Designing of Cellular Mobile Networks Using Modern Heuristics

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

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.

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).

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
  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.
• They 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.
• if a user moves from cell B to cell C, we are in
  the presence of a complex hand-off.

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.

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)

• 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.

14
SA - Algorithm
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.

16
SA - Metropolis Procedure
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.

18
SimE - Algorithm
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.

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.

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.

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.

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.

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.

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.

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

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.

28
Results for SA
29
SA Solution Cost
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.

31
SA Percentage Gain
32
SA Percentage Gain
33
SA Percentage Gain

• Figure shows the comparison between initial
  solution cost and the best solution cost for the
  first five problem instances (15150).
• An improvement in percentage gains in the range
  of 55-66 is observed.

34
SA Percentage Gain
35
SA Percentage Gain

• Figure shows the comparison for the remaining
  five problem instances (200500).
• An improvement in percentage gains in the range
  of 67-69 is seen.
• Comparatively, the range of percentage gains is
  smaller than those obtained for problem instances
  of smaller size .

36
SA Percentage Gain
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.

38
Results for SimE
39
SimE Solution Cost
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.

41
SimE Percentage Gain
42
SimE Percentage Gain
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 56-69 is
  observed.

44
SimE Percentage Gain
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
  (200-500).
• An improvement in the range of 73-78 is
  observed.
• Comparatively, the range of percentage gains is
  smaller than those obtained for problem instances
  of smaller size .

46
SimE Percentage Gain
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.

48
Comparison of Solution Costs
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.

50
Comparison of Solution Costs
51
Comparison of Solution Costs
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.

53
Comparison of Percentage Gains
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 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.

55
Comparison of Percentage Gains
56
Comparison of Percentage Gains
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 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.

58
Comparison of Run Times
59
Comparison of Run Times
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.

61
Comparison of Run Times
62
Comparison of Run Times
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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Comparison of Run Times
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.

66
Comparison for Additional Constraints
67
Comparison for Additional Constraints
68
Comparison for Additional Constraints
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.

70
Comparison for Additional Constraints
71
Comparison for Additional Constraints
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.

73
Comparison for Additional Constraints
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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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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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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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.