Designing Optical Networks Using Simulated Annealing Algorithm ConTEL99_prezentacija

Croatian Telecomm - TKC Rijeka

DESIGNING OPTICAL ACCESS NETWORKS

USING SIMULATED ANNEALING (SA)

ALGORITHM

Branko Luki

ConTEL 99, 5th International Conference on Telecommunications June 15-17, 1999, Zagreb, Croatia


TIPICAL ACCESS NETWORK IN RESIDENTIAL AREA

AP 500-1000 subscribers

FP

DP 4-50 sunscribers

CORE NETWORK ACCESS NETWORK

AP:access point - OLT, ADM, XTC

FP: flexible point - first point of branching in double-star topology

DP: distribution point - ONU, or FTTx


optical fiber

splitter

OLT or adequote node

meanhole

cable conduit

subscriber

PON NETWORK MAPPING ON

CONDUIT NETWORK

overlay PON structure

conduit network

OLT


SIMULATED ANNEALING (SA)

Annealing the process in which a solid is heated up sufficiently to allow the atoms and molecules to rearange themselves into a stress-free state and then cooled gradually so as to lock the new configuration into place

Simulated annealing a probabilistic technique for solving combinatorial optimisation problems. In simulating annealing (SA), the value of the objective function being minimised is analogous to the energy of the solid; minimising is equivalent to finding the minimum value of the function


SIMULATED ANNEALING (SA) - continued

SA begins with a random solution and then modifies that solution slightly to create a new potential solution. If the new solution satisfies the constraints and has a lower cost than the existing solution, it is accepted without question. However, if the new solution has a higher cost, than the decision as to whether it will be accepted is made on the basis of a probability that is governed by the current temperature of the system.

Occasionally accepting lower-valued solutions allows the process to break out of potentially sub-optimal local maxima.

SA method is a statistically based optimisation technique and can be presented as Boltzman distribution,

P EZ T

e

E

k TB{ }( )

E

1


SIMULATED ANNEALING (SA) - continue Metropolis and his coauthors were still in 1953 discussed the problem of annealing simulate the evolution to thermal equilibrium of a solid for a fixed value of the temperature.

This is known as Metropolis algorithm. Kirckpatrick and his coauthors in 1982 i 1983 and Cerny in 1985 were undependently proposed and realized postupak of annealing of solid with Metropolis algorithm for solute combinatorial optimisation problems (TSP travel-salesman problem)


METROPOLIS ALGORITHM

begin

initial configuration 0, set 0,

initial value of contol parameter T0, set TkT0,

while (stopping criterion is not satisfied) do

begin

while (not yet in equilibrium state) do

begin

new configuration is neighbours configuration of ;

let C() and C() be value of objective function of configurations and ,

if C() < C() then /* step to better solution accept */

accept new configuration ; set C()C(), else /* slowly step to worse solution: possible accept */

calculate probability Prob = e-C( ' )-C( )

T

for new configuration,

generate random number random(0,1),

if random(0,1) Prob then set C()C() endif

end begin

decrease value of control parameter Tk, Tk+1= Tk,

end while

end begin

end while

presents the best solution

end begin


SIMULATED ANNEALING (SA) ALGORITHM

GENERATE INITIAL

SOLUTION

PERTURBATION

OF CURRENT SOLUTION

TO CREATE NEW SOLUTION

Does the new solution

have a lower cost

then the current one?

On the basis of probability

should the solution be

accepted?

NO

NO

YES YES

ACCEPT

NEW

SOLUTION

Have

the stoping criteria

been met?

YES

NO

ACCEPTED

SOLUTION

ITERATE


SA - Implementation Considerations

Modelling of the Objective

Function

How can the objective function be represented efficiently, bearing in mind that minimising the generation of infeasible solutions can reduce the optimisation time significantly?

Initialisation What will be the starting point for the optimisation?

Starting value of Control

Parameter (Starting

Temperature)

If the starting value of control parameter is too low, optimisation process will converge too quickly and may produce suboptimal solution.

Cooling Schedule At what rate will the temperature be lowered? If the annealing process is cooled too quickly, potentially undesirable features may be locked into the solution and produce suboptimal result.

Perturbation How will the current solution modified to create the new solution?

Termination What criteria will be used to decide when to terminate the annealing process?


OPTIMAL LENGTH OF OPTICAL FIBRES OF

PON STRUCTURE DOUBLE-STAR TREE

l = min l + min minopt kk=1

S2S2=1

N(S2)

S2S2=1

N(S2)

l l

OLT

1

2

3

4

.

.

.

K

l1

l2

l3

l4

.

.

.

lK

lKmin

k1

k2

.

.

.

kNs2

p1

.

.

.

pNs1

1

.

.

.

Ns2

1

.

