8. Dynamic Routing Control Based on a Genetic Algorithm

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A Dynamic

Routing Control Based on

a

Genetic Algorithm

Norio Shimamoto, Atsushi Hiramatsu, and Kimiyoshi Yamasaki

IT

Communication Switching Laboratories

3-9-11 Midori-cho Musashino-shi, Tokyo 180,

JAPAN

TEL:+81422 59 2822

FAx:+81422 59 2473

Abstract

This paper demonstrates that a dynamic

routing control based on a Genetic Algorithm can

provide flexible real-time management of the

dynamic traffic changes in broadband networks. We

propose a string structure, each of whose elements

represents paths between each pair of origin and

destination terminal nodes, and a new technique

using the past solutions as the initial data for new

searches. These techniques dramatically improve

the efficiency and convergence speed of the Genetic

Algorithm. Computer simulations show that the

Genetic Algorithm using the proposed techniques

can generate the exact solution of path arrangement

and can find a routing arrangement that keeps the

traffic loss-rate bellow a target value even after

changes in traffic.

1. Introduction

In the future B-ISDN (Broadband Integrated

Services Digital Network) providing multimedia

communication services, changes in traffic are

expected to be more dynamic and less predictable

than in today's networks. The various methods for

dynamic rout ing have therefore been proposed [11[21

131

are generally categorized into two groups: time-

dependent an d network-state-dependent. Time-

dependent methods change the rou ting table

according to the traffic patte rns tha t are expected at

each scheduled time and therefore cannot

accommodate unexpected traffic changes. State-

dependent methods, on the other hand, are flexibly

adaptive to dynamic traffic changes because they

generate

a

new routing table in real-time according

to changes in the monitored trafflc. The problem

with state-dependent method is tha t finding

satisfactory solutions requires a huge amount of

calculation power. For each traffic change, we have

t o find the optimal combination of paths between

every pair of nodes, but it is impossible

to

get the

optimal solution within

a

practical control cycle

because there are almost infinitely many possible

paths in an actual network. Practical and effective

methods for finding quasi-optimal solutions have

therefore been investigated.

Neural Networks and Genetic Algorithms,

for example, are new approaches that seem

promising ways for solving such complicated large

problems. ATM call admission and link capacity

controls using Neural Networks have already been

reported [41[51,

as

ha s th e use of Genetic Algorithms

for ATM bandwidth allocation [SI.

A Genetic Algorithm is a method for solving

an optimization problem through the evolution of

genes : paramete rs t o be optimized are coded by

st r ings of characters o r numbers, and genetic

operations (Reproduction, Selection, Crossover, and

Mutation) are iterated [71. The main advantages

of

Genetic Algorithms are the following:

1)

Because

only primitive procedures like cut and exchange

of strings are used for generating new genes from

old, it is easy t o handle large problems simply by

using long strings; (2) Because only values of the

objective function for optimization are used to select

genes, this algorithm can be robustly applied t o

problems with any kinds of objective functions, such

as nonlinear, indifferentiable, or step functions; (3)

Because th e genetic operations ar e performed at

random and also include mutation, it is possible to

avoid being trapped by local-optima. Communication

networks present large-scale optimization problems

with various kinds of objective functions, and

Genetic Algorithms should be s uita ble for such

0-7803-0999-5/93/ 03.00 1993 1123



problems.

This paper proposes a new dynamic routing

method based on a Genetic Algorithm. A new string

structure and genetic operations suitable for network

problems is proposed, and an optimization method

that uses past solutions as the initial data for new

searches

is

also proposed. These techniques

dramatically improve the efficiency and convergence

speed of the Genetic Algorithm. Finally we

demonstrate the capability of the proposed Genetic

Algorithm by presenting the results obtained from

computer simulation of

a

path arrangement problem

and a dynamic routing problem.

2. Routing problem and Genetic Algorithm

2.1 Routing problem

The network model considered in this paper

is

a set

of

M switching nodes connected by L physical

links.

