Communication Networks E. Mulyana, U. Killat
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A Hybrid Genetic Algorithm
Approach for OSPF Weight Setting
Problem
PGTS 2002 – Gdansk (Poland) – 23/24.09.2002
Communication Networks E. Mulyana, U. Killat
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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
Communication Networks E. Mulyana, U. Killat
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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)
Communication Networks E. Mulyana, U. Killat
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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)
Communication Networks E. Mulyana, U. Killat
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Objective Functions
• Objective Function 1 : Staehle, Köhler, Kohlhaas
maximum & average utilization
• Objective Function 2 : Minimizing changes
ij uv ij
uv
ij
t
c
l
Eta
1)(
r
kk
r
kk
k
ww
wwy
,
,
0
1
w1r, w
2r, … , w
kr, … , w
|E|r
w1 , w
2 , … , w
k , … , w
|E|
Ek
kty
Eta
1)(
Communication Networks E. Mulyana, U. Killat
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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)
Communication Networks E. Mulyana, U. Killat
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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
Communication Networks E. Mulyana, U. Killat
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Forming a new generation
• Reproduction
– Crossover
– Arbitrary Mutation
• „Targeted“ Mutation
AV C1 C2 C3 C4
P1 P2
O2 O1
Reproduction
„Targeted“
Mutation
Communication Networks E. Mulyana, U. Killat
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Reproduction
const 2
const 1 0.03
0.53
5 5 6 5 7
1 2 3 3 4 Parent 1 (P1)
Parent 2 (P2)
Intermediate 1
(I1)
Intermediate 2
(I2)
Random 0.81 0.59
5
1
0.02
1
8
0.09
6
3
0.35
5
3 7
4
Communication Networks E. Mulyana, U. Killat
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„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
Communication Networks E. Mulyana, U. Killat
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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
Communication Networks E. Mulyana, U. Killat
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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)
Communication Networks E. Mulyana, U. Killat
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A Test Network
Communication Networks E. Mulyana, U. Killat
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Results (2)
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Results (3)
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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
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Thank You !
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Convergence
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Increasing Traffic