1. Designing of Cellular Mobile Networks Using Modern Heuristics
Thesis Presentation By
Abdul Subhan

2. Outline Introduction Background Problem Description
Implementation Approach
Experimental Analysis & Results
Conclusion & Future Work
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3. Introduction
Mobile telephones are used extensively in the world today and more than 500,000 new subscribers a month are joining GSM and PCS networks.
There are huge amount of subscribers, scarce existing network resources and intensive competition in the telecommunication market.
Having more efficient and demand adaptive network design is a key factor for survival of cellular mobile network providers today.
Upcoming applications of cellular mobile network systems for data communication (3G, 4G and UMTS) demand more optimum and flexible network structure.
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4. Introduction
The thesis deals with the designing an efficient cellular mobile network.
The focus is on designing the terrestrial access network.
The assignment of cells (BTS) to switches (BSC).
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5. Background
Merchant and Sengupta tried to solve the problem using deterministic algorithms and provided the basic formulation of the problem in their paper.
Their work proposed three heuristic solutions for the problem and showed that two of them perform extremely well.
Following on the same lines S. Pierre and F. Houeto extended the above work.
They solved the problem using tabu search, a non–deterministic iterative algorithm.
S. Menon and R. Gupta improved upon the work of S. Pierre and F. Houeto and provided results which were obtained in shorter durations.
They presented a hybrid heuristic, named Price Influenced Simulated Annealing (PISA), which integrated ideas from linear programming into a simulated annealing framework.
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6. Problem Description
Area of coverage is geographically divided into hexagonal cells.
Switches serving a given user could change if the user moves from his current cell.
The operation of detecting that a user has changed a cell and carrying out the required updates constitutes a hand-off.
User who moves from cell B to cell A causes a simple hand-off.
if a user moves from cell B to cell C, we are in the presence of a complex hand-off.
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7. Problem Statement
For a set of cells and switches (whose positions are known), accomplish the following:
Assign the cells to the switches in a way that minimizes the cost function.
The cost function integrates a component of link cost and a component of hand-off cost.
The assignment must take into account the switches capacity constraints that make them capable to host only a limited number of calls.
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8. Problem Formulation n : Number of cells. m : Number of switches.
hij : Cost per unit of time for hand-off.
cik : Link cost between cell ‘i’ & switch ‘k’.
λi : Number of calls per time unit destined to cell ‘i’.
Mk : Call processing capacity of switch ‘k’.
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9. Problem Formulation
Let n be the number of cells to be assigned to m switches.
Let us define a variable xik .
Zijk is equal to 1 if cells i and j, with i ≠ j, are both connected to the same switch k, otherwise 0.
Yij takes the value 1 if cells i and j are both connected to the same switches and 0 if cells i and j are connected to different switches.
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10. Problem Formulation – Cost Function
The goal is to minimize the cost function f.
Each cell must be assigned to only one switch.
The limited processing capacity of switches imposes a constraint.
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11. Problem Formulation – Port Constraint
The additional constraint is of the maximum number of ports, that are used for a cell’s BTS connectivity, on each switch.
The addition of constraint on the number of ports on a switch has immense practical significance.
In certain scenarios, the number of ports present may be less and the switch may still have enough processing capacity left.
But in certain other scenarios, the processing capacity may have been exhausted but a certain number of ports would still be available on the switch.
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12. Implementation Approach
The problem is solved using non-deterministic iterative heuristic algorithms.
Two algorithms were applied to the problem.
Simulated Annealing (SA).
Simulated Evolution (SimE).
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13. Simulated Annealing (SA)
It is a general adaptive heuristic and belongs to the class of non-deterministic algorithms.
One typical feature is that, besides accepting solutions with improved cost, it also, to a limited extent, accepts solution with deteriorated cost.
It is this feature that gives the heuristic the hill climbing capability.
Simulated annealing, like all other iterative techniques, is very greedy with respect to run time.
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14. SA - Algorithm
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15. SA - Metropolis Procedure
The core of the algorithm is the Metropolis procedure, which simulates the annealing process at a given temperature T.
The Metropolis procedure receives as input the current temperature T, and the current solution CurS which it improves through local search.
Metropolis is also be provided with the value M, which is the amount of time for which annealing must be applied at temperature T.
The SA algorithm simply invokes Metropolis at decreasing temperatures.
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16. SA - Metropolis Procedure
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17. Simulated Evolution (SimE)
Simulated evolution is based on an analogy with the principles of natural selection thought to be followed by various species in their biological environments.