A

sample network model with M=8 and L=12

is shown in Fig. 1. Each pair of nodes in the network

is connected by one logical link called a path, which

is created by sharing the capacities of some of the

[Route table]

Path(1) Path 28)

(between nodes 1 and 2)

(between nodes 7 and

8)

[Configuration string]

t

path 1) ~aih 2) a t h ( 3 )

1 2

1

4 .... .

[Networ k configuration]

Selected routeSelected route

(1-8-3-2)

Physical

ink

0

Fig.

1

8-node network

model

and an example

of

a configuration string.

physical trunk s connecting the pair of nodes. A path

carries traffic (calls) in both directions, s o the

capacity required for each path is the sum of the

traffic demand in both directions and the total

number of paths is M M-1)/2.

There are usually many possible

combinations of physical links that can make up a

path between any two nodes. For example,

a

path

between nodes 1 and

2

in Fig. 1 could be such

combinations of physical links as 1-2, 1-8-3-2, 1-7-2,

and so on. These combinations of physical links are

called possible routes for the pat h. A routing

algorithm selects one of possible routes for each path,

and a set of the selected routes is called a network

configuration.

A network configuration determines the

routes for all paths and, therefore, the traffic

demand for each physical link. When the trafftic

demand for a physical link exceeds the capacity of

the link, the fraction of traffic that the link cannot

carry is called the call loss-rate. Given

a

network

model and traffic demands between all pair of nodes,

the routing problem is t o find the network

configuration that minimizes the call loss-rate. The

search space for this kind of optimization problem is

large even for a small network.

For

the network

shown in Fig. 1, there are about 10 possible routes

for each path, so the number of total combinations is

about

loa8

2.2

Route table

and

gene

coding

In

a

dynamic routing problem, the network

model is constant and only the

traffic

demands are

changing. All possible routes for each pair of nodes

can therefore be thoroughly searched in advance and

arranged in

a

route table in order of length. In the

proposed Genetic Algorithm, each route for a path is

identified by a route

No. ,

which is its row number

in the route table.

A gene is a string of route No's. for all paths.

This gene is called a configuration string, and its

length is M M - 1 ) / 2 . A simple example of a

configuration stri ng is shown also in Fig. 1 . By



changing the combinations of route No s. in a string,

various patterns of network configuration can be

generated easily.

F o r

a

large-scale network, the number of

possible routes for each path may become very large.

Tomake the route tables small in this situation, the

number

of

candidate route is limited and only

K

shortest routes are listed in

a

route table for each

path.

Another coding method has been proposed by

Pan and Wang [SI. n their method, for each path

all possible traffic demand distribution patterns over

possible routes are

first

listed in a table, and a gene

is

a string of traffic distribution pattern No's. for all

paths. This coding method is not practical because

the number of all possible traffic distribution

patterns is huge. Furthermore, this coding method i s

not suitable for finding

a

network configuration

assigning a route for each path.

2.3 Optimization procedure

The outline of our optimization procedure,

schematically illustrated in Fig. 2, is described as

follows:

1) nitialization of configuration strings

All elements in a configuration string are initially

selected

at

random from corresponding route tables.

N

different strings are created by repeating this

procedure, and these are the f irst generation. A set of

Initialization

[Initial generation]

Gene pool

Evaluation*

-Genetic operation

Crossover

Mutation

[Next generation]

Solution : he best gene

in the last generation

ReproductiordSelection

Reproduction

[T--][--rossover Mutation

Exchange

(Number

of

cutting

sites

=3)

Fig.

2.

Optimization procedure in the prop osed

Genet ic Algor ithm.

these strings is called a gene pool, and

N

is the

population of the gene pool.

2) Evaluation of strings

A fitness is calculated for each string in the gene

pool. The fitness is a value of the objective function

for the network configuration represented by the

string.

(3)Reproduction and Selection of strings

According to their fitness values, some of strings are

reproduced and some are eliminated from the gene

pool in such a way that strings having large fitness

values reproduce more and strings having small

values die off. The number of the strings is always

restricted

to

N.

(4) Crossover

Two

strings are picked a t random from the gene pool,

randomly selected parts of them are exchanged, and

then these new strings are return to the gene pool. A

sophisticated method for determining the number of

cutting sites may be necessary t o speed evolution.

