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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/).

As a promising tool for monitoring the physical world, directional sensor networks (DSNs) consisting of a large number of directional sensors are attracting increasing attention. As directional sensors in DSNs have limited battery power and restricted angles of sensing range, maximizing the network lifetime while monitoring all the targets in a given area remains a challenge. A major technique to conserve the energy of directional sensors is to use a node wake-up scheduling protocol by which some sensors remain active to provide sensing services, while the others are inactive to conserve their energy. In this paper, we first address a Maximum Set Covers for DSNs (MSCD) problem, which is known to be NP-complete, and present a greedy algorithm-based target coverage scheduling scheme that can solve this problem by heuristics. This scheme is used as a baseline for comparison. We then propose a target coverage scheduling scheme based on a genetic algorithm that can find the optimal cover sets to extend the network lifetime while monitoring all targets by the evolutionary global search technique. To verify and evaluate these schemes, we conducted simulations and showed that the schemes can contribute to extending the network lifetime. Simulation results indicated that the genetic algorithm-based scheduling scheme had better performance than the greedy algorithm-based scheme in terms of maximizing network lifetime.

Wireless sensor networks (WSNs) have been employed in various fields such as environmental monitoring, battlefield surveillance, smart spaces,

For the target coverage problem, it is essential that sensors monitor all the targets continuously for as long as possible. Each sensor has a limited battery. Once sensors are randomly scattered, it is hardly possible to replace or recharge their battery [

Many attempts have been made to maximize network lifetime based on node wake-up scheduling protocols. In particular, these studies have assumed that WSNs have omnidirectional sensors, each of which can sense an omnidirectional range at each instance [

In this paper, we discuss the problem of target coverage scheduling in DSNs whose directional sensors have limited battery capacity and are randomly deployed to cover all targets. The connectivity issue of the deployed directional sensors is not considered in solving this problem. Instead, we assume that there are mobile robots to move to each fixed sensor and collect the sensed data [

The rest of this paper is organized as follows. Section 2 provides the related work on target coverage scheduling in wireless sensor networks. In Section 3, we formally define the MSCD problem. A target coverage scheduling scheme based on a greedy algorithm to solve the problem is also presented in this section. In Section 4, we propose another target coverage scheduling scheme based on a genetic algorithm. This section also provides detailed descriptions of our genetic algorithm. In Section 5, we present the performance evaluation of these schemes with simulations. Section 6 concludes the paper. This paper is an updated and extended version of [

The concept of target coverage is a fundamental measure of the quality of service (QoS) of the sensing function. The goal is to have each target in the physical space of interest within the sensing range of at least one sensor. A survey on target coverage problems in wireless sensor networks is presented in [

However, above related work discussed only the target coverage problem under the WSNs in which sensors have omnidirectional sensing ranges. Directional sensors differ from omnidirectional sensors in that the coverage region of a sensor is determined by both its location and orientation. Therefore, the target coverage problem aiming at directional sensors will be more complicated than that focusing on omnidirectional sensors. This paper is an extension of the MSC problem addressed in [

In summary, our work differs from previous studies in several ways. First, the MSCD problem for target coverage in DSNs is formulated. Second, we also present a heuristic solution with the greedy algorithm for the MSCD problem. Moreover, a global search solution with genetic algorithms is designed to find more cover sets than the heuristic solution. Finally, in the design process of genetic algorithms, we use diverse genetic operations suitable for the MSCD problem, such as a two-dimensional representation method that can encode candidate cover sets into chromosomes, two types of crossover operators (for inter-cover sets and intra-cover sets) that can efficiently search global optimum to solve the MSCD problem, a mutation operator that can tune the orientations of directional sensors in DSNs, and a fitness function that can lead to finding as many cover sets as possible and, at the same time, exhausting the residual energy of directional sensors completely until the network lifetime is extended maximally. There are no reports yet, to the best of our knowledge, about a target coverage scheduling scheme based on genetic algorithms for extending the network lifetime while monitoring all targets in DSNs.

In this section, we define the Maximum Set Covers for DSNs (MSCD) problem and present a greedy algorithm to solve the problem.

Let us consider a DSN composed of _{1},_{2},…,_{N}_{1},_{2},…,_{M}

_{i,j}_{i}_{i}

_{i,j}

_{k}_{k}_{k}_{k}

_{m}_{m}

_{i}_{i}_{i}

_{k}_{k}

Before formally formulating the target coverage problem in DSNs, we illustrate an example of a DSN in which three directional sensors with three directions can cover five targets. In _{m}_{i}_{i,j}_{i}_{1,1},_{1,2},_{1,3},_{2,1},_{2,2},_{2,3},_{3,1},_{3,2},_{3,3}}. A target can be monitored only when it is within the sensing range of at least one directional sensor. _{1} = {_{3,3}}, _{2} = {_{1,1}}, _{3} = {_{2,3}}, _{4} = {_{2,3}} and _{5} = {_{1,1}}. From this figure, we can know that {_{2},_{5}}, {_{3},_{4}}, and {_{1}} are monitored simultaneously by _{1}, _{2} and _{3} (more specifically by _{1,1}, _{2,3} and _{3,3}). Therefore, {_{1,1},_{2,3},_{3,3}} can represent a cover set. If two directions in _{1} and _{3}, _{1,1} and _{3,3}, are switched to _{1,2} and _{3,1}, respectively, we can obtain a new cover set. _{1,2},_{2,3},_{3,1}}.

