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IEEE WIRELESS COMMUNICATIONS LETTERS, VOL. 2, NO. 1, FEBRUARY 2013
Jenga-Inspired Optimization Algorithm for Energy-Efficient Coverage of Unstructured WSNs Joon-Woo Lee, Student Member, IEEE, Joon-Yong Lee, Student Member, IEEE, and Ju-Jang Lee, Fellow, IEEE
Abstract—The Energy-Efficient Coverage (EEC) problem in unstructured Wireless Sensor Networks (WSNs) is an important issue because WSNs have limited energy. In this letter, we propose a novel stochastic optimization algorithm, called the JengaInspired Optimization Algorithm (JOA), which overcomes some of the weaknesses of other optimization algorithms for solving the EEC problem. The JOA was inspired by Jenga which is a well-known board game. We also introduce the probabilistic sensor detection model, which leads to a more realistic approach to solving the EEC problem. Simulation results are conducted to verify the effectiveness of the JOA for solving the EEC problem in comparison with existing algorithms. Index Terms—Energy-efficient coverage, wireless sensor networks (WSNs), Jenga-inspired optimization algorithm (JOA), sensor activity scheduling method, lifetime maximization.
I. I NTRODUCTION
W
IRELESS Sensor Networks (WSNs) are divided into structured and unstructured WSNs. All or some of the sensor nodes in a structured WSN are deployed in a preplanned manner at fixed locations. On the other hand, an unstructured WSN contains a dense collection of sensor nodes, which are randomly placed into the field. Unstructured WSNs are usually used in the environment or area where humans cannot directly accessible to construct WSN, e.g. deep sea or nuclear accident area [1]. Typical sensors in most unstructured WSNs use batteries as an energy source, but it is generally infeasible to replace or recharge the discharged batteries. Solving the EEC problem in WSNs may depend on efficient scheduling, which can conserve the limited energy supply and prolong network lifetime through careful planning of the activities of devices in the WSNs [2]-[10]. The activity scheduling method requires that devices be densely deployed in a monitored region. Therefore, we do not need all devices in the WSNs to cover the area of interest. Only a subset of devices actually carries out the sensing task, and the other devices can be maintained in a sleep state to save energy. Accordingly, to achieve a longer WSN lifetime, it is important to find the maximum number of disjoint subsets of devices in the scheduling method. Many algorithms have been proposed to solve the EEC problem. The EEC problem was converted into a binary integer programming problem, so that a greedy algorithm could be applied [5]. A greedy search is based on a local
Manuscript received September 6, 2012. The associate editor coordinating the review of this letter and approving it for publication was H. Jiang. J.-W. Lee and J.-J. Lee are with the Department of Electrical Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, 305701, Korea (e-mail:
[email protected];
[email protected]). J.-Y. Lee is with the Intelligent Robotics and Communication Laboratories, ATR International, Kyoto, 619-0288, Japan (e-mail:
[email protected]). Digital Object Identifier 10.1109/WCL.2012.100912.120648
search in which the search ability is specifically sensitive to an initial condition. To obtain a global solution, stochastic optimization algorithms were also used to schedule device activities, which included Genetic Algorithms (GA) [6]-[7], Particle Swarm Optimization (PSO) algorithms [8], and Ant Colony Optimization (ACO) algorithms [8]-[9]. However, these global optimization algorithms require a longer computation time, as compared with a greedy method, as a result of global searches. In this letter, we propose a new stochastic optimization algorithm, called the Jenga-Inspired Optimization Algorithm (JOA), which can solve the EEC problem more efficiently. In order to improve on the weaknesses of conventional algorithms, the framework of the JOA is based on a greedy method for fast convergence and employs a stochastic approach for the ability to conduct random exploration. These features allow the JOA to demonstrate a better performance than that of conventional approaches. We also introduce the probability sensor detection model [11], which represents a more realistic approach to solving the EEC problem. The JOA was inspired by Jenga, which is a well-known board game. In Jenga, players take turns removing a block from a block tower and placing the removed block at the top of the tower, creating a taller and increasingly unstable structure as the game progresses. If the tower collapses, the game is finished. In the JOA, players take turns deactivating a device from a network of active devices, as in Jenga. Next, if the WSN is unable to cover a Point of Interest (PoI) as a result of the inactive device, another player takes a turn. The JOA finds the optimal solution for maximizing the WSN’s lifetime as the algorithm progresses. II. E NERGY-E FFICIENT C OVERAGE (EEC) P ROBLEM We define the Energy-Efficient Coverage (EEC) problem, as follows: Energy-Efficient Coverage (EEC) Problem Given a monitored region A, a set S of sensors (S = {s1 , s2 , · · · , si , · · · , sNS }), a set P of PoIs (P = {p1 , p2 , · · · , pj , · · · , pNI }) and a cost ci of the sensor i (i = 1, 2, · · · , NS ), find a set C of the subsets C(tS ) (tS = 1, 2, · · · , TS ) of sensors that cover all of the PoIs in region A with a minimum total cost for a time slot until the WSN fails to cover any of the PoIs in region A. Then TS is the lifetime of the WSN.
