A Hybrid Genetic Algorithm Approach for OSPF Weight Setting Problem

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

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 : 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)(


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 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

Forming a new generation

• Reproduction

– Crossover

– Arbitrary Mutation

• „Targeted“ Mutation

AV C1 C2 C3 C4

P1 P2

O2 O1

Reproduction

„Targeted“

Mutation


9

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


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

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

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

A Test Network


14

Results (2)


15

Results (3)


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

Thank You !


18

Convergence


19

Increasing Traffic

Education

A Hybrid Genetic Algorithm Approach for OSPF Weight Setting Problem