Heuristic Methods for Topological Design of Telecommunication Networks Andrzej Mysłek, Piotr Karaś...

Heuristic Methods for Topological Design of Telecommunication Networks

Andrzej Mysłek, Piotr Karaś

Institute of TelecommunicationsWarsaw University of Technology

2nd Polish-German Teletraffic SymposiumSeptember 23-24, 2002, Gdańsk, Poland

Problem formulation Methods Numerical results Conclusions2/15


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



Outline

• Problem formulation: TNLLP

• Heuristics applied

• Numerical results

• Conclusions



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



Network resources

• access (edge) nodes• transit nodes

• access links• transit links

• demands



Network cost

– fixed installation cost of each transit node– fixed installation cost of each link– capacity-dependent cost of each link

C = v lvεv + e (keσe+ ceye)



TNLLP as MIP

link-path formulationminimise C = v lvεv + e (keσe+ ceye)

subject toΣj xdj = hd d=1,2,...,D (demand realisation)

ΣdΣj aedjxdj = ye e=1,2,...,E (link capacity)

ye Yeσe e=1,2,...,E (link presence)

Σe bevσe Gvεv v=1,2,...,V (node presence)



Minoux Algorithmstep 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 link1 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 gain3 reallocate flows going throughthe link being eliminated4 if improvement possiblego to step 2

elimination



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



th

eee

th

eee

ee yyfory

yyforyfyC

)()(

thth

ee

th

ee

e

yyf

ionlinearisatforloadlinkthresholdy

elinkoffunctionostcoriginalyf

elinkofloady

)(

)(

Adaptive Function Loop (AFL)

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



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 Pd=1-Pa

– bulk disconnection for full allocation states performed– stops after predefined number of steps



Hybrid GRASP (HYB)

procedure HybridGRASP(var bestSolution);begin

repeat

SimulatedAllocation(solution);BulkFlowShifting(solution);UpdateBestSolution(solution,bestSolution);

until TerminationCriterion();

end;



Results - objective

0,0%

5,0%

10,0%

15,0%

20,0%

25,0%

30,0%

35,0%

40,0%

45,0%

(4,4)N14

(4,5)N14

(4,6)N14

(5,4)N14

(5,5)N14

(5,6)N14

(4,4)N28

(4,5)N28

(4,6)N28

(5,4)N28

(5,5)N28

(5,6)N28

network (n,k)

% d

iffe

ren

ce f

rom

th

e b

es

t IFS

IFS-AFL

MGA

MGA- AFL

aMGA

aMGA- AFL

YAG

YAG- AFL

IFS, YAGaMGA-AFL, aMGA, MGA, MGA-AFL

IFS-AFL



Results - objective (contd.)

0,0%

1,0%

2,0%

3,0%

4,0%

5,0%

6,0%

(4,4)N14

(4,5)N14

(4,6)N14

(5,4)N14

(5,5)N14

(5,6)N14

(4,4)N28

(4,5)N28

(4,6)N28

(5,4)N28

(5,5)N28

(5,6)N28

network (n,k)

% d

iffe

ren

ce f

rom

th

e b

es

t

BFS

BFS- AFL

SAL

HYB

BFS

BFS-AFL

HYB

SAL



Results - running times

1

10

100

1000

(4,4)N14

(4,5)N14

(4,6)N14

(5,4)N14

(5,5)N14

(5,6)N14

(4,4)N28

(4,5)N28

(4,6)N28

(5,4)N28

(5,5)N28

(5,6)N28

network

run

nin

g t

ime

[s

]

IFS-AFL

MGA- AFL

aMGA- AFL

BFS

BFS- AFL

YAG- AFL

SAL

HYB

BFS-AFL

SAL

HYB

IFS-AFLYAG-AFL

MGA-AFLaMGA-AFL

BFS



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

Heuristic Methods for Topological Design of Telecommunication Networks Andrzej Mysłek, Piotr Karaś...

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