end of the path belonging node i and the sink.

If initial energy of the node is then node dies when total energy consumed by node is equal to the initial energy of node.

The node is sleeping and periodically wakes up for the transmission of the data packet. If the node wakes up for the time period of Ta for transferring a data packet and transfer total n data packets during his life time then

From equation (11) & (12) we have

If there are N number of nodes in the network then the total initial Energy is .

For a relatively small target area where the farthest node is 5 hops away to the sink, less than 8% of the energy is consumed before the system is down. With the size of application area increased, the problem becomes more serious. For a field with a maximum of 35 hops, when the network fails, only 2% of energy has been spent [4]. Thus the random and uniform distribution functions are not suitable for sensor node deployment.

By using path loss models to estimate the received signal level as a function of distance, it become possible to predict the SNR. Log-Normal Shadowing is the most used radio propagation model in WSN application. Measurements have shown that at any value of d, the path loss PL(d) at particular location is random and distributed log normally(normal in DB) about the mean distance dependent value. That is


Where n is the path loss exponent which indicates the rate at which the path loss increases with distance, do is the close-in reference distance which is determined from measurements close to the transmitter, d is the T-R separation distance, represents the expected signal strength (in dBm) at the receiver placed at distance d (in meters) from the transmitter which delivers as output power (in dBm) and is zero mean Gaussian distributed random variable (in dB) with standard deviation σ (also in dB). Antenna gains included in channel attenuation .

For receiving the signal or data packet it is necessary that the SNR is greater than its threshold value. Probability of successfully receiving the data packets or signals is given by

4. Genetic Algorithm:

Genetic algorithms became popular through the work of John Holland in the early 1970s [ref]. Genetic algorithms are inspired by Darwin's theory of evolution. Algorithm is started with a set of solutions (represented by chromosomes) calledpopulation. Solutions from one population are taken and used to form a new population. The next step is to select from this population the fittest individuals, and from them, get new individuals by crossover and mutation. This process runs iteratively. After each generation, the surviving individuals become fitter and fitter.

4.1 Individual representation and selection: The chromosome should in some way contain information about solution which it represents. In this algorithm every individual is a collection of sensors <S1, S2, S3, … SN>. Every sensor i stores its location (ri, θi), power level (Pi) and a number Di. The sensor is deployed if Di is 1 and not deployed if Di is 0. Here we assume that the maximum number of sensors to be N. We place an additional constraint over the individual that the sensors are always sorted by their θi values. Floyd-Warshall algorithm has been used for the construction of the spanning tree. The population costs and associated chromosomes are ranked from lowest to highest cost and the best are selected to continue, the others are deleted. The algorithm uses rank based fitness scaling and stochastic uniform selection in each generation or iteration of the algorithm.

Crossover: Crossover is a genetic operator that combines two chromosomes (parents) to produce a new chromosome (offspring). Basic idea behind crossover is that the new chromosome may be better than both of the parents if it takes the best characteristics from each of the parents. In this algorithm we use scattered crossover. This operator randomly selects some crossover points within a chromosome then interchanges the two parent chromosomes at those points to produce two new offspring. Re-sorting of the child chromosome is applied after the crossover.

Mutation: It is responsible of new traits appearing within population by random alteration of an individual's code. Mutation is a genetic operator that alters one or more gene values in a chromosome from its initial state. The mutation can make an individual fitter or not. If it is fit enough he will pass to the next generation otherwise he would disappear from the population at the next generation. Mutation is an important part of the genetic search as it helps to prevent the population from convergence at local optima. Re-sorting of the mutated chromosome is applied after the mutation operation.

Cost functions and fitness: The cost functions or objectives are mathematical expressions of what we want to optimize. On the basis of them the fitness of chromosomes are evaluated. Therefore, if a chromosome brings the fitness evaluation to a value closer to the optimal point than the others, that chromosome is said to be the fittest. When there is more than one objective, to measure the global fitness, we can use a sum of weighted normalized cost functions. This approach transforms the MOO problem to a single objective optimization problem. This way of simplifying the problem is straightforward because it is easy to implement.

