2. Related Work
- Propose a novel coverage-enhancing algorithm based on DE for WSNs. The algorithm can achieve a balance between network coverage and mobile sensor moving distance.
- Propose a moving-distance optimization scheme which can reduce the number of mobile sensors needed to be moved as well as greatly reduce the overall moving cost.
3. The Two-Phase Coverage-Enhancing Algorithm
3.1. Initial Assumptions
- All sensors have the same sensing range Rs and communication range Rc = 2Rs.
- Each sensor knows its location by a certain mechanism, such as Global Positioning System (GPS), and the location information can be sent to the base station (BS).
- Mobile sensor nodes are able to move to the scheduled positions, where the scheduled positions are within their mobility range.
- The proposed algorithm is implemented in a centralized architecture, and the BS is responsible for the execution of the algorithm and broadcasting the movement plan of mobile sensors.
3.2. Problem Formulation
3.3. Phase I: The Coverage-Enhancing Algorithm Based on Differential Evolution (CEADE)
3.3.1. Coding and Initialization
3.3.5. Termination Condition
3.4. Phase II: Refinement
- Reduce the number of mobile sensor nodes that need to be moved. Since our DE algorithm searches for target positions of all mobile sensors simultaneously, the sensing areas of some sensors may be overlapping when they are located in their candidate target positions. The sensing areas of some mobile sensors may even be fully covered by those of the other sensors. In that case, such mobile sensors can be viewed as redundant nodes if they move to their candidate target positions, which means they do not need to move at the very beginning. As shown in Figure 1, small black solid circles represent sensor nodes and large gray solid circles represent the sensing areas of sensors. When sensor si moves from Pi0 to Pi1, the regional coverage rate Rarea(S) has no change, so we can infer that sensor si does not need to move. The number of mobile sensors that need to be moved can be reduced by this means, which can reduce the total moving distance of the mobile sensors.
- Exchange the candidates’ target positions of two mobile sensor nodes if this can reduce the total moving distance of mobile sensors. Figure 2a shows that the total moving distance of si and sj is d1 + d2 before exchanging the total moving distance, while Figure 2b shows that the total moving distance is d3 + d4 after exchange. Since d1 + d2 > d3 + d4, the total moving distance of si and sj can be reduced after the exchange of the candidate target positions. Furthermore, the coverage area of the sensor network will not change after such an exchange, but the area coverage-distance rate will increase.
- Replace the movement of the mobile sensor node that needs to move by that of a substitute mobile sensor node that does not need to move. The goal of this step is to avoid making a mobile sensor move for a long distance because moving a sensor for a long distance consumes too much energy. If the sensor is out of power shortly after it reaches the destination, this movement is wasted and another mobile sensor has to be found and relocated . The condition of the replacement is that the movement can reduce the total moving distance but without reducing the coverage area of the sensor network. As shown in Figure 3a, sensor si does not need to move, and sensor sj is planned to move from Pj0 to Pj1. Let A1 be the coverage area of the sensor network in Figure 3a after sensor sj moves from Pj0 to Pj1, and A2 be the coverage area of the sensor network in Figure 3b after sensor si moves from Pi0 to Pj1 but sj remains static. Since A2 ≥ A1 and d3 < d2, the algorithm will make sensor si instead of sj move to the candidate target position of sensor sj while sensor sj remains static. This replacement neither reduces the coverage area of the sensor network, nor increases the number of mobile sensors needed to move. Instead, it reduces the average moving distance of mobile sensors and thus improves the area coverage–distance rate.
|Algorithm 1. Pseudocode for the moving distance reduction scheme.|
| /* Pi0(xi0,yi0) and Pi1(xi1,yi1) are the initial position and the candidate target position of the ith mobile sensor si, i = 1, …, m. */|
1. For i = 1 to m do
2. moved[i] = true
3. For i = 1 to m do
4. P = Pi1, Pi1 = Pi0
5. If (Rarea(S) reduces) Pi1 = P; moved[i] = false;
7. For i = 1 to m do
8. For j = 1 to m do
9. d1 = , d2 = , d3 = , d4 = .
10. If (i ≠ j) and (moved[i]) and (moved[j]) and (d1 + d2 > d3 + d4)
13. For j: = 1 to m do
14. For i: = 1 to m do
15. d2 = , d3 =
16. if (moved[j]) and (not moved[i])
17. if (d2 > d3) P = Pj1,Pi1 = Pj1,Pj1 = Pj0
18. if (Rarea(S) reduces ) Pj1 = P; Pi1 = Pi0
4. Experimental Results
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|Number of Mobile Sensor Nodes||18||36||54||72||90||108||126|
|Number of static sensor nodes||42||84||126||168||210||252||294|
|Sensing range (m)||10||7||5.7||4.9||4.4||4||3.7|
|Communication range (m)||20||14||11.4||9.8||8.8||8||7.4|
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