experimental results - optlwpage.unina.it/claudio.sterle/experimentation-optl... · 2016-01-21 ·...

Operations Research Group - University "Federico II" of Naples

Contacts: [email protected], [email protected]

Experimental Results

for omni-directional and directional sensor network in two and three dimensional coverage problems

(accepted for publication on Optimization Letter

Claudio Sterle*, Antonio Sforza

[email protected] * Department of Electrical Engineering and Information Technology, University "Federico II" of Naples, Via Claudio 21, 80125, Naples, Italy + Department of Industrial Engineering, University "Federico II" of Naples, Piazzale Tecchio, 80125, Naples, Italy - This document integrates the experimental result section reported in the paper approach for omni-directional and problems" accepted for publication on Optimization Leand the results of the coverage models with additional constraints - The interested reader is addressed to the paper for the notation and parameter definition.- The input data of the tested instances cannot be published for privacy reasons but can be provided by the authors on request. Abstract The problem of designing a region of interest by has been widely treated in literature. This problem is referred to in literature as the sensor placement problem (SPP) and in the most generalthe location of one or more kind of sensors with the aim of covering all the region of interest or a significant part of it. In this paper we propose a unified and stepwise solving approach for two and threcoverage problems to be used for omni The proposed approach is based on schematizing the region of interest and the sensor potential locations by a grid of points and representing the sensor cove On this basis, the SPP reduces to an optimal coverage problem and can be formulated by integer linear programming (ILP) models. We will resume the main also a discussion on some straight extensions and variants which allow to take into account the specific features of the sensors, related monitoring tasks and strategic decisions in some hints to effectively use the proposed approach. The paper concludes with an application of the proposed approach to a real test case and a discussion of the obtained results.

University "Federico II" of Naples


Experimental Results

A unified approach

directional and directional sensor network in two and three dimensional coverage problems

accepted for publication on Optimization Letter

, Antonio Sforza*, Annunziata Esposito Amideo*, Carmela Piccolo

claudio.sterle@unina, [email protected],

[email protected], [email protected]

Department of Electrical Engineering and Information Technology, University "Federico II" of Naples, Via Claudio 21,

Department of Industrial Engineering, University "Federico II" of Naples, Piazzale Tecchio, 80125, Naples, Italy

This document integrates the experimental result section reported in the paper directional and directional sensor network in two and three dimensional coverage

accepted for publication on Optimization Letter. In particular the results of the 2D case and the results of the coverage models with additional constraints in the 3D case

The interested reader is addressed to the paper for the notation and parameter definition.The input data of the tested instances cannot be published for privacy reasons but can be provided

The problem of designing a wireless sensor network (WSN) to cover, monitor and/or control a region of interest by has been widely treated in literature. This problem is referred to in literature as the

) and in the most general case it consists in determining the number and the location of one or more kind of sensors with the aim of covering all the region of interest or a

In this paper we propose a unified and stepwise solving approach for two and threcoverage problems to be used for omni-directional and directional sensor networks.

The proposed approach is based on schematizing the region of interest and the sensor potential locations by a grid of points and representing the sensor coverage area by a circle or by a circle sector.

reduces to an optimal coverage problem and can be formulated by integer ) models. We will resume the main ILP models used in our approach, providing

ion on some straight extensions and variants which allow to take into account the specific features of the sensors, related monitoring tasks and strategic decisions in WSN design. Moreover we give some hints to effectively use the proposed approach.

aper concludes with an application of the proposed approach to a real test case and a

directional and directional sensor network in two and three dimensional coverage problems

accepted for publication on Optimization Letter)

, Carmela Piccolo+

Department of Electrical Engineering and Information Technology, University "Federico II" of Naples, Via Claudio 21,

Department of Industrial Engineering, University "Federico II" of Naples, Piazzale Tecchio, 80125, Naples, Italy

This document integrates the experimental result section reported in the paper "A unified directional sensor network in two and three dimensional coverage

In particular the results of the 2D case in the 3D case are reported.