The evolutionary process advances slowly when the

number of cutting s ites is small, but if too many sites

are cut superior strings representing good network

configurations may be broken by crossover. In the

algorith m pres ent here , we randomly vary the

number of cutting sites between 1, 2, and 3.

5 )Mutation

This operation is the random change, with a small

probability P of some elements in a string.

After these operations, the string in the gene

pool are the new generation. Procedures (2) through

(51,

are repeated until a quasi-optimal string is found

for the objective function. The network configuration

represented by this string is satisfactory for most

actual purposes.

2.4

Re-use ofpa st solutions

In the procedure just described, all the first-

generation strings a re initialized a t random in

expectance of obtaining the optimal solution without

being trapped by local optima. This procedure,

however, it is not effective for rapidly getting a

solution satisfying the control targe t. We therefore

1125



propose a more effective method that uses the past

results

as a

part

of

the initial data for the current

search (Fig. 3). A pool of strings preserves the pas t

strings (the obtained routing patterns), and capacity

of this pool

is

set

at

less than the population. When

this past-solution pool is full, the oldest string is

discarded. (A new string the same as an old one is

neglected.) For each search, all strings in the past-

solution pool are copied as initial strings and the rest

of initial strings are determined randomly. We expect

useful parts of the past strings t o be exchanged in

genetic operations and t o survive the advance of

generations. We also expect the table t o eventually

become a collection of optimal solutions for various

kinds of traffic patterns. The number of iterations is

therefore reduced, especially for periodic traffic

change with some fluctuations. For

a

traffic change

very different from those al ready experienced? the

Genetic Algorithm will

of

course produce a very new

network configuration by combining randomly

generated strings.

3 2 7

1 3 8

4 5

4 5 6

4 5 3 2 7

4 5 3 8

5 6

5 3 2 7

5 8

6 5 3 2 7

6 5 3 8

7 2 3 8

3. Simulation results

3.1

ath arrangement

To demonstrate the basic capability of the

Genetic Algorithm? we fi rs t solved the following

sample problem:

“Without capacity constrains? get the optimal

initial generation

The strings ar e copied

as initial strings.

Past-solution

0001

The obtain ed solution(string)

TrafficChanges (theobt ained solutions)

Fig. 3.

Re-use

of obtained solutions.

link configuration to minimize the sum of all link.”

The node positions for this problem were the same as

those shown in Fig.

1.

For the genetic operations, we

used

a

population N=50 nd a mutation rate P=0.05.

The route tables were determined in advance.

The shortest total length in each generation

rapidly decreases during the

first 100

generations,

and the optimal solution determined by exhaustively

searching all candidates is obtained at the 700-th

generation (Fig. 4). The optimal network (link)

configuration (with routes) is shown in Fig.

5

and the

corresponding routes are listed in Table 1. We

- sol I

Genetic Algorithm

0

2 400 6 8 loo0

Generation

Fig. 4 Performanceof the Genetic Aigoriihm

and

of

random searches.

Fig. 5 Solution obtained by the Gen etic Algorithm.

Table

1

Path c onfiguration obtained

bYt

path

No

2

3

4

5

6

7

8

9

10

12

13

14

le

Gen eti c AIg

F

8 3

1 8 3 5 4

1 8 3 5

1 8 3 5 6

1 8 3 2 7

1 8

2 3

2 3 5 4

2 3 5

2 3 5 6

2 7

2 3 8

3 5 4

h h m .

path

Na

5

16

17

18

19

D

21

23

24

5

a6

27

28

=19.3

1126



compared the Genetic Algorithm with random

searches in which each element of a string was

randomly changed at random at each generation. We

used two types of the random searches: a single-point

search (population of

11,

and a multi-point search

(population of 50, the same as th e Genet ic

Algorithm). The Genetic Algorithm is clearly much

more effective than either of the random searches.

path No.

1

2

3

4

5

6

7

8

g

10

11

12

13

14

3.2

Routing control

This section uses the same network model to

demonstrate the good performance of the proposed

routing control method.

Assumptions)

(i) Network link configuration

The network link configuration and the capacity

of

the links are shown in Fig.

6.

