Topological design of telecommunication networks

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Topological design of telecommunication networks

• Michal Pióroa,b, Alpar Jüttnerc, Janos Harmatosc,
• Áron Szentesic, Piotr Gajowniczekb, Andrzej
  Myslekb

a Lund University, Sweden b Warsaw University of
Technology, Poland c Ericsson Traffic Laboratory,
Budapest, Hungary
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Outline

• Background
• Network model and problem formulation
• Solution methods
• Exact (Branch and Bound) and the lower bound
  problem
• Minoux heuristic and its extensions
• Other methods (SAN and SAL)
• Comparison of results
• Conclusions

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Background of Topological Design

• problem
• localize links (nodes) with simultaneous routing
  of given demands, minimizing the cost of links
• selected literature
• Boyce et al1973 - branch-and-bound (BB)
  algorithms
• Dionne/Florian1979 BB with lower bounds for
  link localization with direct demands
• Minoux1989 - problems classification and a
  descent method with flow reallocation to indirect
  paths for link localization

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Transit Nodes and Links Localization problem
formulation

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

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Symbols used

• constants
• hd volume of demand d
• aedj 1 if link e belongs to path j of demand
  d, 0 otherwise
• ce cost of one capacity unit installed on link
  e
• ke fixed cost of installing link e
• B budget constraint
• Me upper bound for the capacity of link e
• variables
• xdj flow realizing demand d allocated to path j
  (continuous)
• ye capacity of link e (continuous)
• se 1 if link e is provided, 0 otherwise (binary)

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Network model adequate for IP/MPLS

• LER ? access node
• LSR ? transit node
• LSP ? demand flow

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Optimal Network Design Problemand Budget
Constrained Problem

• ONDP
• minimize
• C Se ce ye Se kese
• constraints
• Sj xdj hd
• SdSj aedj xdj ye
• ye L Mese

• BCP
• minimize
• C Se ce ye
• constraints
• Se kese L B
• Sj xdj hd
• SdSj aedj xdj ye
• ye L Mese

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Solution methods

• Specialized heuristics
• Simulated Allocation (SAL)
• Simulated Annealing (SAN)
• Exact algorithms branch and bound (cutting
  planes)

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Branch and Bound method

• advantages
• exact solution
• heuristics results verification
• disadvantages
• exponential increase of computational complexity
• solving many unnecessary sub-problems

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Branch and Bound - lower bound

• LB proposed by Dionne/Florian1979 is not suitable
  for our network model with non-direct demands
  it gives no gain
• We propose another LB modified problem with
  fixed cost transformed into variable cost
• minimizeC Se xeye Seke
• where
• xe ce ke /Me

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Minoux heuristics

• The original 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

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Minoux heuristics extensions

• individual flow shifting (H1)
• individual flow shifting with cost smoothing (H2)
• Ce(y) cey ke 1 - (1-?)/(y-1)? 1 if y gt
  0
• 0 otherwise.
• bulk flow shifting (H3)
• for the first positive gain (H3F)
• for the best gain (H3B)
• bulk flow shifting with cost smoothing (H4)
• two versions (H4F and H4B)

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Other methods

• Simulated Allocation (SAL) in each step chooses,
  with probability q(x), between
• allocate(x) adding one demand flow to the
  current state x
• disconnect(x) removing one or more demand flows
  from current x
• Simulated Annealing (SAN) starts from an initial
  solution and selects neighboring state
• changing the node or link status
• switching on/off a node
• switching on/off a transit or access link

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Comparison - objective
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Comparison - running time
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Conclusions

• proposed modification of Minoux algorithm can
  efficiently solve TNLLP, especially H4B
• Simulated Allocation seems to be the best
  heuristics
• proposed lower bound can be used to construct
  branch-and-bound implementations
• need for diverse methods - hybrids of the best
  shown here, e.g. Greedy Randomized Adaptive
  Search Procedure using SAL seems to be a good
  solution