K-coverage Problem Research Articles

Optimizing [formula omitted]-coverage in energy-saving wireless sensor networks based on the Elite Global Growth Optimizer

For energy-constrained wireless sensor networks, enhancing network fault tolerance and extending lifetime are of paramount importance. In this study, we focus on addressing the Minimum Power k-Coverage (MinPKC) problem. The objective of MinPKC is to minimize and balance the transmission (Tx) power by sensor nodes (SNs), thus extending network lifetime. Furthermore, MinPKC requires satisfying the constraints of k-coverage for the targets to enhance network fault tolerance. The problem is non-convex, multimodal, and NP-hard. To address this problem, we propose a novel metaheuristic algorithm named Elite Global Growth Optimizer (EGGO), which incorporates efficient global search and elite evolution strategies into the GO and utilizes time-varying multi-strategies for population updates. This study extensively compares EGGO with ten popular algorithms on 20 classic benchmark test functions using the Friedman and Wilcoxon rank-sum tests. The results indicate that EGGO significantly outperforms all the compared algorithms. Ablative experiments confirm the crucial role of the proposed mechanisms in EGGO for improving algorithm performance. Meanwhile, the study implements ten MinPKC methods based on comparative algorithms and compares them with the EGGO-based MinPKC method in terms of total Tx power, network lifetime, and simulation time. The experimental results indicate that the EGGO-based MinPKC method significantly increases the network lifetime by approximately 14.2%, 38.2%, and 1.9% compared to the second-best algorithm, and by 57%, 451%, and 84.8% compared to the GO, while balancing the Tx power among SNs and reducing the total Tx power by approximately 28%, 12.7%, and 0.5% compared to the second-best algorithm, and by 47.1%, 72%, and 30% compared to the GO, respectively, when k=1,2,3. Additionally, a detailed analysis is conducted on the impact of the number of SNs, the maximum target coverage capacity of each SN, as well as the effects of obstacles and their distribution on signal strength attenuation in reducing Tx power. The source code is available at https://github.com/iNet-WZU/EGGO.

Distributed homology-based algorithm for solving Set k-Cover problem in heterogeneous directional sensor networks

Distributed homology-based algorithm for solving Set k-Cover problem in heterogeneous directional sensor networks

Discrete grey wolf optimization algorithm for solving k-coverage problem in directional sensor networks with network lifetime maximization viewpoint

Unlike the traditional wireless sensor networks (WSNs) which apply omni-directional sensors, the directional sensor networks (DSNs) utilize directional sensor nodes. Each directional sensor in DSN is a self-configured in one direction and one coverage range at a same time. In critical industries, the target coverage problem in which every target should be observed by k different sensors increases the reliability and leads the fault tolerant observation. In this case, the huge amount of energy is consumed in comparison with one coverage problem. Since the business continuity in such industries strongly depends on the network lifetime, the energy management and lifetime maximization of such resource-limited networks are still of the most important challenges. To address the issue, this paper formulates the k-coverage challenge to a discrete optimization problem with the network lifespan expansion viewpoint which is an NP-Hard problem. To solve this combinatorial problem, a discrete grey wolf optimization algorithm (D-GWA) is presented. This D-GWA proposes abundant novel exploration and exploitation procedures which permutes discrete search space efficiently. In this regard, the new fitness function is also defined which steers solutions in the directions to engage sensors uniformly in different rounds. It potentially improves network lifetime because of uniform battery usage. During the course of optimization, it utilizes temperature concept of simulated annealing algorithm to running away from local trap. To verify the proposed algorithm in solving k-coverage problem in DSNs, twelve scenarios are conducted. The simulation results experimentally prove that the totally dominance of the proposed algorithm against state-of-the-arts HTOH, LA-based, GWA, and hybrid PSO-GA approaches respectively are the amount of 31.37%, 20.97%, 14.12%, and 7.93% improvement in term of network lifetime expansion. Furthermore, the behavior of D-GWA shows the high potential of scalability in the larger search space.