(ii) Traffic characteristics

For the central nodes 2,3,5, nd 8, he offered loads

increase in the daytime, whereas for the peripheral

nodes, the offered loads increase in the evening (Fig.

7). Loads for the rest of links change randomly

selected route

1 2

1 8 3

1 8 6 4

1 8 6 5

1 8 6

1 7

1 8

2 3

2 7 4

2 3 5

2 3 5 6

2 7

2 3 8

3 5 4

Fig. 6 Link capacity in the netwo rk model.

Table

2.

Base path assig nment (all paths are

the

shortest

route).

15

16

17

18

19

a0

21

23

24

5

a6

27

28

8

3

3 5 6

3 2 7

3

8

4

5

4 6

4

7

4 6 8

5 6

5 3 2 7

5 6 8

6 5 3 2 7

6 8

7 2 3 8

path No1

selected route

between 30 er1 and

40

erl.

(iii) Traffic observation and routing control

Traffic was observed every 15minutes, and the delay

between traffic observation and the control action

was

15

minutes.

(iv) Base path assignment

The shortest path (listed in Table 2) was initially

established between each

t wo

nodes.

Improvement of loss-rate)

The routing controller

searched for a

satisfactory routing, taking into account the observed

traffic pattern. Here the control target was defined

as keeping the highest link loss-rates smaller than

0.

01. The objective function is written as

where A(i, j) i s the total load demanded for a physical

link between node i and j, C(i, j) is the capacity of the

physical link, and F is an Erlang-B formula tha t

estimates the average call loss-rate for the link. The

total load is the sum of all traffic passing through

tha t link.

The routing control goes into action only

when the maximum loss-rate exceeds the target

value. Fig. 8 shows simulation results for the

proposed routing control and for shortest-path

assignment. With the fixed routing, the offered loads

overflow during the busy periods. The proposed

method, however, keeps the loss-rate well under the

target value by changing the path arrangement. For

each path rearrangement,

a

satisfactory solution was

E=max( F[A(i, j>,C(i, l

6 12 16 a0 Hour 6 12 16 Hour

7 7

4 4

(a) Traffic between central nodes

(b) Traffic between peripheral nodes

Fig.

7.

Characteristics

of

offered traffic.

1127



m 0.07

r

ixed routing

0 06

L

v 0.05

-

3

0.04

s 0.02

0 03

E

5

0.01

0

a Hour

4 Controller action

Fig. 8 Performance

of

the proposed routing control.

obtained within 150 generations.

3.3 Effectsof re-using the obtained solutions

In this simulation, the control target and

assumptions were similar to those in Section

3.2,

nd

the demanded traffic was changed periodically with

some fluctuations. If the number of strings copied

from the past-solution pool into the first generation

is too large, the elements of each generation are so

similar those of the previous generation that the

evolution does not progress effectively. In the

simulation,

for

a population of 50, we set the capacity

of

the past solution pool

at

20. The simulation result

(Fig.

9)

hows that number of generations needed t o

reach

a

suitable solution decreases dramatically over

time

as

more of the past strings are preserved. The

proposed technique especially is useful for traffic

changes like these, with periodical fluctuations.

4. Conclusion

We have proposed a routing control based on

a Genetic Algorithm. By using t he configuration

string whose element represents a path between

nodes, we can obtain

a

solution that meets the loss-

rate requirements after relatively few generations

(that is, within

a

short calculating time). Moreover,

the numb er of searching i terat ions ha s been

decreased by using the past routing patterns as

a

par t of the initial data for new searches. The

proposed method is therefore useful for dynamic

routing control during traffic fluctuations, and it can

.

f

0 06

d 0.05

3 0.04

0.03

-

5 0.02

2 0.01

0

1 . - Proposed method

Fig. 9. Perform ances of the propos ed method and the

shortest-path-assignment method (and the number of

generatio ns needed for the proposed method

to

find a

satisfactory solu tion).

be extended t o such network problems as network

design and virtual-path control in B-ISDN networks.

Acknowledgment

We thank Ken-ichi Yukimatsu and Masayuki

Yanagiya of NTT Communication Switching

Laboratories for their valuable suggestions and

discussions.

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8. Dynamic Routing Control Based on a Genetic Algorithm