1. 1 Sensor Deployment –Sequential Deployment 1

2. Sequential Deployment Deploy one or more sensors Get Feedback from them Deploy another set And, so on Disadvantage : Takes long time to deploy a large number of them Needs expensive tools such as helicopter with mobile base station 2

3. SENSOR REPLACEMENT BASED ENERGY MAPPING 3

4. The problem A set of sensors S is deployed in a monitored field F(A)for a period of time T. The field is divided into a grid of cells A. Each cell is assigned a weight where represents the importance of the cell i. The location of each sensor is assumed known; More than one sensor could be deployed in one cell. Sensors are assumed heterogeneous in terms of their energy and mobility. 4

5. Assumptions A sensor could be in different states; it could have its sensing off or on based on the field monitoring requirements. Sensing off, radio off – (sleep mode) Sensing off, radio receiving – (Receiving mode) Sensing off, radio transmitting – (Routing mode) Sensing on, radio receiving – (Sensing and Receiving mode) Sensing on, radio transmitting – (Sensing and Transmitting mode) Sensing on, radio off - (Sensing mode) 5

6. The main idea Knowing the energy map of the network : Knowing the energy map of the network : May lead to early detection to the uncovered areas. Redeploy new sensors Turn off some of the sensors due to their coverage redundancy Wake up some of the nodes when needed Move one or mobile nodes to cover the required uncovered spots 6

7. Redeployment based Energy map Step 1: Step 1: Energy dissipation rate prediction Each sensor predicts its own energy rate based on its history (e.g. Markov Chain..) Step 2: Step 2: sensors send their initial energy and the location, predicted energy dissipation rate to the sink node through a cluster head. Sensors update their energy dissipation rate based on a specific threshold (if the new dissipation rate increased more than the given threshold, the node sends the new dissipation rate) 7

8. Redeployment based Energy map Step 3 Step 3: the sink node constructs the energy map based on the received dissipated energy rate from the sensors. The sink may move one of the mobile sensors to the uncovered spot or wake up one of the sleeping sensors 8

9. 9 Deployment Using Circle Packing

10. 10 Deployment Using Circle Packing Deployment of homogenous sensors Full Coverage Deployment Deployment of connected heterogeneous sensors

11. 11 Deployment of homogenous sensors sSensing rangeDensity 10.5000000000000.785398163397 20.2928932188130.539012084453 30.2543330950300.609644808741 40.2500000000000.785398163397 50.2071067811870.673765105566 60.1876806011470.663956909464 70.1744576301870.669310826841 80.1705406887010.730963825254 90.1666666666670.785398163397 140.1293317937100.735679255543 160.1250000000000.785398163397 250.1000000000000.785398163397 360.0833333333330.785398163397

12. 12 Full Coverage Deployment sSensor’s sensing range (r)s 10.70710678118654752440160.16942705159811602395 20.55901699437494742410170.16568092957077472538 30.55901699437494742410180.16063966359715453523 40.35355339059327376220190.15784198174667375675 50.32616058400398728086200.15224681123338031005 60.29872706223691915876210.14895378955109932188 70.27429188517743176508220.14369317712168800049 80.26030010588652494367230.14124482238793135951 90.23063692781954790734240.13830288328269767697 100.21823351279308384300250.13354870656077049693 110.21251601649318384587260.13176487561482596463 120.20227588920818008037270.12863353450309966807 130.19431237143171902878280.12731755346561372147 140.18551054726041864107290.12555350796411353317 150.17966175993333219846300.12203686881944873607

13. 13 Sequential Packing-based Deployment Algorithm (SPDA) Given Sensors Sensing Ranges Sensors Communication Ranges Bounded Monitored Field Objective Best Connected Deployment Scheme Max. Coverage. Min. Overlapped Areas Benefit from the properties learned from the optimal deployment

14. Sequential Packing-based Deployment Algorithm 14

15. Sequential Packing-based Deployment Algorithm 15

16. 16 Potential Points

17. 17 Correctness of the Algorithm

18. Optimization Techniques Mathematical / constraint Programming/ Integer Programming Mathematical / constraint Programming/ Integer Programming Genetic Algorithm Genetic Algorithm Simulated Annealing Simulated Annealing Network Analysis Network Analysis Branch & Bound Branch & Bound Tabu Search Tabu Search