A Computational Geometry-based Approach for Planar k -Coverage in Wireless Sensor Networks

The problem of coverage is one of the most crucial issues among the problems in the lifecycle of the development of wireless sensor networks (WSNs). It is still open and stirs as much concern in the research community in this area. The problem of k -coverage in WSNs is even more challenging. In this article, we investigate the k -coverage problem in planar (or two-dimensional) WSNs, where each point in a field of interest (FoI) is covered by at least k sensors simultaneously, where k ≥ 1. Our contribution is four-fold: First, we determine the optimal planar convex tile that maximizes the usage of the sensors’ sensing range. Then, we propose a few sensor placement strategies based on the degree of coverage k using a hexagonal tiling-based approach. In addition, we compute the sensor density (i.e., number of sensors per unit area) for each of the above sensor placement strategies. Second, we propose a generalized one using irregular hexagons, which are denoted by IRH(r/n) , where r stands for the radius of the sensors’ sensing range and n ≥ 2 is a natural number. Also, we derive the corresponding sensor density. Moreover, we prove that IRH(r/n) are capable of tiling the Euclidean plane using a mathematical induction proof. Third, we compute the relationship between the sensing range r of the sensors and their communication range R for the above sensor placement strategies. Fourth, we corroborate our analysis with simulation results.

A hybrid-order local search algorithm for set k-cover problem in wireless sensor networks

A hybrid-order local search algorithm for set k-cover problem in wireless sensor networks

Solving the Problem of Target k-Coverage in WSNs Using Fuzzy Clustering Algorithm

Solving the Problem of Target k-Coverage in WSNs Using Fuzzy Clustering Algorithm

An energy aware grouping memetic algorithm to schedule the sensing activity in WSNs-based IoT for smart cities

Wireless Sensor Networks (WSNs) are the main component in the Internet of Things (IoT) and smart cities to sense our environment, gather essential and meaningful data, and forward it to the base station (BS). Nowadays, IoT utilizes WSN as a necessary platform for sensing and communication of the data. One of the main strategies to minimize consumption of energy in a WSN with highly dense sensors is to maximize sleeping sensors at each time. This way implies to schedule the activity of sensors, i.e. determining when a sensor node is kept idle (sleep mode) and when a sensor node is activated to sense environment (active mode). Due to heterogeneity of the sensor nodes in WSNs-based IoT for smart cities, one approach for scheduling the sensing activity is clustering the sensors into K mutually different subsets, so that every subset of sensors alone can cover all targets of the network. In this case, we can solve finding the maximum number of sensor subsets, or equivalently sensor covers problem, by conversion it to SET K-COVER problem. In this paper, an energy aware Grouping Memetic Algorithm (GMA) is proposed for solving the SET K-COVER problem. The proposed GMA varies in four general ways from any of the other evolutionary algorithms for solving the SET K-COVER problem. First, to transform solution structures linked to the SET K-COVER problem into chromosome genes, a new encoding scheme was being used. Second, specific genetic operators appropriate for the chromosomes are used, based on the encoding used. Third, to direct the search process in the solution space of the SET K-COVER problem, a novel proper fitness function is proposed. Fourth, a local improvement algorithm which uses a sensor dominance rule is proposed. This study, carried out detailed experiments of different numbers of targets and different numbers of sensors in WSNs to assess the proposed algorithm. In several instances of the problem, the experiments demonstrate that the algorithm works considerably better in terms of solution quality than many other heuristics and evolutionary algorithms and significantly outperformed the evolutionary algorithms in terms of runtime, suggesting the usefulness of the proposed algorithm to increase the lifetime of WSN in IoT and smart cities.