The interested reader is addressed to the paper for the notation and parameter definition. The input data of the tested instances cannot be published for privacy reasons but can be provided

) to cover, monitor and/or control a region of interest by has been widely treated in literature. This problem is referred to in literature as the

case it consists in determining the number and the location of one or more kind of sensors with the aim of covering all the region of interest or a

In this paper we propose a unified and stepwise solving approach for two and three dimensional directional and directional sensor networks.

The proposed approach is based on schematizing the region of interest and the sensor potential rage area by a circle or by a circle sector.

reduces to an optimal coverage problem and can be formulated by integer models used in our approach, providing

ion on some straight extensions and variants which allow to take into account the specific design. Moreover we give

aper concludes with an application of the proposed approach to a real test case and a



1. Real case description The unified approach for the sensor placement problem presented in the work "A unified approach for omni-directional and directional sensor network in two and three dimensional coverage problems" (to be published in Optimization Letter) has been experienced on a real indoor 2D and 3D case related to a railway station located in the west area of Naples. In particular the aim was to design a video sensor networks to monitor the entire public area of the station (hence offices and private areas have not been taken into account). It is important to highlight that this work proceeds what has been done by the authors during the METRIP project (Methodological Tool for Railway Infrastructure Protection). The interested reader is referred to: - Sforza et al. (2013). DOI: 10.1007/978-3-319-03964-0_17; - Sforza et al. (2015). DOI: 10.1007/978-3-319-04426-2_9; - Marrone et al (2015). DOI:10.1007/978-3-319-04426-2_10. In these works, experimental results related to other sample test cases are reported. The region of interest has been schematized by a parallelepiped of dimensions 75 m, 35 m and 5 m. A representation of the plant of the RI is reported in Figure 1, where the violet box highlights the public area under investigation (Figure 2). The black boxes in Figure 2 are used to indicate the offices and private areas which are not taken into account for privacy reasons. In the construction of the G grid of the RI we used three different values of the step size along the length (x axis) and along the width (y axis): 2.5, 5 and 10. Concerning the height, for the 3D case, we choose just three planes to be monitored: ground floor, 1 m floor and 1,7 m floor.

Figure 1. Railway station plant and region of interest.



Figure 2. Railway station plant and privacy zones.

We considered as important points all the ones in these planes corresponding to doors and windows, stairs, escalators and turnstiles. Moreover we considered as important all the points located along the yellow lines of the four tracks present in the station. All these points have to be always covered by at least one sensor. Moreover it is important to recall that turnstiles have to be frontally covered by a camera located at a maximum distance of 5 m; yellow lines have to covered by a camera orthogonally located and "looking" in the opposite way with respect to train travel direction. In the construction of the L grid we used the same step size k adopted for the RI discretization. Concerning the height of the sensors we used as possible values just the ones imposed by the security legislation in dependence of the target to be covered (generally 2,80 m). The sensors to be placed were characterized by the following parameters: R =25 m; θ = 90°; θ = 45° (hence we considered 8 orientations with overlapping coverage areas). The tilt angle β has been considered as fixed and equal to 45° in all the 5-tuples.



