Skip to main content
SpringerLink
Log in

Global Optimization Approaches to Sensor Placement: Model Versions and Illustrative Results

  • Chapter
  • First Online:
Modeling and Optimization in Space Engineering

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 73))

  • 2494 Accesses

Abstract

We investigate the optimized configuration of sensor cameras to be placed in a suitably defined three-dimensional cubic region E, in order to maximize the coverage of a completely embedded cube C⊂E. The sensing regions associated with each of the cameras are convex, but not necessarily identical. In order to handle this important practical problem, we present mixed integer linear programming (MILP) and mixed integer nonlinear programming (MINLP) model formulations and propose corresponding solution approaches. Illustrative numerical results are presented, and certain application aspects are also discussed.

MSC Classification (2000) 68T20, 90C11, 90C30, 90C59, 90C90

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Abrams, Z., Goel, A., Plotkin, S.: Set k-cover algorithms for energy efficient monitoring in wireless sensor networks. In: Proceedings of the 3rd International Symposium on Information Processing in Sensor Networks, Berkeley, CA, USA, 26–27 April 2004, pp. 424–432 (2004)

    Google Scholar 

  2. Altınel, I.K., et al.: Effective coverage in sensor networks: binary integer programming formulations and heuristics. In: Proceedings of the IEEE International Conference on Communications (ICC'06), vol. 9, pp. 4014–4019. Istanbul, Turkey, 11–15 June 2006

    Google Scholar 

  3. Akyildiz, I.F., et al.: Wireless sensor networks: a survey. Comput. Netw.: Int. J. Comput. Telecommun. Netw. 38(4), 393–422 (2002)

    Google Scholar 

  4. Alam, S.M., Haas, Z.J.: Coverage and connectivity in three-dimensional networks. In: Proceedings of MobiCom’06, Los Angeles, CA, USA, 23–29 Sept 2006

    Google Scholar 

  5. Barbosa, J., et al.: Optimal camera placement for total coverage. In: Proceedings of the 2009 I.E. international conference on Robotics and Automation, Kobe, Japan, 12–17 May 2009, pp. 3672–3676 (2009)

    Google Scholar 

  6. Berry, J., et al.: Sensor placement in municipal water networks with temporal integer programming models. J. Water Resour. Plann. Manage. 132(4), 218–224 (2006)

    Article  Google Scholar 

  7. Biswas, P., Ye, Y.: Semidefinite programming for ad hoc wireless sensor network localization. In: Proceedings of the 3rd International Symposium on Information Processing in Sensor Networks (IPSN ’04), pp. 46–54. Berkeley, CA, USA, 26–27 April 2004. (2009)

    Google Scholar 

  8. Bomze, I.M., et al. (eds.): Developments in Global Optimization. Kluwer, Dordrecht (1997)

    MATH  Google Scholar 

  9. Buczak, A.L., et al.: Genetic algorithm convergence study for sensor network optimization. Inf. Sci. Inf. Comput. Sci. 133(3–4), 267–282 (2001)

    MATH  Google Scholar 

  10. Cardei M., et al.: Energy-efficient target coverage in wireless sensor networks. In: Proceedings of the 24th Annual Joint Conference of the IEEE Computer and Communication Societies (INFOCOM), vol. 3, pp. 1976–1984. Miami, FL, USA, 13–17 March 2005

    Google Scholar 

  11. Cerpa, A., et al.: Habitat monitoring: application driver for wireless communications technology. Comput. Comm. Rev. 31(2) (2001). Supplement

    Google Scholar 

  12. Chakrabarty, K., et al.: Grid coverage for surveillance and target location in distributed sensor networks. IEEE Trans. Comput. 51(12), 1448–1453 (2002)

    Article  MathSciNet  Google Scholar 

  13. Chen, F., Jiang, P., Xue, A., et al.: An algorithm of coverage control for wireless sensor networks in 3d underwater surveillance systems. In: Huang, D.S. (ed.) ICIC 2008, LNCS 5226, pp. 1206–1213. Springer, Berlin (2008)

