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Designing of Cellular Mobile Networks Using Modern Heuristics

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Title: Designing of Cellular Mobile Networks Using Modern Heuristics


1
Designing of Cellular Mobile Networks Using
Modern Heuristics
  • M.S Thesis Oral Examination
  • Presenter
  • Abdul Subhan

2
Outline
  • Introduction
  • Background
  • Problem Description
  • Implementation Approach
  • Experimental Analysis Results
  • Conclusion Future Work

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 and 4G) demand
    more optimum and flexible network structure.

4
Introduction
  • The thesis deals with the designing of an
    efficient cellular mobile network.
  • The focus is on designing the terrestrial access
    network.
  • The assignment of cells to switches (BSC MSC).

5
Background
  • Merchant and Sengupta tried to solve the problem
    using deterministic algorithms and provided the
    basic formulation of the problem in their paper.
  • Proposed three heuristic solutions for the
    problem and showed that two of them perform
    extremely well.
  • S. Pierre and F. Houeto extended the above work.
  • Solved the problem using tabu search, a
    nondeterministic 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.
  • Presented a hybrid heuristic, named Price
    Influenced Simulated Annealing (PISA), which
    integrated ideas from linear programming into a
    simulated annealing framework.

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.
  • User moving from cell B to cell C experiences
    complex hand-off.

7
Problem Statement
  • For a set of cells and switches (whose positions
    are known), 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.

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.
  • ?i Number of calls per time unit destined
    to cell i.
  • Mk Call processing capacity of switch k.

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.

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.

11
Problem Formulation Port Constraint
  • The additional constraint is of the maximum
    number of ports, that are used for a cells 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.

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).

13
Simulated Annealing (SA)
  • 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.

14
SA - Metropolis Procedure
  • The core of SA 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 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.

15
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.
  • SimE is a general search strategy for solving a
    variety of combinatorial optimization problems.
  • It starts from an initial assignment, and then,
    following an evolution-based approach, it seeks
    to reach better assignments from one generation
    to the next.
  • The three main components of the SimE are the
    evaluation, selection and allocation
    functions.

16
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.

17
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 then initialized and
    the input data from the file is read.

18
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.

19
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.

20
Neighbor Function
  • One of the most important component of SA is the
    neighbor 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.

21
Allocation Function (SimE)
  • The most important component of SimE is the
    allocation function.
  • Figure shows the flow chart of the allocation
    function used in the implementation of SimE.
  • The main task of this function is to allocate
    cells within the solution such that the fitness
    of each cell is improved and a new valid solution
    is produced.

22
Results Analysis
  • Results for SA
  • Results for SimE
  • Comparison of Proposed Algorithms
  • Comparison of Solution Costs
  • Comparison of Run Times
  • Comparison for Additional Constraints

23
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.

24
Results Analysis
  • It was observed that the SimE performs better
    than SA and other heuristics, both, in terms of
    solution cost and run time.
  • Results show that we have improved solution costs
    from SimE compared to SA and those reported in
    literature.
  • Gain in the range of (55 69) for SA.
  • Gain in the range of (55 78) for SimE.
  • Results achieved by SimE in shorter durations
    compared to SA and those reported in literature.
  • SimE showed better performance even for larger
    problem sizes.

25
SA Solution Cost
(link handoff)
26
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.

27
SA Percentage Gain
(link handoff)
28
SA Percentage Gain
(link handoff)
29
SA Percentage Gain
  • Figure shows the comparison between initial
    solution cost and the best solution cost for
    problem instances between (15150) and (200
    500).
  • An improvement in percentage gains in the range
    of 55-66 is observed for problems (15 150).
  • An improvement in percentage gains in the range
    of 67-69 is seen for problems (200 500).
  • Comparatively, the range of percentage gains is
    smaller than those obtained for problem instances
    of smaller size .

30
SA Percentage Gain
31
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 saturation in percentage gain
    for some larger problem instances.

32
SimE Solution Cost
(link handoff)
33
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.

34
SimE Percentage Gain
(link handoff)
35
SimE Percentage Gain
(link handoff)
36
SimE Percentage Gain
  • Figures shows comparison of initial solution cost
    versus the cost of best solution obtained by SimE
    for problem instances (15 150) and (200 500).
  • An improvement in the range of 56-69 is
    observed for problem instances (15 150).
  • An improvement in the range of 73-78 is
    observed for problem instances (200 500).
  • Comparatively, the range of percentage gains is
    smaller than those obtained for problem instances
    of smaller size .

37
SimE Percentage Gain
38
SimE Percentage Gain
  • Figure shows percentage improvement in SimE for
    all 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.

39
Comparison of Solution Costs
(link handoff)
40
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.
  • For smaller problems instances, both versions
    show similar performance.
  • The difference in performance gets wider for
    larger problem instances.

41
Comparison of Solution Costs
(link handoff)
42
Comparison of Solution Costs
  • Figure shows the comparison of solution costs
    between SimE, SA, TS, and SA-P for different
    problem instances.
  • The SA algorithm shows better performance than
    the SA-P but not as good as TS.
  • The SimE algorithm performs better than each of
    the three algorithms.
  • The SimE algorithm provides lower cost solutions
    even for large-sized problems.

43
Comparison of Percentage Gains
44
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 55 69 for SA,
    and 56 78 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.

45
Comparison of Percentage Gains
46
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 29 66 is seen
    when compared to SA-P, and in the range of 11
    30 when compared to TS (15-200).
  • An improvement in the range of 11 32 is seen
    when compared to SA.

47
Comparison of Run Times
48
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.
  • The trend for SimE has a lower slope, indicating
    a lower sensitivity to increase in problem size.

49
Comparison of Run Times
50
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.
  • The run times are very high for larger sized
    problems.
  • SA shows a non-linear increase in run time.

51
Comparison of Run Times
52
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.

53
Comparison for Additional Constraints
(link handoff)
54
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 of SA.
  • The gap starts increasing from problem instance
    (150 6).
  • A constant gap in solution cost is maintained
    between the two versions.

55
Comparison for Additional Constraints
(link handoff)
56
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.
  • The gap starts increasing from problem instance
    (150 6).
  • A larger gap is seen between the solution costs,
    particularly, for larger problem instances.

57
Comparison for Additional Constraints
(link handoff)
58
Comparison for Additional Constraints
  • Figure shows the comparison of the final solution
    costs between SimE and SA with port constraint.
  • Both SimE and SA showed similar performance for
    most of the problem instances.
  • For larger problem instances SA performs slightly
    better than SimE.

59
Comparison for Additional Constraints
(link handoff)
60
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.
  • SA shows stability even after inclusion of port
    constraints, where as SimE does not.

61
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.

62
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.

63
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 thesis work will be a perfect starting point
    for any future research in this area.

64
Thank You
  • Question Answers

65
(No Transcript)
66
Backup Slides
67
SA - Algorithm
68
SA - Metropolis Procedure
69
SimE - Algorithm
70
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.

71
Results for SA
72
SA Percentage Gain
73
Results for SimE
74
SimE Percentage Gain
75
Comparison of Solution Costs
76
Comparison of Percentage Gains
77
Comparison of Run Times
78
Comparison of Run Times
79
Comparison for Additional Constraints
80
Comparison for Additional Constraints
81
Comparison for Additional Constraints
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