Practical sensors detect monitored events, such as temperature, pressure, heat, and force, that occur at a PoI by measuring the received energy (or intensity of the signal). The intensity of the energy is exponentially reduced as the distance between the PoI and sensor increases, unlike in the Boolean
c 2013 IEEE 2162-2337/13$31.00
LEE et al.: JENGA-INSPIRED OPTIMIZATION ALGORITHM FOR ENERGY-EFFICIENT COVERAGE OF UNSTRUCTURED WSNS
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[8], the cost of an active sensor i is calculated as follows: ci = κER,i
(2)
where κ is a constant related to the characteristics of the sensor, and κ ∈ (0, 1). ER,i is the residual energy of sensor i. PoI j is covered by the WSN if some of the sensors detect events occurring at PoI j with a probability λ(j) of detection, i.e., the value of λ(j) is larger than the threshold , which is a user-defined parameter. The probability λ(j) can be calculated as follows: (1 − λi (j)) ≥ ε (3) λ(j) = 1 − si ∈Sj
Fig. 1. One example of optimal cover sensor set found by JOA in Scenario 1 (100 sensors, 10 PoIs).
disc model. Our model formulation was introduced in [11] and is as follows. Let λi (j) denote the probability of detection of events at PoI j by sensor i. ⎧ 0 if dij > ru ⎨ m −a(d ij −rs ) (1) λi (j) = if rs < dij ≤ ru e ⎩ dij < rs if 1 where dij is the Euclidean distance between the sensor i and PoI j. The variables a and m are decay factors. Events at PoI j are definitely detected if PoI j is within a distance of rs , which is similar to the detection range in the Boolean disc model. The detection probability decreases exponentially as the distance becomes greater than rs . The signal intensity of the event is smaller than that of the noise when the distance is greater than ru , and therefore, the probability should be zero. The variables a, m, rs , and ru depend on the characteristics of the sensor and on environmental factors [11]. To solve the EEC problem, as in the other papers [5], [8], we make several assumptions. First, we assume that the communication range rc of the device is at least twice its sensing range, rs (i.e., rc ≥ 2rs ). We also assume that we know the exact position of the devices and PoIs. We divide the operation time into time slots, and the scheduling algorithm is recursively performed to select and optimize a set of sensors to cover all of the PoIs with a minimum total cost for the time slot, as shown in Fig. 1, which provides an example of the optimal subset at a certain time slot, that obtained from the simulation in this letter. Eventually, a set of these subsets, obtained for each time slot, is an optimal solution to the EEC problem, and the number of time slots that succeed at the minimum cost coverage reflects the lifetime of the WSN. In a time slot, selected sensors are active, while others remain deactivated. We assume that a sensor does not consume any energy in its inactive state and that an active sensor consumes a specific, constant amount of energy per unit of time in this letter. The energy consumption model can be replaced with various types for the simulation and experiment by changing the function ER,i in Eq. (2). The cost associated with each sensor increases according to its energy consumption. It is necessary to keep in mind that the cost is just a score to be used for the evaluation of the obtained subsets. According to
where Sj is a set of sensors that covers the PoI j and Sj ⊂ S. According to [5], the EEC problem can be expressed as an integer programming problem and is described as follows: minimize
N S
(4)
ci xi
i=1
subject to ∀pj ∈ P,
N S
αij xi ≥ δ, xi ∈ {0, 1}
(5)
i=1
where αij is a function of λi (j) and is calculated as αij = −ln(1 − λi (j)). The probability λi (j) is the probability of detection of events occurring at PoI j by sensor i, as mentioned in Eq. (1). xi is the value that determines whether sensor i is selected. Variable δ is related to the smallest number of sensors and is calculated as δ = −ln(1 − ). Eq. (5) shows that each PoI must be covered by at least small number of sensors. III. J ENGA -I NSPIRED O PTIMIZATION A LGORITHM (JOA) As mentioned above, we will introduce a novel optimization algorithm, called the JOA, for solving the EEC problem in this section. The JOA is divided into two parts as shown in Algorithm 1. The first part is for preparation and initialization, and the second part has a double loop. In the first stage of the JOA, we collect position information from the sensors and PoIs and store those in the matrix ISensor and IP oI respectively. Especially, matrix ISensor also stores the information of the residual energy of each sensor, ER,i . And we also collect the information about the number of PoIs that can be covered by each sensor and store that in the 1 × NS vector ICover . Afterward, we set the adjustable user parameters, i.e., the