19. Comparing IP and CP Complementary technologie s Integer programming Objective function: relaxations Constraint programming Feasibility: domain reductions Might need to experiment with both CP particularly useful when IP formulation is hard or relaxation does not give much information

20. Genetic Algorithms “ Genetic Algorithms are good at taking large, potentially huge search spaces and navigating them, looking for optimal combinations of things, solutions you might not otherwise find in a lifetime. ” - Salvatore Mangano Computer Design, May 1995

21. Genetic Algorithms Directed search algorithms based on the mechanics of biological evolution Developed by John Holland, University of Michigan (1970’s) To understand the adaptive processes of natural systems To design artificial systems software that retains the robustness of natural systems

22. Conceptual Algorithm

23. Genetic Algorithms Inspired by natural evolution Population of individuals Individual is feasible solution to problem Each individual is characterized by a Fitness function Higher fitness is better solution Based on their fitness, parents are selected to reproduce offspring for a new generation Fitter individuals have more chance to reproduce New generation has same size as old generation; old generation dies Offspring has combination of properties of two parents If well designed, population will converge to optimal solution

24. Crossover and Mutation Crossover Two parents produce two offspring There is a chance that the chromosomes of the two parents are copied unmodified as offspring There is a chance that the chromosomes of the two parents are randomly recombined (crossover) to form offspring Generally the chance of crossover is between 0.6 and 1.0 Mutation There is a chance that a gene of a child is changed randomly Generally the chance of mutation is low (e.g. 0.001)

25. Genetic Algorithms BEGIN Generate initial population; Compute fitness of each individual; REPEAT /* New generation /* FOR population_size Select two parents from old generation; /* biased to the fitter ones */ Recombine parents for two offspring; Compute fitness of offspring; Insert offspring in new generation END FOR UNTIL population has converged END

26. Basic Principles Coding or Representation String with all parameters Fitness function Parent selection (‘struggle for life’) Reproduction Crossover Mutation Convergence When to stop

27. Coding or Representation Representing the optimization problem in a gene and chromosome format Ex: deploy n sensors on m areas that maximizes the coverage. Can you represent the problem in a form of chromosome? Representation 1: Sensors are the genes and areas are the fillers Chromosome Size is? Representation 2: areas are the genes and the sensors are the fillers Chromosome Size is? s1s2s3s4…sn a3a5.. A1A2A3A4…Am s1s5..

28. Fitness function Defines the effectiveness of each chromosome. Ex. Maximizes the coverage s1s2s3s4…sn a3a5..

29. Simulated Annealing 29

30. Simulated Annealing Simulated Annealing (SA) is commonly said to be the oldest among the metaheuristics and surely one of the first algorithms that had an explicit strategy to avoid local minima. The fundamental idea is to allow moves resulting in solutions of worse quality than the current solution (uphill moves) in order to escape from local minima. The probability of doing such a move is decreased during the search.

31. Simulated Annealing The algorithm starts by generating an initial solution (either randomly or heuristically constructed) and by initializing the so-called temperature parameter T. The temperature T is decreased during the search process, thus at the beginning of the search the probability of accepting uphill moves is high and it gradually decreases, converging to a simple iterative improvement algorithm. This process is similar to the annealing process of metals and glass, which assume a low energy configuration when cooled with an appropriate cooling schedule. The search process shows that the algorithm is the result of two combined strategies: random walk and iterative improvement.

32. Simulated Annealing

33. Sensor Deployment on Critical Infrastructures 33

34. 34 Infrastructure (Monitored Fields) 34 Hot Spots Monitoring Requirements Monitoring Time (Horizon) Urgent monitoring Monitoring is must Monitoring is required Monitoring is Okay

35. 35 Infrastructure (Monitored Fields) 35 Hot Spots Monitoring Requirements Monitoring Time (Horizon) Urgent monitoring Monitoring is must Monitoring is required Monitoring is Okay

36. 36 The Deployment Problem Sensor Characteristics  Energy (Lifespan)  State-Switching (on/off)  Mobility  Mobility Cost  Sensing Range  Communication Range Monitored fields  Hot Spots  Coverage The Problem is to deploy the given sensors to: 1- Maximize the coverage 2- Maximize the security of the monitored field. 3- Exploit sensors capabilities  Monitoring time  Sensing Reliability Common Parameters 36

37. 37 Solutions Optimal Approach Evolution-Based Approaches Sensor Deployment 37

