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# A Hybrid Genetic Algorithm Approach for OSPF Weight Setting Problem

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Archive of my talk at PGTS 2002 – Gdansk (Poland) – 23/24.09.2002

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### A Hybrid Genetic Algorithm Approach for OSPF Weight Setting Problem

1. 1. Communication Networks E. Mulyana, U. Killat 1 A Hybrid Genetic Algorithm Approach for OSPF Weight Setting Problem PGTS 2002 – Gdansk (Poland) – 23/24.09.2002
2. 2. Communication Networks E. Mulyana, U. Killat 2 Introduction • OSPF (IGP) use administrative metric – Not adapt on the traffic situation  Unbalanced load distribution • Mechanism to increase network utilization and avoid congestion – Changing the link weights for a given demand – The problem is NP-hard
3. 3. Communication Networks E. Mulyana, U. Killat 3 OSPF Routing Problem (1) • Each link has a cost/weight  [1 ... 65535] • Routers compute paths with Dijkstra‘s algorithm • ECMP  even-splitting • Given a demand and a set of weights  Load distribution (does not depend on link capacities)
4. 4. Communication Networks E. Mulyana, U. Killat 4 OSPF Routing Problem (2) Find a set of weights with minimal cost Dijkstra , ECMP Objective (cost) Function Network topology and link capacities Predicted traffic demand Set of weights Cost value Utilization (max, av)
5. 5. Communication Networks E. Mulyana, U. Killat 5 Objective Functions • Objective Function 1 : Staehle, Köhler, Kohlhaas  maximum & average utilization • Objective Function 2 : Minimizing changes   ij uv ij uv ij t c l E ta 1 )( r kk r kk k ww ww y       , , 0 1 w1 r, w2 r, … , wk r, … , w|E| r w1 , w2 , … , wk , … , w|E|            Ek kt y E ta 1 )(
6. 6. Communication Networks E. Mulyana, U. Killat 6 General Routing Problem • Lower bound for shortest path (SP) routing • No SP constraints, no splitting constraints • LP formulation: Objective Function Flow Conservation Utilization Upper Bound (t)
7. 7. Communication Networks E. Mulyana, U. Killat 7 The Proposed Hybrid-GA The big picture The population dynamic Reproduction Mutation Heuristic Search Best chromosome Population 50 chromosomes Selection (parents) 8 chromosomes Selection (remove 10%) Population 45 chromosomes Offsprings 8 chromosomes Search result (1 or 0 chromosome) Population 53 or 54 chromosomes Selection (best 50 chromosomes) Start Population Exit Condition Heuristic Search Selection Reproduction Mutation Add new Population Selection yes no
8. 8. Communication Networks E. Mulyana, U. Killat 8 Forming a new generation • Reproduction – Crossover – Arbitrary Mutation • „Targeted“ Mutation AVC1 C2 C3 C4 P1 P2 O2O1 Reproduction „Targeted“ Mutation
9. 9. Communication Networks E. Mulyana, U. Killat 9 Reproduction const 2 const 1 0.03 0.53 5 5 6 5 7 1 2 3 3 4Parent 1 (P1) Parent 2 (P2) Intermediate 1 (I1) Intermediate 2 (I2) Random 0.810.59 5 1 0.02 1 8 0.09 6 3 0.35 5 3 7 4
10. 10. Communication Networks E. Mulyana, U. Killat 10 „Targeted“ Mutation 0.4 1.4 0.1 0.8 0.3 0.6 0.1 0.6 0.7 1.2 0.4 0.6 5 1 6 5 7 1 8 3 3 4 I1 I2 Util. I1 Util. I2 Average Average Av - 0.2 Av + 0.2 Utilization 5 1 6 5 7 1 8 3 3 4 3 5 4 7 3 Offspring 1 Offspring 2 0.1 1.4 0.1 1.2 0.3
11. 11. Communication Networks E. Mulyana, U. Killat 11 Heuristic Search • Individual-based search • Best chromosome as input C=A Improvement? ( fail < treshold ) Apply Heuristic B better than C? C=B fail = 0 fail ++ yes Chromosome B yes no no Chromosome C Chromosome A
12. 12. Communication Networks E. Mulyana, U. Killat 12 Results (1) • Objective function (2) • at = 10 Original (reference) GA Max. 42.9% Av. 22.4% Max. 35.7% Av. 22.7% 4 weight changes : (2,1) (3,4) (4,5) (5,6)
13. 13. Communication Networks E. Mulyana, U. Killat 13 A Test Network
14. 14. Communication Networks E. Mulyana, U. Killat 14 Results (2)
15. 15. Communication Networks E. Mulyana, U. Killat 15 Results (3)
16. 16. Communication Networks E. Mulyana, U. Killat 16 Conclusion • Hybrid genetic algorithm to OSPF routing problem, with „targeted“ mutation and search heuristic • Propose an objective function to minimize changes • Compare the result to one with objective function from Staehle, Köhler, Kohlhaas
17. 17. Communication Networks E. Mulyana, U. Killat 17 Thank You !
18. 18. Communication Networks E. Mulyana, U. Killat 18 Convergence
19. 19. Communication Networks E. Mulyana, U. Killat 19 Increasing Traffic