number of players (NP ) and turns (NT ), and the threshold for the smallest probability of detection at every PoI. We also initialize set C to store the optimal subset of sensors in every time slot and initialize variable TS to store the final value of time slot tS , i.e., the lifetime of the WSN for the EEC. After the parameters are set, the JOA begins the new time slot. The score board, ΩS , is initialized in every new time slot, tS , and the value of the element ΩS,i (tS ) is determined as the product of the residual energy of sensor i at time slot tS , ER,i (tS ), and the number of the PoIs covered by sensor i, ICover,i (tS ), i.e. ΩS,i (tS ) = ER,i (tS ) · ICover,i (tS ). The matrix ISensor contains information regarding ER . We also initialize the NP × NS matrix IP layer as all 1, which means that all of the sensors are active at the beginning of the new
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IEEE WIRELESS COMMUNICATIONS LETTERS, VOL. 2, NO. 1, FEBRUARY 2013
Algorithm 1 JOA for EEC problem [ISensor , IP oI , ICover ] = GetInf ormation(); SetP arameters(NP , NT , ); // NP : # of Players, NT : # of Turns Initialize(C, TS ); tS ← 0; // tS : Time Slot while Termination condition doesn’t meet do // New time slot start. tS ← tS + 1; nT ← 0; // nT : Turn Number // ΩS : Score Board Initialize(ΩS , IP layer , LRank ); while nT ≤ NT do // New Turn start. nT ← nT + 1; while Player k meets Eq. (5) do i ← RouletteSelect(pS ); IP layer,k (i) ← 0 if Eq. (5) don’t meet then IP layer,k (i) ← 1 end if end while // Sort using Eq. (4) and Cut LRank by NP . Sort(LRank (2NP )); LRank (NP ) = Cut(LRank (2NP )); Cbest ← LRank (1); U pdateScore(ΩS ); end while C(tS ) ← CBest ; U pdateInf ormation(ISensor , ICover ); end while return C, TS ;
time slot. The vector IP layer,k is used to store information regarding which sensor is removed by player k, i.e., if player k removes sensor i, then element IP layer,k (i) has a value of 0. The cell LRank is an archive to store the rank information calculated every time after all players finish their turn, and it is also initialized at this time. Each player has NT turns in a time slot. As in Jenga, player k takes turns switching off device i, which is randomly determined by roulette wheel selection with a selection probability of pS (i) as follows: ΩS,i (nT ) pS (i) = ΩS (nT )
(6)
Player k takes turns removing sensors during turn nT until it no longer satisfies Eq. (5). If player k fails to cover all PoIs, player k + 1 takes his turn nT . After all players finish their turn, nT , we calculate the cost using Eq. (4) with the NP sets found for turn nT and NP having survived sets in the LRank until turn nT − 1. Next, we determine the ranking of 2 × NP and cut the NP sets in order. We store them in LRank again, and after determining the ranking, the score board, ΩS , is updated according to the following formulas. ΩS,i (nT + 1) = ΩS,i (nT ) +
NP k=1
Cost(LRank (1)) (7) nk · Cost(LRank (k))
where nk is the number of active sensors that survived from the selections of player k. The last term in Eq. (7) is designed to reward according to the ranking. The first rank gets 1/n1 points, and the others are rewarded by the score divided the cost (or fitness, which is calculated by Eq. (4)) of the first rank by their own costs, and those values are less than 1/n1 points. After the score update is completed, all of the players take turn nT + 1 with the information collected until turn nT and
repeats this process for NT turns. Once turn NT is completed (i.e., the current time slot is finished), we can obtain an optimal cover set like as shown in Fig. 1. Eventually, CBest is the optimal cover set of sensors at the time slot tS . Before the new time slot tS+1 begins, the matrix ISensor is modified by the principle that all sensors used lose energy at a constant amount, and the cost of all sensors used is calculated again with Eq. (2). Also, the information contained in the vector ICover is updated, i.e. the PoI which a certain sensor cannot cover anymore is excluded from counting the number of PoIs that can be covered by that sensor. This whole process so far iterates until either Eq. (5) is no longer satisfied by any of the PoIs, or the WSN fails to cover any PoIs. The final set C cell is the eventual solution of the EEC problem, and the number of the time slot, TS , becomes the lifetime of the WSN. IV. S IMULATION R ESULTS AND D ISCUSSIONS We conducted simulations to verify the effectiveness of the JOA over existing optimization algorithms in terms of lifetime and computation time. The algorithms used in the simulation are as follows: a greedy-based approximation algorithm in [5], the conventional ACO algorithm and PSO algorithm in [8], and the Three Pheromones ACO (TPACO) algorithm in [10]. The TPACO algorithm uses three types of pheromones, unlike conventional