38. 38 The Problem Modeling  Set of Cells (Zones) Z  Weight for Each Zone  Monitoring time (Horizon) T 38  Energy (Lifespan)  Max. Allowed Number of Switching  Max Allowed Number of Moves  Mobility Cost  Sensing Reliability 35 610 57 208 407 80 t1t2t3

39. 39 The Mathematical Formulation : A binary variable to indicate if sensor s is serving zone i at time t 1 if sensor s is active 0 otherwise. : A binary variable to indicate if sensor s is inactive on zone i at time t 1 if s is inactive 0 otherwise. : A binary variable to indicate if sensor s is moved from zone i to zone j at time t 1 if s is moved 0 otherwise : A binary variable to indicate if sensor s is turned “On” on zone i at time t 1 if s is turned on 0 otherwise : A binary variable to indicate if sensor s is turned “Off” on zone i at time t 1 if s is turned on 0 otherwise

40. 40 Objective Function Maximize To Relate and Objective : Cover High Weights Zones by the Most Reliable Sensors Sensors either On or Off If a sensor is turned Off at time t in zone i, it Will be Off in the same zone at time t+1 If a sensor is turned On at time t in zone i and it was Off at t-1, assume it was Off in the same zone at time t-1 If a sensor was Off and also Off at t+1, it will stay Off in the same zone. If a sensor was Off at time t, then turned On at later time, assume it was Off at the Same zone

41. 41 Other Constraints Each sensor is used on one zone only Each zone is covered by one sensor only Assignment Constraints Mobility Constraints If both terms are 1, then there is a move Limit the number of mover to the Max per sensor Guarantee that one of the terms are 1

42. 42 Other Constraints Sensors Lifespan Constraint Sensors Switching Constraints

43. 43 Solutions Evolution Approaches 43

44. 44 Evolution-Based Approach Genetic Algorithms Chromosomes Crossover operators Mutation operator Stopping Criteria Simulated Annealing Solution Acceptance probability Stopping Criteria

45. Group Activity Think of a suitable representation to the problem using Genetic Algorithms

46. 46 Genetic Algorithms Chromosomes 000100100001 S1 S2 t1t2t1t2 z1 z2 z3  A chromosome is a string of bits (genes)  Its length is equal to number of sensors * number of zones * horizon  Each sensor pattern is a part from the chromosome  Chromosome representation is purposely selected for  multiple crossover and mutation operators  Example : 2 sensors, 3 zones, and 2 units of time

47. 47 Crossover Operators SingleChromosome Single Chromosome Time Exchange Time Exchange Sensor Exchange Sensor Exchange Multi-Chromosomes Multi-Chromosomes Time Exchange Time Exchange Sensors Exchange Sensors Exchange 000100100001 S1 S2 t1t2t1t2 z1 z2 z3 001010100100 S1 S2 t1t2t1t2 z1 z2 z3

48. 48 Mutation Operator  Number of genes to be flipped are randomly selected

49. 49 Correction Process  Generated chromosomes might violate the sensors feasibility constraints  Within a sensor  Can not serve on multiple zones at the same time  Sensors limitations must be considered  Among sensors  Zones cannot be monitored by more than one sensor

50. Stopping Criteria Coverage Percentage is reached Number of Iterations Number of Iterations without improvement in the fitness 50

51. Simulated Annealing 51

52. 52 Simulated Annealing 1. Generate an initial solution, evaluate its value (gain), and store it as the highest gain found so far. 2. Get a new solution by searching the neighborhood of the current solution. 3. Evaluate the gain of the new solution. 4. If the gain is greater than the highest gain found so far, accept it (uphill move). 5. If the gain of the new solution is less than the upper bound gain found so far, still accept this new inferior solution but with some probability (downhill move) 6. Decrease the probability of acceptance of inferior solutions (based on a temperature schedule) after every iteration (to help in convergence). 7. Repeat step 2 through 6, till the temperature approaches the highest value.

53. 53 Acceptance Probability Probability of acceptance of new solution given the solution Probability of acceptance of new solution (X k+1 ) given the solution (X k ) P(X k+1, X k ) = t1t2t3 Z10Z4Z2Z4Z30Z4Z2 s1s2s3s1s2s3s1s2s3 Solution StructureSolution Structure

54. Stopping Criteria Coverage Percentage is reached Number of Iterations Number of Iterations without improvement in the fitness 54