The main objective of this paper is to maximize the network lifetime of a DSN. After all sensors are randomly scattered to monitor all the targets in a given target area, they have a fixed location. Without loss of generality, we can assume that all sensors have equal-number of directions and initially the same battery power. Then, the directions of sensors can belong to multiple cover sets, each of which has a different active time (_{k}

We organize the directions in _{i,j}_{i}_{i}_{i,j,k}

We define the

_{i}_{i}

_{c}_{c}

_{c}_{s,t}_{i,j,c}_{i,j}_{i,j}_{c}_{s,t}_{s}

_{s,t}_{k}_{i}

_{s,t}

_{k}_{k}

In Step 3, the concept of the critical target is used as a criterion of target selection. The critical target is defined as the target covered by least number of sensors. More importantly, it is a bottleneck in the view point of network lifetime;

We use the same value of _{i}_{1,1},_{2,3},_{3,2}} and _{j}_{1,1}, _{2,3}, _{3,2}}, for _{1,1},_{2,3},_{3,2}} is used for schedule and its active time is

So far, we have described the greedy algorithm-based target coverage scheduling scheme to solve the MSCD problem. Even if this scheme can find the cover sets to maximize the network lifetime of a DSN in real time, its performance is extremely sensitive to how close an initial candidate is to an optimal solution. Thus, the scheme can lead to a local minimum solution due to its heuristic search. A more sophisticated method to solve the MSCD problem is required. In the next section, we will propose a genetic algorithm-based target coverage scheduling scheme that can find the optimal solution to the MSCD problem by evolutionary global search. In this paper, the greedy algorithm-based scheme will be used as a baseline for comparison.

This section presents a genetic algorithm-based target coverage scheduling scheme that can solve the MSCD problem. After describing an overview of genetic algorithms, we present a detailed model of our genetic algorithm to find an optimal solution for extending the network lifetime of a DSN.

Genetic algorithms have attempted to mimic some of the processes taking place in natural evolution. Intuitively, they proceed by creating successive generations of better solutions by applying genetic operations [

The modeling of genetic algorithms for a given problem includes four basic steps: representation, fitness function, reproduction, and genetic operators. Representation is the encoding process converting the problem’s phenotypes into genotypes;

In the next subsections, we describe the detailed steps for modeling of a genetic algorithm to solve the MSCD problem.

Each chromosome in a population represents a candidate solution encoded as the direction of sensors for the MSCD problem. _{i,k}

When an initial population is constructed, every gene in the chromosome is randomly set to an integer value using

One column in the chromosome shown in _{k}_{k}

_{k}

_{k}

_{1} and _{2} are covered respectively by any two directions _{1} and _{2} in _{k}_{1} ⊄ _{2} and _{2} ⊅ _{1}.

The total network lifetime is calculated as _{k}

The two-dimensional chromosome presented in _{1} and _{2} represent sub-objective functions for the network lifetime and the residual energy of all sensors, respectively. _{1} and _{2} represent the parameters determining the significance of two sub-objective functions, respectively.

In _{1} the range from zero to one. For the sub-objective function _{2}, we use a hyperbolic tangent function due to its smoothness property. Using the slope parameter _{i}_{2} is also from zero to one. To make the evolutionary process more efficient, the values of _{1} and _{2} presented in _{2} _{1} ≤ 1. This means that the first sub-objective function (_{1}) has much influence on achieving the maximization of the network lifetime than the second sub-objective function (_{2}). _{2} is used as an auxiliary function to extend the network lifetime.

The reproduction process is the core of a genetic algorithm. In the reproduction process, selection mechanisms are used to organize a new population from the current population [

Given the population size

Here, we describe crossover and mutation operators to achieve the extended network lifetime in a DSN. In general, a crossover is a process that takes two parents and produces offstring from them with the aim of obtaining better chromosomes in the next generation. After a crossover point is randomly chosen, the part from the beginning of chromosome to the crossover point is copied from one parent, and the rest is copied from the second parent [

_{a}_{b}

Mutation is used to maintain the genetic diversity in a population [_{m}_{k,i}_{i}_{k}_{k,i}_{i}

In this section, we evaluate and analyze the performance of the proposed two schemes through simulations. The performance comparison for the schemes is also presented.

To conduct our simulations, we implemented a simulator with JDK 6.0. Using the simulator, we constructed a simulation environment to build a directional sensor network environment.

