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Energy-Efficient Sensor Network Design Subject to Complete Coverage and Discrimination Constraints

Energy-Efficient Sensor Network Design Subject to Complete Coverage and Discrimination Constraints. Frank Y. S. Lin, P. L. Chiu IM, NTU SECON 2005. Presenter: Steve Hu. Outline. Problem Description Problem Formulation Solution Procedure Computational Results Conclusion.

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Energy-Efficient Sensor Network Design Subject to Complete Coverage and Discrimination Constraints

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  1. Energy-Efficient Sensor Network Design Subject to Complete Coverage and Discrimination Constraints Frank Y. S. Lin, P. L. Chiu IM, NTU SECON 2005 Presenter: Steve Hu

  2. Outline • Problem Description • Problem Formulation • Solution Procedure • Computational Results • Conclusion

  3. Problem Description • The detection radius of sensor is 1 • A complete coverage/discrimination sensor field with 3 by 5 grids

  4. Problem Description • Completely discriminated: unique power vector for each grid point • Ex: <1,0,0,0,0,0> for grid point (1,3) <0,0,1,1,0,0> for grid point (3,2)

  5. Problem Description • If we want to prolonged life time K times, two options: • (1) Deploy K duplicate sensor networks on a sensor field • (2)No duplicate sensor networks, but divide the network in K covers

  6. Overall placement Cover 1 Cover 2 Cover 3

  7. Problem Description No duplicate but divide in 3 covers Total sensor number: 14 Duplicate 3 times Total sensor number: 6 * 3 = 18

  8. Problem Description • Lemma 1 • Gr: the number of covering grids

  9. Problem Description • Lemma 2: A grid point can be covered by a set of sensors. The maximum cardinality of the set exactly equals the number of covering grid points of a sensor that is allocated in the grid point.

  10. Problem Description • Lemma 3: On rectangular sensor field with a finite area, the upper bound of the number of covers, Ur, is

  11. Problem Description • By Lemma 3

  12. Problem Formulation • Given Parameters: • A = {1,2,…,m}: The set of indexes for candidate locations where sensor can be allocated. • B = {1,2,…,n}: The set of the indexes for grid points that can be covered and located by the sensor network, m <= n • K: The number of covers required (with upper bound regards to radius) • aij: Indicator which is 1 if grid point i can be covered by sensor j, and 0 otherwise • cj: Cost function of sensor j

  13. Problem Formulation • Decision Variables: • Xjk: 1 if sensor j is designated to cover k of sensor network, and 0 otherwise • Yj: Sensor allocation decision variable, which is 1 if sensor j is allocated in the sensor network and 0 otherwise

  14. Problem Formulation • Objective function:

  15. Problem Formulation • Constraints: (Coverage Constraint) B: every grid point in the field aij: 1 if grid point i can be covered by sensor j, and 0 otherwise A: candidate sensor location

  16. Problem Formulation • Constraints: (Discrimination Constraint)

  17. Solution Procedure • Lagrangean Relaxation • a method for obtaining lower bounds (for minimization problems) • Ex:

  18. Solution Procedure • Lagrangean Relaxation ( ) with

  19. Solution Procedure • Lagrangean Relaxation ( ) • This (19.5) is the smallest upper bound we can found by Lagrangean Relaxation.

  20. Solution Procedure Original LR

  21. Solution Procedure Since there are two decision variable(Xjk, Yj) =>divide into two subproblem

  22. Solution Procedure Pjk Qj

  23. Solution Procedure • After optimally solving each Lagrangean relaxation problem (by subgradient method), a set of decision variables can be found, but may not feasible • Propose a heuristic algorithm for obtaining feasible solutions

  24. Solution Procedure

  25. Solution Procedure

  26. Solution Procedure

  27. Computational Results • algorithm tested on 10 by 10 sensor area

  28. Computational Results • algorithm tested on 10 by 10 sensor area

  29. Computational Results • algorithm tested on 10 by 10 sensor area 0.80 / 3 = 26.7%

  30. Computational Results • algorithm tested on 10 by 10 sensor area 80 / 40 = 2

  31. Computational Results • algorithm tested on 10 by 10 sensor area

  32. Computational Results • algorithm tested on 10 by 10 sensor area • The solution time of the algorithm is below 100 seconds in all cases. The efficiency of the algorithm thus can be confirmed.

  33. Computational Results • algorithm tested on different size of sensor area

  34. Conclusion • Proposed algorithm is truly novel and it has not been discussed in previous researches • Prolong the networking lifetime almost to theoretical upper bound

  35. Conclusion • My opinion and what I learned here • Algorithm description is too rough • An example to formulate a problem into integer programming • Use Lagangean Relaxation to obtain lower bounds for minimization problems

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