Heuristic Methods for Topological Design of Telecommunication Networks

1
Heuristic Methods for Topological Design of
Telecommunication Networks
2nd Polish-German Teletraffic Symposium September
23-24, 2002, Gdansk, Poland

• Andrzej Myslek, Piotr Karas
• Institute of Telecommunications
• Warsaw University of Technology

2
Topological design

• determine network structure and demand allocation
  pattern
• minimise the cost of the network
• node and link costs are considered
• original ideas and selected methods from
  literature

3
Outline

• Problem formulation TNLLP
• Heuristics applied
• Numerical results
• Conclusions

4
Transit Node and Link Localisation Problem

• Given
• a set of access nodes with geographical locations
  
• traffic demand between each access node pair
• possible locations of transit nodes
• find
• the number and locations of the transit nodes
• locations of links connecting nodes
• routing (flows) and links capacities
• minimising the total network cost

5
Network resources

• access (edge) nodes
• transit nodes
• access links
• transit links
• demands

6
Network cost

• fixed installation cost of each transit node
• fixed installation cost of each link
• capacity-dependent cost of each link
• C Sv lvev Se (kese ceye)

7
TNLLP as MIP

• link-path formulation
• minimise
• C Sv lvev Se (kese ceye)
• subject to
• Sj xdj hd d1,2,...,D (demand realisation)
• SdSj aedjxdj ye e1,2,...,E (link capacity)
• ye Yese e1,2,...,E (link presence)
• Se bevse Gvev v1,2,...,V (node presence)

8
Minoux Algorithm

• step 0 (greedy) allocate demands in the random
  order to the shortest paths if a link was
  already used for allocation of another demand use
  only variable cost, otherwise use variable and
  installation cost of the link
• 1 calculate the cost gain of reallocating the
  demands fromeach link to other allocated links
  (the shortest alternative path is chosen)
• 2 select the link, whose elimination results in
  the greatest gain
• 3 reallocate flows going throughthe link being
  eliminated
• 4 if improvement possiblego to step 2

9
Flow shifting

• Individual Flow Shifting (IFS)
• (greedy) initial allocation of demands
• subsequent demands reallocated (randomly)
• Bulk Flow Shifting (BFS)
• randomly chosen link is switched off
• affected demands are rerouted individually and
  globally
• if reallocation does not improve network cost we
  rollback

10
Adaptive Function Loop (AFL)

• AFL modifies link cost function in each step
• link cost function is partially linearised

11
Other methods

• Yaged Algorithm (YAG)
• recalculation of shortest paths for all of the
  demands
• marginal link costs dfe(ye)/dye taken as link
  weights
• stops when fixed point is reached
• Simulated Allocation (SAL)
• works with partial allocation states (some
  demands are not allocated)
• in each step allocation or disconnection is
  chosen with the probabilities Pa and Pd1-Pa
• bulk disconnection for full allocation states
  performed
• stops after predefined number of steps

12
Hybrid GRASP (HYB)

• procedure HybridGRASP(var bestSolution)
• begin
• repeat
• SimulatedAllocation(solution)
• BulkFlowShifting(solution)
• UpdateBestSolution(solution,bestSolution)
• until TerminationCriterion()
• end

13
Results - objective
14
Results - objective (contd.)
15
Results - running times
16
Conclusions

• Results
• the best BFS-AFL (overall performance, but slow)
• SAL, HYB and BFS in 5 minimum cost limit
• YAG, MGA and enhancements - poor results
• best methods running times grow exponentially
• Further possible improvement
• SAL allocation and disconnection
• Local Search phase for HYB
• path selection for all methods