Simulated Evolution algorithm (SimE) is a general search strategy for solving a variety of combinatorial optimization problems.
The SimE algorithm starts from an initial assignment, and then, following an evolution-based approach, it seeks to reach better assignments from one generation to the next.
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18. SimE - Algorithm
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19. SimE – Selection Function
This function determines which cells will retain their current locations and which should be assigned to new locations.
For each cell a random number [0,1] is generated and compared with the goodness.
If goodness is smaller than the random number, the cell is added to the “Selection List”.
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20. General Implementation Model
Developed a General implementation model for implementing the required algorithms.
Figure shows a flow chart indicating the flow of the complete application program.
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21. General Implementation Model
Figure shows the flow chart indicating the sequence of events within the main function.
The “Read Command Line” function is executed to read the input command.
The required variables are initialized and the input data from the file is read.
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22. General Implementation Model
The Block “B” executes the initial solution generation function.
The initial solution is assigned to the Current Solution and Best Solution variables.
The timer is started and the program enters the algorithm specific block.
Finally, the timer is stopped and the final solution is validated.
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23. Initial Solution Generation
The function for initial solution generation is called to generate a valid random initial solution.
The flow chart of this function is as shown in figure.
The initial solution is generated randomly and validated for constraint satisfaction.
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24. Neighbor Generation Function
One of the most important component of SA is the neighbor generation function.
The accuracy and efficiency of the neighbor generation function has a major impact on the performance of the algorithm.
A valid Current Solution is passed to the neighbor generation function.
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25. Allocation Function (SimE)
The most important component of SimE is the allocation function.
The flow chart of the allocation function used in the implementation of SimE is as shown in figure.
The main task of this function is to allocate cells within the solution such that the fitness (goodness) value of each cell is improved and a new valid solution is produced.
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26. Results & Analysis Results for SA Results for SimE
Comparison of Proposed Algorithms
Comparison of Solution Costs
Comparison of Run Times
Comparison for Additional Constraints
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27. Results & Analysis
Considered different problem instances with number of cells varying between 15 and 500 and the number of switches varying between 2 and 12.
Twenty data sets were generated of each type and the algorithms were executed on a Red Hat Linux system.
A series of test runs were conducted on the generated data sets to determine the efficiency of the algorithms, in terms of percentage of feasible solutions generated and the minimization of solution cost value.
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28. Results for SA
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29. SA – Solution Cost
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30. SA – Solution Cost
Figure shows the best solution costs obtained by SA for different problem instances.
100% feasible solutions were produced in each of the test runs conducted on the generated data sets.
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31. SA – Percentage Gain
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32. SA – Percentage Gain
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33. SA – Percentage Gain
Figure shows the comparison between initial solution cost and the best solution cost for the first five problem instances (15–150).
An improvement in percentage gains in the range of % is observed.
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34. SA – Percentage Gain
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35. SA – Percentage Gain
Figure shows the comparison for the remaining five problem instances (200–500).
An improvement in percentage gains in the range of % is seen.
Comparatively, the range of percentage gains is smaller than those obtained for problem instances of smaller size .
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36. SA – Percentage Gain
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37. SA – Percentage Gain
Figure shows the percentage gain (minimization) obtained for all the problem instances.
An improvement in the range of 55-69% is seen over all the problem instances.
The trend shows a drop in percentage gain for some larger problem instances.
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38. Results for SimE
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39. SimE – Solution Cost
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40. SimE – Solution Cost
Figure shows the best solution costs obtained by SimE for different problem instances.
In this case as well, 100% feasible solutions were produced in each of the test runs conducted on the generated data sets.
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41. SimE – Percentage Gain
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42. SimE – Percentage Gain
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43. SimE – Percentage Gain
Figure shows comparison of initial solution cost versus the cost of best solution obtained by SimE for the first five problem instances (15-150).
An improvement in the range of % is observed.
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44. SimE – Percentage Gain
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45. SimE – Percentage Gain
Figure shows comparison of initial solution cost versus the cost of best solution obtained by SimE for the remaining five problem instances ( ).
An improvement in the range of % is observed.
Comparatively, the range of percentage gains is smaller than those obtained for problem instances of smaller size .
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46. SimE – Percentage Gain
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47. SimE – Percentage Gain
Figure shows percentage improvement in SimE for different problem instances.
An improvement in the range of 56-78% is seen over all the problem instances.