    Google Scholar 

  14. Drezner, Z., Suzuki, A.: Covering continuous demand in the plane. J. Oper. Res. Soc. 61, 878–881 (2010)

    Article  MATH  Google Scholar 

  15. Dhillon, S.S., Chakrabarty, K., Iyengar, S.S.: Sensor placement for grid coverage under imprecise detections. In: Proceedings of the International Conference on Information Fusion, pp. 1581–1587. Annapolis, MD, USA, 8–11 July 2002

    Google Scholar 

  16. Dhillon, S.S., Chakrabarty, K.: Sensor placement for effective coverage and surveillance in distributed sensor networks. In: Proceedings of the IEEE Wireless Communications and Networking Conference, pp 1609–1614. New Orleans, LA, USA, 16–20 March 2003

    Google Scholar 

  17. Erdem, U., Sclaroff, S.: Optimal placement of cameras in floor-plans to satisfy task requirements and cost constraints. In: OMNIVIS Workshop, pp. 30–41. Prague, Czech Republic, 16 May 2004

    Google Scholar 

  18. Fleishman, S., Cohen-Or, D., Lischinski, D.: Automatic camera placement for image-based modeling. Comput. Graphics Forum 19(2), 101–110 (2000)

    Article  MATH  Google Scholar 

  19. Fusco, G., Gupta, H.: Selection and orientation of directional sensors for coverage maximization. In: Proceedings of the 6th Annual IEEE Communications Society Conference on Sensor, Mesh and Ad Hoc Communications and Networks, pp. 556–564. Rome, Italy, 22–26 June (2009)

    Google Scholar 

  20. Gao, J.F., Shi, Y.J.: A simple coverage-evaluating approach for wireless sensor networks with arbitrary sensing areas. Inform. Process. Lett. 106(4), 159–161 (2008)

    Article  MathSciNet  Google Scholar 

  21. Gentile, C.: Distributed sensor location through linear programming with triangle inequality constraints. IEEE Trans. Wireless Comm. 6(7), 2572–2581 (2007)

    Article  Google Scholar 

  22. Harada, J., Shioda, S., Saito, H., Path: Coverage properties of randomly deployed sensors with finite data-transmission ranges. Comput. Netw.: Int. J. Comput. Telecommun. Netw. 53(7), 1014–1026 (2009)

    MATH  Google Scholar 

  23. Horst, R., Pardalos, P.M. (eds.): Handbook of Global Optimization, 1st edn. Kluwer, Dordrecht (1995)

    MATH  Google Scholar 

  24. Horst, R., Tuy, H.: Global Optimization: Deterministic Approaches. Springer, Berlin (1996)

    MATH  Google Scholar 

  25. Hörster, E., Lienhart, R.: On the optimal placement of multiple visual sensors. In: Proceedings of the 4th ACM international Workshop on Video Surveillance and Sensor Networks (VSSN ’06), Santa Barbara, California, USA, 27 Oct 2006. ACM, New York (2002)

    Google Scholar 

  26. Howard, A., Mataric, M.J., Sukhatme, G.S.: Mobile sensor network deployment using potential fields: a distributed, scalable solution to the area coverage problem. In: Proceedings of the International Symposium on Distributed Autonomous Robotics Systems (DARS02), pp 299–308. Fukuoka, Japan, 25–27 June 2002

    Google Scholar 

  27. Huang CF, Tseng YC, Lo LC (2004) The coverage problem in three-dimensional wireless sensor networks. In: Global Telecommunications Conference 2004 (GLOBECOM ’04 IEEE), vol. 5, pp. 3182–3186. Dallas, Texas, Nov 29–Dec 3, 2004

    Google Scholar 

  28. IBM Corporation: ILOG CPLEX Optimizer. In: High Performance Mathematical Optimization Engines. IBM Corporation Software Group, Route 100 Somers, NY, USA. WSD14044-USEN-01 (2010)

    Google Scholar 

  29. Kang, C.W., Golay, M.W.: An integrated method for comprehensive sensor network development in complex power plant systems. Reliability Eng. Syst. Safety 67, 17–27 (2000)

    Article  Google Scholar 

  30. Lazos, L., Poovendran, R.: Stochastic coverage in heterogeneous sensor networks. ACM Trans. Sensor Netw. 2(3), 325–328 (2006)