.

Ns1

.

lNs2min lNs1min

lmin = lKmin + lNs2min +

lNs1min


CIRCUMSTANCES FOR OPTIMISATION PROBLEM OF

PON DOUBLE-STAR TREE TOPOLOGY

the splitters locate in nodes with weigth equal zero (0),

ONUs locate in ending nodes (nodes with degree equal 1, and nodes with weigth

greater than zero,

each ONU links to splitters of second level,

each splitter of second level links to splitters of first level,

each splitter of first level links to root node (central office, head-end),

splitting ratio of solitters is 1:2i, i=1, 2, 3, 4, 5


RESULTS OF OPTIMISATION PON DOUBLE-STAR TREE TOPOLOGY

Results for real problem with 19 nodes

starting value

of control

parameter

ending value of

control

parameter

decrement

factor

number of

iterations

optimal length of fibers (m)

splitting-ratio of

splitters of

1st level

splitting-ratio of

splitters of

2nd level

execute time

(s)

c0 cf a maxiter minlength s1 s2 t

500 100 0,75 10 1708 1:8 1:8 7 1000 100 0,75 10 1769 1:4 1:8 10

500 100 0,75 50 1729 1:4 1:4 32 1000 100 0,75 50 1675 1:8 1:8 50 3433 687 0,75 50 1410 1:4 1:4 15 4553 911 0,75 50 1649 1:8 1:8 18

60634 4042 0,75 50 1874 1:2 1:8 163 98376 6558 0,75 50 1604 1:4 1:8 165

500 100 0,75 100 1392 1:4 1:4 64 1000 100 0,75 100 1696 1:4 1:8 101 3939 788 0,75 100 1800 1:16 1:16 30 5657 1131 0,75 100 1901 1:4 1:4 34

14427 2885 0,75 100 1718 1:4 1:4 33 24212 4842 0,75 100 1754 1:16 1:16 34 57312 11462 0,75 100 1584 1:4 1:4 33 66864 13373 0,75 100 1719 1:8 1:8 34 12009 801 0,75 100 2107 1:2 1:16 55 3379 225 0,75 100 1677 1:8 1:8 55

42753 2850 0,75 100 1708 1:8 1:32 56 119305 7954 0,75 100 1558 1:4 1:4 57 182480 12165 0,75 100 1925 1:4 1:4 55 407026 21135 0,75 100 1787 1:32 1:32 55 944746 62983 0,75 100 1707 1:16 1:16 56

3240 648 0,75 500 1482 1:4 1:4 145

3926 785 0,75 1000 1601 1:2 1:8 332


RESULTS OF OPTIMISATION PON DOUBLE-STAR TREE TOPOLOGY

Results for real problem with 119 nodes

starting value

of control

parameter

ending value

of control

parameter

decrement

factor

number of

iterations

optimal length

of fibers

(m)

splitting-ratio

of splitters of

1st level

splitting-ratio

of splitters of

2nd level

execute time

(s)

c0 cf a maxiter minlength s1 s2 t

32396 6479 0,75 5 15397 1:8 116 2181

27676 5537 0,75 5 16490 1:8 1:8 8131

1265 300 0,75 10 16169 1:8 1:8 3485

414285 27619 0,75 10 16732 1:8 1:16 5356


RESULTS OF APLICATION SIMULATED ANNEALING OPTIMISATION METHOD

ON REAL AREA OF PON DOUBLE-STAR TREE TOPOLOGY

Podruje Podmurvice u Rijeci 119 vorova ukupno

1 vor smjetaj UPS-a 72 vora teine vee od nula (stambene zgrade i mali poslovni prostori) 46 vorova teine jednake nula (kabelski zdenci - mjesta predvidiva za smjetaj djelitelja)

Rijeka, 09.01.1998.

Broj ONU jedinica po objektu (zgradi)

Objekt 1 UPS 960 prikljuaka

Objekt korisnika ONU_256 ONU_128 ONU_64 ONU_32 ONU_12 ONU_4 ONU_2 ukupno ONU jedinica

2 0 0 0 0 0 0 0 0 0

3 0 0 0 0 0 0 0 0 0

4 0 0 0 0 0 0 0 0 0

5 173 1 0 0 0 0 0 0 1

6 0 0 0 0 0 0 0 0 0

7 75 0 1 0 0 0 0 0 1

8 173 1 0 0 0 0 0 0 1

9 0 0 0 0 0 0 0 0 0

10 148 1 0 0 0 0 0 0 1

11 48 0 0 1 0 0 0 0 1

12 0 0 0 0 0 0 0 0 0

13 99 0 1 0 0 0 0 0 1 .

.

.

