an alternative genetic algorithm to optimize ospf weights

Communication Networks E. Mulyana, U. Killat

1

An Alternative Genetic Algorithm to

Optimize OSPF Weights


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

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

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

Objective Functions

• Objective Function 1 : Stähle, 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

k

y

ij uv ij

uv

ij

ty

E

a

c

l

Eta

1)(


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

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

Forming a new generation

• Reproduction

– Crossover

– Arbitrary Mutation

• „Targeted“ Mutation

AV C1 C2 C3 C4

P1 P2

O4 O1

Reproduction

„Targeted“

Mutation

O3 O2

„Targeted“

Mutation


9

Reproduction

5 5 6 5 7

1 2 3 3 4 Parent 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

„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

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

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

A Test Network


14

Results (3)


15

Results (4)


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

Thank You !


18

Convergence


19

Increasing Traffic

an alternative genetic algorithm to optimize ospf weights

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