    Article  Google Scholar 

  31. Li, D., Sun, X.: Nonlinear Integer Programming. Springer, New York (2006)

    MATH  Google Scholar 

  32. Liberti, L., Maculan, N. (eds.): Global Optimization: From Theory to Implementation. Springer, New York (2005)

    Google Scholar 

  33. Meguerdichian, S., et al.: Coverage problems in wireless ad-hoc sensor networks. In: Proceedings of the INFCOM 2001 Conference, pp. 1380–1387. Anchorage, Alaska, USA, 22–26 April 2001

    Google Scholar 

  34. Meguerdichian, S., Potkonjak, M.: Low power 0/1 coverage and scheduling techniques in sensor networks. Technical Report 030001, Computer Science Department, University of California Los Angeles (2003)

    Google Scholar 

  35. Miorandi, D., Altman, E.: Coverage and connectivity of ad hoc networks in presence of channel randomness. In: Proceedings of IEEE INFOCOM ’05, pp. 491–502. Miami, USA, 13–17 March 2005

    Google Scholar 

  36. Mittal, A., Davis, L.: Visibility analysis and sensor planning in dynamic environments. In: 8th European Conference on Computer Vision (ECCV 2004), vol. 1, pp. 175–189. Prague, Czech Republic, 11–14 May 2004

    Google Scholar 

  37. Mockus, J., et al.: Bayesian Heuristic Approach to Discrete and Global Optimization. Kluwer, Dordrecht (1996)

    Google Scholar 

  38. Molina, A., Athanasiadou, G.E., Nix, A.R.: The automatic location of base-stations for optimised cellular coverage: a new combinatorial approach. In: IEEE 49th Vehicular Technology Conference, vol. 1, pp. 606–610. Houston, Texas, USA, 16–20 May 1999

    Google Scholar 

  39. Nowak, I.: Relaxation and Decomposition Methods for Mixed Integer Nonlinear Programming. Springer, New York (2005)

    MATH  Google Scholar 

  40. Onur, E., et al.: Coverage in sensor networks when obstacles are present. In: Proceedings of the IEEE International Conference on Communications (ICC ‘06), vol. 9, pp. 4077–4082. Istanbul, Turkey, 11–15 June 2006

    Google Scholar 

  41. Pardalos, P.M., Romeijn, H.E.: Handbook of Global Optimization, 2nd edn. Kluwer, Dordrecht (2002)

    MATH  Google Scholar 

  42. Pintér, J.D.: Global Optimization in Action. Kluwer, Dordrecht (1996)

    MATH  Google Scholar 

  43. Pintér, J.D.: Global optimization: software, test problems, and applications. In: Pardalos, P.M., Romeijn, H.E. (eds.) Handbook of Global Optimization, 2nd edn, pp. 515–569. Kluwer, Dordrecht (2002))

    Google Scholar 

  44. Pintér, J.D.: Software development for global optimization. In: Pardalos, P.M., Coleman, T.F., (eds.) Global Optimization: Methods and Applications, pp. 183–204. Fields Institute Communications vol. 55. Published by the American Mathematical Society, Providence, RI (2009)

    Google Scholar 

  45. Pottie, G.J., Kaiser, W.J.: Wireless integrated network sensors. Comm. ACM 43, 51–58 (2000)

    Article  Google Scholar 

  46. Rowe, E.G., Wettergren, T.A.: Coverage and reliability of randomly distributed sensor systems with heterogeneous detection range. Int. J. Distrib. Sensor Netw. 5(4), 303–320 (2009)

    Article  Google Scholar 

  47. Sahni, S., Xu, X.: Algorithms for wireless sensor networks. Int. J. Distrib. Sensor Netw. 1(1), 35–56 (2005)

    Article  Google Scholar 

  48. Shen, C., Srisathapornphat, C., Jaikaeo, C.: Sensor information networking architecture and applications. IEEE Personal Comm. 8(4), 52–59 (2001)

    Article  Google Scholar 

  49. So, A.M., Ye, Y.: Theory of semidefinite programming for sensor network localization. Math. Program. 109(2), 367–384 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  50. Sorokin, A., et al.: Mathematical programming techniques for sensor networks. Algorithms 2, 565–581 (2009)