Our simulation environment assumes that the different numbers of targets (

In the greedy algorithm-based target coverage scheduling scheme, the parameter of a contribution function (_{i}

Our greedy algorithm-based and genetic algorithm-based target coverage scheduling schemes are evaluated according to the following three experimental factors.

Number of directional sensors: This is used to investigate whether the two schemes solve the MSCD problem defined in our paper. We then compare the performance of the two schemes in terms of how much the network lifetime is extended with the different numbers of targets and directional sensors.

Sensing ranges: This is used to investigate the performance of the two schemes with regard to the diverse sensing ranges of directional sensors. As the sensing ranges grow narrower, the target coverage of directional sensors shrinks. We expect that wider sensing ranges would lead to a larger number of cover sets than the narrower ranges.

Distribution of directional sensors with different sensing ranges: When directional sensors have different sensing ranges, it is important to investigate the effects to find optimal cover sets. We will make the distribution of the number of directional sensors with different sensing ranges and then analyze how the distribution affects the performance of the two schemes.

In the next subsections, we present the simulation results to analyze the effect of these factors on the network lifetime and compare the performance of the two schemes in terms of the network lifetime of DSNs. The results presented here have been average over 10 simulation runs.

To investigate the influence of the number of directional sensors, we fixed the sensing ranges to 250 m. Directional sensors from 10 to 50 were used to cover 5 and 10 targets, respectively, and the performance was evaluated for each of the two schemes.

Comparing the two schemes with regard to their network lifetime, our genetic algorithm-based target coverage scheduling scheme markedly extends the network lifetime compared with our greedy algorithm-based scheme, regardless of the number of directional sensors. This result indicates that the genetic algorithm-based scheme can find an optimal solution to the MSCD problem by global evolutionary search, in contrast to the greedy algorithm-based scheme, which is dependent on a heuristic search.

The evaluation process of our genetic algorithm-based scheme is shown in

In this simulation, we examined the performance of the two schemes according to the changes in sensing ranges of directional sensors. The lifetime variation was evaluated with the sensing ranges from 150 to 300 m when 10, 30, and 50 directional sensors were used to cover 5 and 10 targets, respectively.

The results presented in

In this simulation, we evaluated the effect of the distribution of directional sensors with different sensing ranges on the performance of the two schemes. To evaluate this effect, we made a distribution of directional sensors with respect to sensing ranges.

The network lifetime of type

This paper discussed the target coverage scheduling for DSNs. In contrast to conventional sensor networks, DSNs are composed of a number of directional sensors with limited sensing ranges and directions, and thus target scheduling to maximize the network lifetime requires a highly sophisticated optimization technique. We have presented two target scheduling schemes, the greedy algorithm-based and the genetic algorithm-based schemes, to solve the MSCD problem that is known to be NP-complete. Throughout our simulations, different numbers of directional sensors, various sensing ranges, and heterogeneous directional sensors were used to investigate the effect of each on the performance of the two schemes. Simulation results showed that the schemes can find the cover sets monitoring all the targets in an energy-efficient way. They also showed that, by an evolutionary global search technique, the genetic algorithm-based scheme achieves a longer network lifetime than the greedy algorithm-based scheme does. As our future work, we plan to extend the schemes to maximize the network lifetime of DSNs considering the multi-hop connectivity of sensors as well as the coverage of the given targets.

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. 2010-0015637), and also supported by the IT R&D program of MKE/KEIT (10035245: Study on Architecture of Future Internet to Support Mobile Environments and Network Diversity).

Illustrative example of a directional sensor network. _{1,1}, _{2,3}, _{3,3}}; _{1,2},_{2,3},_{3,1}}.

The greedy algorithm to solve the MSCD problem.

Chromosome representation.

Example of two crossover operations.

An example of target and sensor deployment.

Comparison of network lifetimes according to the number of directional sensors.

Evolution process of average fitness for ten runs of our genetic algorithm.

Comparison of network lifetimes according to changes in sensing ranges.

Comparison of network lifetimes for distribution of directional sensors with different sensing ranges.

Parameters and values used in our simulations.

Parameters | Values |
---|---|

Number of targets ( |
5, 10 |

Number of directional sensors ( |
10, 20, 30, 40, 50 |

Number of directions ( |
3 |

Sensing range | 150 m, 200 m, 250 m, 300 m |

Population size ( |
100 |

Number of generations | 300 |

Crossover probability (_{c} |
0.1 |

Mutation probability (_{m} |
0.05 |

Slope parameter for _{2} ( |
0.3 |

Weighted parameter for _{1} (_{1}) |
0.9 |

Weighted parameter for _{2} (_{2}) |
0.1 |

Distribution of directional sensors with different sensing ranges.

Type | Sensing ranges (m)
| ||
---|---|---|---|

200 | 250 | 300 | |

33% | 33% | 33% | |

20% | 20% | 60% | |

60% | 20% | 20% |