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

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. 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. 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. 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. Communication Networks
E. Mulyana, U. Killat
5
Objective Functions
• Objective Function 1 : Staehle, Köhler, Kohlhaas 
maximum & average utilization
• Objective Function 2 : Minimizing changes
 
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ta
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


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,
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w1
r, w2
r, … , wk
r, … , w|E|
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w1 , w2 , … , wk , … , w|E| 
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 
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ta
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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. 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. 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. 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. 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. 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. 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. Communication Networks
E. Mulyana, U. Killat
13
A Test Network

14. Communication Networks
E. Mulyana, U. Killat
14
Results (2)

15. Communication Networks
E. Mulyana, U. Killat
15
Results (3)

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. Communication Networks
E. Mulyana, U. Killat
17
Thank You !

18. Communication Networks
E. Mulyana, U. Killat
18
Convergence

19. Communication Networks
E. Mulyana, U. Killat
19
Increasing Traffic