    Article  Google Scholar 

  51. Stoyan, Y.G., Romanova, T.Y.: Mathematical models of placement optimisation: two- and three-dimensional problems and applications. In: Fasano, G., Pintér, J.D. (eds.) Modeling and Optimization in Space Engineering. Springer, New York (2013)

    Google Scholar 

  52. Strongin, R.G., Sergeyev, Y.D.: Global Optimization with Non-convex Constraints. Kluwer, Dordrecht (2000)

    MATH  Google Scholar 

  53. Tawarmalani, M., Sahinidis, N.V.: Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming. Kluwer, Dordrecht (2002)

    MATH  Google Scholar 

  54. Venkatesh, S., Buehrer, R.M.: A linear programming approach to NLOS error mitigation in sensor networks. In: Proceedings of the 5th International Conference on Information processing (IPSN ’06), pp. 301–308. Nashville, TN, USA, 19–21 April 2006

    Google Scholar 

  55. Xing, G., et al.: Integrated coverage and connectivity configuration for energy conservation in sensor networks. ACM Trans. Sensor Netw. 1(1), 36–72 (2005)

    Article  Google Scholar 

  56. Wang, H.B., Yao, K., Erstrin, D.: Information-theoretic approaches for sensor selection and placement in sensor networks for target localization and tracking. J. Commun. Networks 7(4), 438–449 (2005)

    Google Scholar 

  57. Yao, Y., et al.: Can you see me now? Sensor positioning for automated and persistent surveillance. IEEE Trans. Syst. Man Cybernetics, Part B: Cybernetics 40(1), 101–115 (2010)

    Article  Google Scholar 

  58. Zabinsky, Z.B.: Stochastic Adaptive Search for Global Optimization. Kluwer, Dordrecht (2003)

    MATH  Google Scholar 

  59. Zhang, M., Du, X., Nygard, K.: (2005) Improving coverage performance in sensor networks by using mobile sensors. In: Proceedings of the Military Communications Conference (MILCOM 2005), vol. 5, pp. 3335–3341. Atlantic City, NJ, USA, 17–20 Oct 2005

    Google Scholar 

  60. Zou, Y., Chakrabarty, K.: Sensor deployment and target localization in distributed sensor networks. ACM Trans. Embed. Comput. Syst. 3(1), 61–91 (2004)

    Article  Google Scholar 

  61. Zou, Y., Chakrabarty, K.: Uncertainty-aware and coverage-oriented deployment for sensor networks. J. Parallel Distrib. Comput. 64(7), 788–798 (2004)

    Article  Google Scholar 

  62. Zou, Y., Chakrabarty, K.: A distributed coverage- and connectivity-centric technique for selecting active nodes in wireless sensor networks. IEEE Trans. Comput. 54(8), 978–991 (2005)

    Article  Google Scholar 

Download references

Acknowledgments

Thanks are due to Stefano Gliozzi (Business Consulting Services, IBM) for useful discussions related to the subject and for his valuable support of our related experimental analysis and results.

Author information

Authors and Affiliations

  1. Thales Alenia Space Italia S.p.A., Str. Antica di Collegno 253, 10146, Turin, Italy

    Giorgio Fasano

  2. Pintér Consulting Services Inc., Halifax, Canada

    János D. Pintér

Authors
  1. Giorgio Fasano
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. János D. Pintér
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Giorgio Fasano .

Editor information

Editors and Affiliations

  1. Thales Alenia Space SpA, Str. Antica di Collegno 253, Turin, 10146, Italy

    Giorgio Fasano

  2. Stoneybrook Court 114, Halifax, B3M 3J7, Nova Scotia, Canada

    János D. Pintér

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer Science+Business Media New York

About this chapter

Cite this chapter

Fasano, G., Pintér, J.D. (2012). Global Optimization Approaches to Sensor Placement: Model Versions and Illustrative Results. In: Fasano, G., Pintér, J. (eds) Modeling and Optimization in Space Engineering. Springer Optimization and Its Applications, vol 73. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4469-5_10

Download citation

Publish with us

Policies and ethics

Search

Navigation