Ukupan broj ONU jedinica na promatranom podruju iznosi --> 72


Broj djelitelja u ovisnosti o omjeru djeljenja i hijerarhiji djelitelja

Broj djelitelja 1_og reda 18 kom za omjer djeljenja 1: 2






Lokacije djelitelja 2_og reda

Djelitelji 2_og reda omjera djeljenja 1: 2

smjeteni su u vorovima 44 75 114 33 90 31 35 78 110 22 65 42 3 3 103 2

65 86 75 42 103 86 22 2 78 65 97 109 48 33 6 67

75 90 44 67

Djelitelji 2_og reda omjera djeljenja 1: 4


3 9

Lokacije djelitelja 1_og reda

Djelitelji 1_og reda omjera djeljenja 1: 2 na koje su vezani

djelitelji 2_og reda omjera djeljenja 1: 2


109 39



smjeteni su u vorovima 97 22 90 25 60 4 114 58 70




smjeteni su u vorovima 60 21 42 65 21


djelitelji 2_og reda omjera djeljenja 1:16

smjeteni su u vorovima 110 25 63


djelitelji 2_og reda omjera djeljenja 1:32

smjeteni su u vorovima 114 110

Parametri primjene metode simulated annealing

tstart= 33705. tend= 2247. tfakt= .75 maxit= 50

Vrijeme izvrenja programa iznosi -62160 sekundi

Putevi od pojedine ONU jedinice do nadlenog djelitelja 2_og reda

Djelitelj 2_og reda omjera djeljenja 1: 4 smjeten je u voru 50

4 najkraa puta iz vora 50

28-ti put 51 50 duljina 28_og puta iznosi 15

29-ti put 53 52 50 duljina 29_og puta iznosi 39



Duljina odabranih putova iznosi 166 m

Djelitelj 2_og reda omjera djeljenja 1: 4 smjeten je u voru 109





71-ti put 118 117 114 109 duljina 71_og puta iznosi 73

72-ti put 119 117 114 109 duljina 72_og puta iznosi 90


Putevi od pojedinog djelitelja 2_og reda do nadlenog djelitelja 1_og reda

Djelitelj 1-og reda omjera djeljenja 1: 4 smjeten je u voru 2


14-ti put 67 2 duljina 14_og puta iznosi 15

11-ti put 58 60 63 65 67 2 duljina 11_og puta iznosi 153

12-ti put 77 75 72 70 2 duljina 12_og puta iznosi 158

5-ti put 56 58 60 63 65 67 2 duljina 5_og puta iznosi 178


Djelitelj 1-og reda omjera djeljenja 1: 4 smjeten je u voru 16




9-ti put 114 109 102 100 14 16 duljina 9_og puta iznosi 241

12-ti put 77 86 3 9 12 100 14 16 duljina 12_og puta iznosi 260


Putevi od OLT_a do djelitelja 1_og reda smjetenih u 2 16 86 26 67

put 2 1 duljina puta 25


put 16 14 100 12 9 3 86 77 75 72 70 2 1 duljina puta 444

put 86 77 75 72 70 2 1 duljina puta 230

put 26 25 22 21 56 58 60 63 65 67 2 1 duljina puta 359

put 67 2 1 duljina puta 40

Ukupna duljina odabranih putova iznosi 1098 m

Sveukupna duljina putova iznosi 17973 m

Pronaena optimalna sveukupna duljina PON strukture je za

omjer djeljenja ks1=1: 4 i ks2=1: 4

minlen(2,2)=17973 m


Outline of calculated values of randomly choosed configurations

with application of simulated annealing method


Shematic view

of optimal PON double-star tree in one real area in Rijeka


Topographic view of

optimal PON double-star tree in some area in Rijeka


CONCLUSION AND FUTURE WORK

We analyse a PON on double-star topology.

Cost function is full length of all optical fibres.

We use a SA method.

Optimal solution give us: i) a path-ways from root node to each 1-level splitters, from 1st level splitters

to 2nd level splitters, and from 2nd level splitters to end-users; ii) locations of all splitters; iii) splitting ratio for each splitter.

A practicaly result is:

posibility of use for connection plan of fibers between end-users and 2nd level splitters, then 2nd level splitters and 1st level splitters, and 1st level splitters and root node.


CONCLUSION AND FUTURE WORK

The open problem is:

to make an efectively way to determine starting solution of PON.

We work on problem of influence between PON double-star topology and ring topology, i.e. rearrangement of PON double-star topology into ring topology. About this, is possible redesign of an part of PON, and conection with ring structure, or build a new ring structure on reconstruction of current buildings, build a new bussines buildings in residential area, on demand of great residential buildings for broadband or higher bitrate.

An interesting is discuss about deployment from current solutions based on cupper cable technology (xDSL), to new solutions based on optical fibres technology and architectures (FTTB, FTTH).


THE END

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