The trend shows a continuous increase in percentage gain over all the problem instances.
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48. Comparison of Solution Costs
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49. Comparison of Solution Costs
Figure shows the comparison of solution costs between SimE and SA for different problem instances.
It can be observed that SimE performs better than SA in terms of final solution cost.
The difference in performance gets wider for larger problem instances.
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50. Comparison of Solution Costs
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51. Comparison of Solution Costs
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52. Comparison of Solution Costs
Figure shows the comparison of solution costs between SimE, SA, TS, and SA-P for different problem instances.
The SimE algorithm performs better than each of the three algorithms.
The SimE algorithm provides lower cost solutions even for large-sized problems.
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53. Comparison of Percentage Gains
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54. Comparison of Percentage Gains
Figure shows the comparison of percentage improvements in SA and SimE for different problem instances.
An improvement in the range of % for SA, and % for SimE, is seen over all the problem instances.
A higher efficiency, in terms of percentage gains, is seen in SimE when compared to SA, particularly, for large sized problems.
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55. Comparison of Percentage Gains
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56. Comparison of Percentage Gains
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57. Comparison of Percentage Gains
Figure shows the percentage improvement gained in solution cost by SimE compared to those obtained by SA-P, TS, and SA.
An improvement in the range of % is seen when compared to SA-P, and in the range of % when compared to TS (15-200).
An improvement in the range of % is seen when compared to SA.
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58. Comparison of Run Times
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59. Comparison of Run Times
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60. Comparison of Run Times
The test cases were generated for variable number of cells and four switches.
Figure compares the run times for SimE with the run times for TS and H heuristics.
For all test cases the SimE algorithm is much faster than the other two heuristics.
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61. Comparison of Run Times
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62. Comparison of Run Times
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63. Comparison of Run Times
Figure compares the run times for SA with the run times for TS and H heuristics.
It is observed that the SA has higher run times for larger problem sets when compared to the other two heuristics.
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64. Comparison of Run Times
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65. Comparison of Run Times
Figure compares the run times for SimE with the run times for SA.
Run time for SA almost increases exponentially with increasing problem sizes.
Run time for SimE shows a linear increase with increasing number of problem sizes.
SimE is much faster than SA, particularly, for large sized problems.
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66. Comparison for Additional Constraints
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67. Comparison for Additional Constraints
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68. Comparison for Additional Constraints
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69. Comparison for Additional Constraints
Figure provides the comparison of the final solution costs between SA without port constraint and SA (WPC) with the inclusion of port constraint.
A similar trend is seen in both versions with a gap in solution cost maintained between the two.
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70. Comparison for Additional Constraints
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71. Comparison for Additional Constraints
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72. Comparison for Additional Constraints
Figure shows the comparison of the final solution costs between SimE without port constraint and SimE with the inclusion of port constraint.
A larger gap is seen between the solution costs, particularly, for larger problem instances.
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73. Comparison for Additional Constraints
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74. Comparison for Additional Constraints
Figure shows the comparison of solution costs between SimE, SA, TS, and SA-P for different problem instances.
Even with port constraint, both SA and SimE, perform better than SA-P.
SA and SimE perform as good as TS except for the last problem instance.
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75. Conclusion & Future Work
The cellular network design problem is a complex and hard (NP-Hard) problem.
This complex problem was modeled as mathematical programming problem.
Solutions were provided using non-deterministic iterative heuristic algorithms (SA and SimE).
It was observed that the SimE performs better than SA and other heuristics, both, in terms of solution cost and run time.
Performance of any iterative heuristic is closely related to the level of interaction with the problem and the elements of the problem.
The higher the level of interaction with the problem elements the better the algorithm performs.
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76. Conclusion & Future Work
Data structures of the existing algorithms can be fine tuned such that the execution time may be further reduced.
Other non-deterministic iterative heuristics such as Genetic Algorithms (GA), Stochastic Evolution (StocE), etc. can be implemented.
Parallelization of the existing algorithms for handling large sized problem instances.
The problem can be further modified to include new objectives and constraints.
Implemented algorithms can be further developed into a complete software package by integrating them with a front--end user interface to take inputs.
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77. Conclusion & Future Work
A solid foundation for a long lasting series of research objectives to be accomplished in future.
It marks the begin of a fruitful journey into the unique area of application of iterative heuristics for designing cellular mobile networks.
This work is just the tip of an ice berg, a lot needs to be explored.
This thesis work will be a perfect starting point for any future research in this area.
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