1. Heuristic Methods for Topological Design of Telecommunication Networks Andrzej Mysłek, Piotr Karaś Institute of Telecommunications Warsaw University of Technology 2 nd Polish-German Teletraffic Symposium September 23-24, 2002, Gdańsk, Poland

2. Problem formulationMethodsNumerical resultsConclusions 1/15 2 nd Polish-German Teletraffic Symposium September 23-24, 2002, Gdańsk, Poland 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. Problem formulationMethodsNumerical resultsConclusions 2/15 2 nd Polish-German Teletraffic Symposium September 23-24, 2002, Gdańsk, Poland Outline Problem formulation: TNLLP Heuristics applied Numerical results Conclusions

4. Problem formulationMethodsNumerical resultsConclusions 3/15 2 nd Polish-German Teletraffic Symposium September 23-24, 2002, Gdańsk, Poland 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. Problem formulationMethodsNumerical resultsConclusions 4/15 2 nd Polish-German Teletraffic Symposium September 23-24, 2002, Gdańsk, Poland Network resources access (edge) nodes transit nodes access links transit links demands

6. Problem formulationMethodsNumerical resultsConclusions 5/15 2 nd Polish-German Teletraffic Symposium September 23-24, 2002, Gdańsk, Poland Network cost –fixed installation cost of each transit node –fixed installation cost of each link –capacity-dependent cost of each link C =  v l v ε v +  e (k e σ e + c e y e )

7. Problem formulationMethodsNumerical resultsConclusions 6/15 2 nd Polish-German Teletraffic Symposium September 23-24, 2002, Gdańsk, Poland TNLLP as MIP link-path formulation minimise C =  v l v ε v +  e (k e σ e + c e y e ) subject to Σ j x dj = h d d=1,2,...,D(demand realisation) Σ d Σ j a edj x dj = y e e=1,2,...,E(link capacity) y e  Y e σ e e=1,2,...,E(link presence) Σ e b ev σ e  G v ε v v=1,2,...,V(node presence)

8. Problem formulationMethodsNumerical resultsConclusions 7/15 2 nd Polish-German Teletraffic Symposium September 23-24, 2002, Gdańsk, Poland Minoux Algorithm step0 (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 1calculate the cost gain of reallocating the demands from each link to other allocated links (the shortest alternative path is chosen) 2select the link, whose elimination results in the greatest gain 3reallocate flows going through the link being eliminated 4if improvement possible go to step 2 elimination

9. Problem formulationMethodsNumerical resultsConclusions 8/15 2 nd Polish-German Teletraffic Symposium September 23-24, 2002, Gdańsk, Poland 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. Problem formulationMethodsNumerical resultsConclusions 9/15 2 nd Polish-German Teletraffic Symposium September 23-24, 2002, Gdańsk, Poland Adaptive Function Loop (AFL) AFL modifies link cost function in each step link cost function is partially linearised

11. Problem formulationMethodsNumerical resultsConclusions 10/15 2 nd Polish-German Teletraffic Symposium September 23-24, 2002, Gdańsk, Poland Other methods Yaged Algorithm (YAG) –recalculation of shortest paths for all of the demands –marginal link costs df e (y e )/dy e 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 P a and P d =1-P a –bulk disconnection for full allocation states performed –stops after predefined number of steps

12. Problem formulationMethodsNumerical resultsConclusions 11/15 2 nd Polish-German Teletraffic Symposium September 23-24, 2002, Gdańsk, Poland Hybrid GRASP (HYB) procedure HybridGRASP(var bestSolution); begin repeat SimulatedAllocation(solution); BulkFlowShifting(solution); UpdateBestSolution(solution,bestSolution); until TerminationCriterion(); end;

13. Problem formulationMethodsNumerical resultsConclusions 12/15 2 nd Polish-German Teletraffic Symposium September 23-24, 2002, Gdańsk, Poland Results - objective

14. Problem formulationMethodsNumerical resultsConclusions 13/15 2 nd Polish-German Teletraffic Symposium September 23-24, 2002, Gdańsk, Poland Results - objective (contd.)

15. Problem formulationMethodsNumerical resultsConclusions 14/15 2 nd Polish-German Teletraffic Symposium September 23-24, 2002, Gdańsk, Poland Results - running times

16. Problem formulationMethodsNumerical resultsConclusions 15/15 2 nd Polish-German Teletraffic Symposium September 23-24, 2002, Gdańsk, Poland 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