ACO algorithms, that it help the ACO algorithm solve the EEC problem efficiently. This algorithm was proposed in our recent paper [10]. We implemented the simulator in MATLAB. All simulations were computed on a PC with an Intel Core2 Duo CPU E4500 @ 2.20GHz and 4GB of RAM. The monitored region was a square grid-based space with a size 10m × 10m at internals of 10cm, i.e. a 100 × 100 grid size. We carried out the simulation using nine scenarios. Table I shows the number of sensors and PoIs, which were positioned randomly on the grid points. As mentioned above, we introduced the probabilistic sensor detection model in the WSN. The parameters of this model were set as follows: rs = 1.5m, ru = 6m, a = 0.5 and m = 0.5. Each device had the same initial energy, 1, which can last for ten active slots, i.e., a sensor consumes 0.1 energy per one time slot while in the active state. It is just an assumption for a fair comparison with other algorithms. The cost associated with each sensor increases according to its energy consumption, as shown in Eq. (2). The parameters of all of the algorithms used the same values in all of the scenarios, and these values for the JOA were defined as follows: NP = 100, NT = 100, and = 0.97. The parameters for the ACO algorithm were set as follows: M = 100, Mc = 500, α = 1, β = 1, and ρ = 0.1. The parameters for the PSO algorithm were set as follows: M = 400, Mc = 2000, ω = 0.99, c1 = 2.5, and c2 = 1.5. Finally, the parameters for the TPACO algorithm were set as follows: M = 30, Mc = 300, ρ = 0.5, and = 0.97. In each scenario, the simulation was performed 30 times with the same map for each algorithm. Table I and Table II depict the average network lifetime and computation time, respectively, for each scenario using different algorithms, and Fig. 2 presents a box plot of the
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TABLE I AVERAGE N ETWORK L IFETIME OF EACH ALGORITHM # 1 2 3 4 5 6 7 8 9
Scenario NS NI 100 10 150 10 200 10 100 20 150 20 200 20 100 30 150 30 200 30
Average Network Lifetime (cycle) Greedy ACO PSO TPACO JOA 32 33.8 34.0 36.4 35.5 55 57.6 57.9 58.9 60.1 104 104.2 103.2 105.3 107 18 10.3 10.7 19.5 19.3 40 43.9 43.8 45.3 45.1 62 67.5 67.7 66.8 70.2 34 33.9 33.1 36 36.1 50 48.9 48.7 50 51.5 47 47 45.4 48.9 50
TABLE II AVERAGE C OMPUTATION T IME OF EACH ALGORITHM Scenario NS NI 100 10 150 10 200 10 100 20 150 20 200 20 100 30 150 30 200 30
Greedy 0.0789 0.2049 0.4053 0.2309 0.2070 0.7008 0.2701 0.6676 0.9338
Average Computation Time (sec) ACO PSO TPACO 60.7179 464.8725 246.0321 139.7663 1237.996 416.8006 379.0425 3982.926 884.9886 74.5836 352.2804 759.6542 190.8719 1485.961 721.0791 468.5984 4653.149 1601.002 140.1967 869.0178 768.6936 243.0420 2261.200 1106.904 278.6919 3235.578 1181.396
JOA 34.7238 79.7083 22.9024 4.3922 7.9162 20.1919 39.8147 81.3320 99.1922
network lifetime for each scenario performed 30 times for each algorithm. For the network lifetimes obtained by each algorithm, the case of the ACO and PSO algorithms occasionally is worse performance than the greedy-based approximation algorithm because of the stochastic uncertainty. The TPACO algorithm and JOA, on the other hand, have consistently longer lifetime than the other algorithms. However, in addition to considering the computation time for the solution, the JOA has better performance than the TPACO algorithm because it determines a better solution for prolonging network lifetimes by shortening computation times. The JOA required much more computation than the greedy-based approximation algorithm which was based on the mathematical calculation method. To reduce the computation time, however, is less important than to prolong the network lifetime in solving the EEC problem. The reason is that the EEC problem is not the optimization problem demanding the solution in real time. Therefore, the simulation results demonstrate that the JOA outperforms the other algorithms. V. C ONCLUSIONS In this letter, we proposed a novel stochastic optimization algorithm, called the JOA, which overcomes some of the weaknesses of other optimization algorithms for solving the EEC problem. The framework of the JOA is based on a greedy method for fast convergence and employs a stochastic approach for the ability to conduct random exploration. These features of the JOA made a better performance than that of conventional approaches possible. And, the comparative simulation has verified this fact in this letter. R EFERENCES [1] J. Yick, B. Mukherjee, and D. Ghosal, “Wireless sensor network survey,” Comput. Networks, vol. 52, no. 12, pp. 2292–2330, Aug. 2008. [2] G. Anastasi, M. Conti, and M. Di Francesco, “Extending the lifetime of wireless sensor networks through adaptive sleep,” IEEE Trans. Ind. Informat., vol. 5, no. 3, pp. 351–365, Aug. 2009.
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