2. Experimentation The complete procedure and the coverage algorithm has been implemented in Java language and the coverage ILP models have been solved to optimality by the optimization software FICOTM Xpress-MP 7.6. The procedure has been run on an Intel® CoreTM i7, 870, 2.93 GHz, 4GB RAM, Windows VistaTM 64 bit. We tested the procedure considering the four covering problems of the paper: SCP, WDCP, MCP and BCP. In the following we report the following results: - 2.1 Coverage without HD effect (2D); - 2.2 Coverage with HD effect (3D); - 2.3 Coverage with mutual distance constraints among the sensors (3D); - 2.4 Coverage of important points (yellow line, turnstiles and stairs) (3D). We finally report the results taking into account all the features of the problem under investigation. It is important to highlight that the results reported in 2.1 are the ones obtained in the 2D case. The ones related to the 3D case are reported in the paper. Instead the results reported in 2.2 to 2.5 are related just to the 3D case and we do not report the information about the related computation time. This choice is motivated by the fact that the tackled real case is described by a coverage matrix of small and medium size. Hence we solved the related instances to optimality with limited and acceptable computation time by Xpress-MP 7.6 (no more than 600 seconds). In any case, for the sake of the completeness, we report a graphical representation of the obtained solutions (representation have been made using mmive module of Xpress-MP). It is important to highlight that, regardless the sizes of the problem under investigation (2D or 3D) all the representations are in two dimensions since the mmive module of Xpress-MP does not support 3D representations. 2.1 Coverage without HD effect Table 1 reports the results of SCP and WDCP. Figures 3 - 5 provide a representation of some solutions. Table 2 reports the results of the MCP. Figures 6 - 8 provide a representation of some solutions. Table 3 reports the results of the BCP. Figures 9 - 11 provide a representation of some solutions

SCP G' OS Covered Points % Cov CPU time (s)

G step=2.5 L step=2.5

3728 x 550 7 550* 100 %* 6.9


1336 x 188 7 188* 100 %* 2.2

G step=10 L step=5.0

816 x 176 7 176* 100 %* 0.2

WDCP (γ = 0.5) G' OS Covered Points % Cov CPU time (s)


3728x550 6 494 89.8% 10


1336x188 6 170 93.1 % 0.8

G step=10 L step=5.0

816x176 6 159 90.3 % 0.2

Table 1: Results of SCP and WDCP.



Figure 3.a.

Figure 3.b.

Figure 3. a) SCP solution with G and L step equal to 2.5. b) WDCP solution with G and L step equal to 2.5.



Figure 4.a.

Figure 4.b.

Figure 4. a) SCP solution with G and L step equal to 5. b) WDCP solution with G and L step equal to 5.



Figure 5.a.

Figure 5.b.

Figure 5. a) SCP solution with G step equal to 10 and L step equal to 5. b) WDCP solution G step equal to 10 and L step

equal to 5.

MCP p G' Covered points % Cov CPU time (s)

G step = 2.5 L step = 2.5

5 3728x550

463 84.1 % 5.2

6 503 91.4% 5.9 7 550 100% 9.1

G step = 5 L step = 5

5 1336x188

No feasible integer solution

0.5

6 176 93.6 % 1.6 7 188 100% 0.4


5 816x176


0.3

6 163 92.6 % 0.2 7 176 100% 0.2

Table 2: Results of MCP.



Figure 6.a.

Figure 6.b.

Figure 6.c.

Figure 6. Solution of MCP with G and L step equal to 2.5. a) p=5; b) p=6; c) p=7.



Figure 7.a.

Figure 7.b.

Figure 7. Solution of MCP with G and L step equal to 5. a) p=6; b) p=7.



Figure 8.a.

Figure 8.b.

Figure 8. Solution of MCP with G step equal to 10 and L step equal to 5. a) p=6; b) p=7.

BCP (ε = 0.4)

P G' Covered Points % Cov M-covered

points % M-Cov

CPU time (s)

G step = 2.5 L step = 2.5

5 3728x550

452 82.2 56 10.2 12.9

6 462 84 197 35.8 22.7 7 493 89.6 246 44.7 33.8


5 1336x188


No feasible

integer solution

5.2

6 169 89.9 60 31.9 8.6 7 174 92.5 90 47.9 9.3


5 816x176


No feasible

integer solution

5.1

6 159 92.6 48 27.3 4.1 7 160 90.9 78 44.3 6.1

Table 3: Results of BCP.



Figure 9.a.

Figure 9.b.

Figure 9.c.

Figure 9. Solution of BCP with G and L step equal to 2.5. a) p=5; b) p=6; c) p=7.