A new genetic-based approach for solving [formula omitted]-coverage problem in directional sensor networks

In recent years, the use of directional sensor networks (DSNs) has continued to rise increasingly, which is due to their extensive use in many situations. In such networks, the main problem is how to cover the targets distributed in a defined area and simultaneously prolong the network lifetime as much as possible. The reason of this problem is the limitation of both sensing angle and energy resource of sensors in such networks. This problem gets more complex in cases where targets need to be covered by more than one sensor direction (i.e., each target needs to be monitored for at least k times). This problem is generally known as target k-coverage problem which its NP-completeness has been already proved in the literature. The k-coverage problem can be considered in over-provisioned and under-provisioned environments. In both of these environments, especially in the latter, it is important to create a balanced coverage, as these environments do not have enough sensors to monitor all targets for k times. Thus, in this paper, we proposed a genetic-based algorithm to solve the problem in over-provisioned environments, then developed the proposed algorithm in another way to solve the problem in under-provisioned networks so that it uses the minimum number of sensors. many experiments were performed to test the efficiency of the proposed algorithm, and the obtained results showed the high capacity of the proposed algorithm in solving the k-coverage problem in both environments.

Connected k-coverage in two-dimensional wireless sensor networks using hexagonal slicing and area stretching

The problem of coverage in two-dimensional (2D) wireless sensor networks is challenging and is still open. Precisely, determining the minimum sensor density (i.e, minimum number of sensors per unit area) that is required to cover a 2D field of interest (FoI), where every point in the field is covered by at least one sensor, is still under investigation. The problem of 2D k-coverage, which requires that every point in a 2D FoI be covered by at least k sensors, where k≥1, is more challenging. In this paper, we attempt to address the 2D connected k-coverage problem, where a 2D FoI is k-covered, while the underlying set of sensors k-covering the field forms a connected network. We propose to solve this problem using an approach based on slicing 2D FoI into convex regular hexagons. Our goal is to achieve k-coverage of a 2D FoI with a minimum number of sensors in order to maximize the network lifetime. First, we compute the minimum sensor density for 2D k-coverage using the regular convex hexagon, which is a 2D paver (i.e., covers a 2D field without gaps or overlaps). Indeed, we found that the regular convex hexagon best assimilates the sensors’ sensing disk with respect to our proposed metric, sensing range usage rate. Second, we derive the ratio of the communication range to the sensing range of the sensors to ensure connected k-coverage. Third, we propose an energy-efficient connected k-coverage protocol based on hexagonal slicing and area stretching. To this end, we formulate a multi-objective optimization problem, which computes an optimum solution to the 2D k-coverage problem that meets two requirements: Maximizing the size of the k-covered area, Ck, so as to minimize the sensor density to k-cover a 2D FoI (Requirement 1) and maximizing the area of the sensor locality, Lk, i.e., the region where at least k sensors are located to k-cover Ck, so as to minimize the interference between sensors (Requirement 2). Fourth, we show various simulation results to substantiate our theoretical analysis. We found a close-to-perfect match between our theoretical and simulation results.

Toward Refined Nash Equilibria for the SET K-COVER Problem via a Memorial Mixed-Response Algorithm

Area coverage and network lifetime are two contradictory issues to the architecture development of a wireless sensor network (WSN). A satisfactory balance could be achieved by deploying abundant sensor nodes randomly and dividing them into <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> exclusive cover sets. Toward self-organized partition with higher efficiency, we address the problem from the perspective of networked potential games and propose a memorial mixed-response algorithm (MMRA), which is implemented in a distributed and synchronous manner. Being viewed as a game player, each sensor node first updates its memory using a temporary action, which is generated by following a mixed response rule. After this, the coordination evolves into the next iteration by each player randomly drawing an action from its memory with equal probabilities. We prove that our algorithm converges with probability 1 to a convention of Nash equilibria, with the worst approximation ratio strictly larger than 0.5. Moreover, it is also found that a tradeoff between solution efficiency and computation time could be achieved via the adjustment of the amount of randomness introduced via the memory length <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> as well as the probability <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p_{m}$ </tex-math></inline-formula> , where better partition results are more likely to be generated using a larger <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> and smaller <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p_{m}$ </tex-math></inline-formula> . Comparisons with existing distributed methods demonstrate the superiority of our method in terms of solution refinement as well as convergence speed.