Having described the design parameters we formalize our fitness function as:

Here is the lifetime of the node which has minimum lifetime. is the lifetime of the ith node given by equation (13)

EC is the total energy consumed as described by equation (10)

A is the total coverage area of all nodes as discussed in section 3 S is the total number of sensors used

are multi-objective weights.

It may be noted that the coefficients have negative signs to convert the whole problem into minimizing problem.

5. Simulation and Result:

We conducted experiments to get useful results as a solution to this MOO problem of WSN layout optimization problem. We implemented a simple genetic algorithm based on the weighted sum of cost functions to find out the optimal points. All simulations were made on a simulated environment. We assume a circular grid of radius 300m. The nodes can be placed anywhere inside this grid. We further assume that there can be maximum of 50 nodes in the region. Each node has 8 power levels. MATLAB and Qualnet were used for the simulations. The genetic algorithm parameters were 250 for number of generations, 0.50 for the selection rate and 0.03 for the mutation rate, and size of population is 150 individuals or chromosomes.

Environment dependent parameters are the main problem in achieving high probability for successfully receiving the data packets or signals. For connected region [21], it is assumed that Probability of successfully receiving the data packets or signals P must be greater than or equal to 90%. Any network that has probability less than 90% is considered as an unreliable link[16].

In our simulation, we take these values to get results. The value of output power level (Pt) of the radio transceiver and corresponding transmitting range (d) is given in table 1. For these given power levels we got these boundaries from the Qualnet simulator for model 802.11b with data rate 2.0 Mbps.

TABLE 1 (Output power level (Pt) of the radio transceiver and corresponding transmitting range (D) )


D (m)

















Value of weighted coefficient of the fitness function is given in table 2.

TABLE 2 (Value of weighted coefficient of the fitness function)
Parameter Coefficient Value

Life Time of Node


Energy Consumed


Coverage Area


No. of Nodes


Figure 4(a) shows the best and the mean fitness values of the population. Figure 4(b) shows the best, mean and worst fitness values. Figure 4(b) shows the sudden emergence of some infeasible individuals which eventually die out in the next generations. This is because of the constraint that the nodes need to be placed in such a manner that the transmission node for every sender node must be large enough to cover the center of the next receiving node. A loss of this constraint by genetic optimization in any generation results in a loss of connectivity between nodes and the solution is regarded as infeasible by assigning it the highest fitness.

Fig 5 shows the layout which represents the trade off among the preferences. As the distance from the sink increases the number of nodes in that region decreases. The coverage objective tries to put the nodes far whereas the energy objective tries to put them closer. So there is a tradeoff between them maintained by the multi-objective weights.

Fig 6 shows the coverage regions of different nodes. As the distance from the sink increases the nodes uses higher power levels to save energy. The nodes with lower power levels basically provide connectivity so that every node has a path to the sink.

6. Conclusion:

In this study, we solve the multi-objective optimization problem of wireless sensor node deployment with the help of genetic algorithm. In our work, we consider the following factors coverage area, lifetime of the network, energy utilization of the network, and the reliability of the network along with the Sink Routing Hole Problem. Different parameters values and weights are implemented to test the convergence properties and robustness. Several tests were conducted in order to assure that the deployment solution is the optimal.

For future work one can go for more complex area that doesn't has regular shape. The presence of multiple sink may be modeled as well. The issue of more coverage area with better connectivity is still an open problem. The Genetic algorithm approach optimizes the Sensor network layout to provide optimal objective value along with high coverage. The high and variable number of sensors makes the genetic search space highly complex. Hybrid methods may be used to better explore the fitness landscape in search of the global minima at the same time maintaining a tradeoff between optimality and time.

Article name: Node-deployment essay, research paper, dissertation