Figure 10.a.

Figure 10.b.

Figure 10. Solution of BCP with G and L step equal to 5. a) p=6; b) p=7.



Figure 11.a.

Figure 11.b.

Figure 11. Solution of BCP with G step equal to 10 and L step equal to 5. a) p=6; b) p=7.



2.2 Coverage with HD effect In the following we will focus on the most interesting case, i.e. the one with G and L step both equal to 2.5, and we will provide the graphical representation of the obtained solutions. This allows us to show the differences between the solutions obtained without taking into account additional features of the problem (previous section) and the ones with the integration of the new features. Figure 12 show the solutions obtained by the four coverage models in case of sensors with HD effect (5 m). For the MCP and BCP the number of sensors p is equal to 7.

Figure 12.a.

Figure 12.b.

Figure 12 (a-b). Solutions of the coverage models with HD effect. a) SCP; b) WDCP.



Figure 12.c.

Figure 12.d.

Figure 12 (c-d). Solutions of the coverage models with HD effect. c) MCP; d) BCP.



2.3 Coverage with mutual distance constraints among the sensors; In the following we will focus on the most interesting case, i.e. the one with G and L step both equal to 2.5, and we will provide the graphical representation of the obtained solutions. This allows us to show the differences between the solutions obtained without taking into account additional features of the problem (previous section) and the ones with the integration of the new features. Figure 13 show the solutions obtained by the four coverage models in case mutual distance constraints among the sensors are taken into account (10 m). For the MCP and BCP the number of sensors p is equal to 7. These instances are more difficult than the previous ones but they have been solved with a maximum computation time of 600 seconds

Figure 13.a.

Figure 13.b.

Figure 13 (a-b). Solutions of the coverage models with mutual distance constraints among the sensors.

a) SCP; b) WDCP.



Figure 13.c.

Figure 13.d.

Figure 13 (c-d). Solutions of the coverage models with mutual distance constraints among the sensors. c) MCP; d) BCP.

2.4 Coverage of important points. Yellow line: In order to have the coverage of the yellow line and in order to use ad-hoc algorithms for "line crossing", we have to locate dedicated sensors. These sensors have to be located along the line and have to look in the opposite way with respect to the train travelling direction. Moreover to make the algorithm effective, the maximum distance between the sensor and the farthest point to be controlled has to be lower than or equal to 25 m. Figure 14 reports the solution to be implemented in case we want to control just the yellow line of the station. Figure 15 show the solutions obtained by the four coverage models in case we integrate them with the constraints related to the coverage of the yellow lines. For the MCP and BCP the number of sensors p is equal to 12.



Figure 14. Sensor location for yellow line control.

Figure 15.a.

Figure 15.b.

Figure 15 (a-b). Solutions of the coverage integrating yellow line control constraints: a) SCP; b) WDCP.



Figure 15.c.

Figure 15.d.

Figure 15 (c-d). Solutions of the coverage integrating yellow line control constraints: c) MCP; d) BCP.

Turnstiles and stairs Turnstiles and stairs have be controlled using dedicated sensors which looks these points frontally. Moreover, in order to use face recognition algorithms, their distance to the target has to be lower than 5 meters.

Figure 16 shows the solutions to be implemented in case we want to control just the stairs and the

turnstiles of the area under investigation. Figure 17 show the solutions obtained by the four coverage models in case we integrate them with all the previous constraints. For the MCP and BCP the number of sensors p is equal to 17.



Figure 16. Sensor location for turnstiles and stairs control

Figure 17.a.

Figure 17.b.

Figure 17 (a-b). Solutions of the coverage models integrating all the additional constraints: a) SCP; b) WDCP.



Figure 17.c.

Figure 17.d.

Figure 17 (c-d). Solutions of the coverage models integrating all the additional constraints: c) MCP; d) BCP.

experimental results - optlwpage.unina.it/claudio.sterle/experimentation-optl... · 2016-01-21 ·...

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