Solving the Problem of Target k-Coverage in WSNs Using Fuzzy Clustering Algorithm

The purpose of the present research was to introduce an algorithm to solve the coverage problem in wireless multimedia networks that can be used to optimize energy consumption and network lifetime. In this regard, the problem of target k-coverage in WSNs was solved by dividing the environment into the proportional area and random selection. This can be done using a fuzzy clustering algorithm. It is worth noting that the results of the proposed algorithm were compared with previous methods such as genetic and annealing algorithm. The simulation results and comparison with other algorithms show a 27% superiority of the proposed algorithm. It is hoped that this method can be used in networks with larger dimensions in the future

Sensor placement optimization for critical-grid coverage problem of indoor positioning

It is more practical and efficient to deploy sensors in critical areas rather than common areas to ensure indoor positioning accuracy and reduce deployment cost. This study focused on the sensor placement optimization for critical-grid coverage problem with two objectives: accuracy and cost. After reviewing some related works, this article proposed a multi-objective optimization model for critical-grid coverage problem of indoor positioning considering k-coverage problem as well as the topological rationality of sensor distribution. Then, NSGA-II algorithm was used to solve the optimizing model of sensor placement. At last, the simulation experiment and real environment validation were conducted for proposed method. The results showed that the optimized schemes obtain a lower error (1.13, 1.21 m) and a higher reduction of sensor deployment cost than the uniform deployment scheme (1.44 m). As a conclusion, the proposed method could reduce the cost of sensor deployment while ensuring the accuracy of indoor positioning for critical areas. It also provides a new direction for improving the accuracy of indoor positioning.

A learning automata-based algorithm to solve imbalanced k-coverage in visual sensor networks

One of the most important problems in directional sensor networks is k-coverage in which the orientation of a minimum number of directional sensors is determined in such a way that each target can be monitored at least k times. This problem has been already considered in two different environments: over provisioned where the number of sensors is enough to cover all targets, and under provisioned where there are not enough sensors to do the coverage task (known as imbalanced k-coverage problem). Due to the significance of solving the imbalanced k-coverage problem, this paper proposes a learning automata (LA)-based algorithm capable of selecting a minimum number of sensors in a way to provide k-coverage for all targets in a balanced way. To evaluate the efficiency of the proposed algorithm performance, several experiments were conducted and the obtained results were compared to those of two greedy-based algorithms. The results confirmed the efficiency of the proposed algorithm in terms of solving the problem.

Gene-Similarity Normalization in a Genetic Algorithm for the Maximum k-Coverage Problem

The maximum k-coverage problem (MKCP) is a generalized covering problem which can be solved by genetic algorithms, but their operation is impeded by redundancy in the representation of solutions to MKCP. We introduce a normalization step for candidate solutions based on distance between genes which ensures that a standard crossover such as uniform and n-point crossovers produces a feasible solution and improves the solution quality. We present results from experiments in which this normalization was applied to a single crossover operation, and also results for example MKCPs.

The Approximability of Multiple Facility Location on Directed Networks with Random Arc Failures

We introduce and study the maximum reliability coverage problem, where multiple facilities are to be located on a network whose arcs are subject to random failures. Our model assumes that arcs fail independently with non-uniform probabilities, and the objective is to locate a given number of facilities, aiming to maximize the expected demand serviced. In this context, each demand point is said to be serviced (or covered) when it is reachable from at least one facility by an operational path. The main contribution of this paper is to establish tight bounds on the approximability of maximum reliability coverage on bidirected trees as well as on general networks. Quite surprisingly, we show that this problem is NP-hard on bidirected trees via a carefully-constructed reduction from the partition problem. On the positive side, we make use of approximate dynamic programming ideas to devise an FPTAS on bidirected trees. For general networks, while maximum reliability coverage is $$(1 - 1/e + \epsilon )$$ -inapproximable as an extension of the max k-cover problem, even estimating its objective value is #P-complete, due to generalizing certain network reliability problems. Nevertheless, we prove that by plugging-in a sampling-based additive estimator into the standard greedy algorithm, a matching approximation ratio of $$1 - 1/e - \epsilon $$ can be attained.

