Archive of my talk at ITC SS 15 / IP 2002

1. Communication Networks
E. Mulyana, U. Killat
1
An Alternative Genetic Algorithm to
Optimize OSPF Weights

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 : Stähle, 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
k
y
ij uv ij
uv
ij
t
y
E
a
c
l
E
ta
1
)(

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 GA
The big picture The population dynamic
Start
Population
Exit
Condition
Selection
Reproduction
Mutation
Add new
Population
Selection
Reproduction
Mutation
Population
50 chromosomes
Selection (parents)
8 chromosomes
Selection
(remove 10%)
Population
45 chromosomes
Offsprings
16 chromosomes
Population
61 chromosomes
Selection
(best 50 chromosomes)

8. Communication Networks
E. Mulyana, U. Killat
8
Forming a new generation
• Reproduction
– Crossover
– Arbitrary Mutation
• „Targeted“ Mutation
AVC1 C2 C3 C4
P1 P2
O4O1
Reproduction
„Targeted“
Mutation
O3 O2
„Targeted“
Mutation

9. Communication Networks
E. Mulyana, U. Killat
9
Reproduction
5 5 6 5 7
1 2 3 3 4Parent 1
Parent 2
Offspring 1
Offspring 2
Random 0.81
const 2
const 1 0.03
0.53
0.59
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
Offspring 1
Offspring 2
Util. O1
Util. O2
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 3
Offspring 4
0.1
1.4 0.1
1.2
0.3

11. Communication Networks
E. Mulyana, U. Killat
11
Results (1)
Result of 6 routers network
6 routers
network
10 routers
network
MIP GA
Max. 35.7%
Av. 22.7%
95% match
(100 runs, 100 iterations)
Max. 96.7%
Av. 82.9%
32% match
(100 runs, 300 iterations)
• Objective function (1)
• at = 10

12. Communication Networks
E. Mulyana, U. Killat
12
Results (2)
• Objective function (2)
• at = ay = 10
Original
(reference)
GA
Max. 42.9%
Av. 22.4%
Max. 35.7%
Av. 22.7%
4 link 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 (3)

15. Communication Networks
E. Mulyana, U. Killat
15
Results (4)

16. Communication Networks
E. Mulyana, U. Killat
16
Conclusion
• Alternative genetic algorithm to OSPF
routing problem, with a mutation heuristic
• Objective function (O.F.) from Stähle,
Köhler, Kohlhaas
• Enhancing this O.F. to minimize weight
changes

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