Target K-coverage problem in wireless sensor networks

Wireless sensor network (WSN) is collection of various sensors placed according to the application requirement to accomplish quality of service (QOS) that is how fine the sensors are covering or monitoring the set of targets that are within their sensing range. The essential problem and a dynamic exploration area in WSNs is coverage in which energy-efficiency is a critical issue. So, it is important to manage the battery utilization of the sensors by arranging and activating these sensors in an energy-efficient and effective way to make the network functional for longer period of time. Minimizing energy consumption and maximizing network lifetime is one of the prime objective of target coverage problem. Here in this work, we suggest an energy-efficient heuristic addressing K-Coverage problem which is an alternative of target coverage problem where every target is shielded by a minimum K-number of sensors to determine a set of different non-disjoint K-Covers. We show that the performance of the proposed heuristic is close to the optimal solution and have shown improvements in lifetime of network.

SENET: A novel architecture for IoT-based body sensor networks

Abstract Wireless sensor networks (WSNs) have been applied to various fields of study including medicine, agriculture, and engineering. Although recently, many architecture styles have been proposed to manage WSNs, most of them have ignored the application of artificial intelligence (AI) in wireless body sensor networks (WBSN). To this end, the present study aims to introduce a novel architecture (SENET), which is based on AI techniques and consists of three main layers. After describing the proposed architecture, the performance of four efficient and popular algorithms, i.e., world competitive contests (WCC), particle swarm optimization (PSO), ant colony optimization (ACO), and genetic algorithm (GA) is investigated for covering WBSNs using k head clusters (the k-coverage problem). The results show not only that the proposed architecture saves energy consumed by the wireless sensors, but also that the WCC algorithm is a suitable option for determining the positions of sensors in the proposed architecture in terms of WSN energy-consumption, the total number of required sensors, and reliability. The results also show that the proposed WCC algorithm, with an average 38.44 value of score on nine scenarios, outperforms other techniques.

Weak k-Barrier Coverage Problem in Underwater Wireless Sensor Networks

Most existing works on barrier coverage assume that sensors are deployed in a two-dimensional (2D) long thin belt region, where a barrier is a chain of sensors from one end of the region to the other end with overlapping sensing zones of adjacent sensors. However, the 2D assumption cannot cover all application scenarios, e.g., underwater wireless sensor networks, where sensors are finally distributed over three-dimensional (3D) underwater environment. In this paper, we investigate weak k-barrier coverage problem in underwater wireless sensor networks. We first analyse how to determine whether a deployed underwater wireless sensor network provides 3D weak k-barrier coverage, and propose a novel and effective scheme to transform the 3D weak k-barrier coverage problem into 2D complete k-coverage problem, based on which we devise an O(n2) time algorithm for the 3D weak k-barrier decision problem. Furthermore, we propose a parallel movement manner, based on which an effective algorithm called Hungarian Method-based sensor assignment algorithm (HMB-SAA) is proposed for constructing weak k-barrier coverage while minimizing the total movement distance of all sensors in underwater wireless sensor networks. Simulation results validate the correctness of our analysis, and show that the proposed algorithm outperforms the GreedyMatch algorithm. To the best of our knowledge, this is the first result for 3D weak k-barrier coverage problem in underwater wireless sensor networks.

Energy-efficient routing protocol based on tree link topology in wireless sensor networks

Wireless sensor networks have been widely used in target monitoring application. It is often assumed in a typical target coverage algorithm that the environment is known, and each target is covered by only one node. However, these algorithms are not scalable. In fact, one target may need to be covered by more than one node, which is the K-coverage problem. Aiming at the application of target monitoring in wireless sensor network, a K-coverage model— kernal matrix based genetic algorithm (KMGA) based on the genetic algorithm—is proposed. The KMGA model ensures that each target is covered by multiple sensors simultaneously. First, multiple Covers are generated as much as possible through genetic algorithm, and then, while coverage requirements are ensured, coverage between Covers is switched based on remaining energies of nodes so as to extend the network life. Experimental data show that the proposed KMGA model can effectively extend the network lifetime and ensure coverage rate.

A Novel Random Scheduling Algorithm based on Subregions Coverage for SET K-Cover Problem in Wireless Sensor Networks

A Novel Random Scheduling Algorithm based on Subregions Coverage for SET K-Cover Problem in Wireless Sensor Networks