THE SWARM EFFECT MINIMIZATION ALGORITHM

Utilized to Optimise the Frequency Assignment Problem

Grant Blaise O’Reilly and Elizabeth Ehlers

Academy for Information Technology, University of Johannnesburg,Auckland Park, Johannesburg, South Africa

Keywords: Swarm intelligence, stigmergy, frequency assignment problem, NP-complete problem.

Abstract: The swarm effect minimization algorithm (SEMA) is presented in this paper. The SEMA was used to

produce improved solutions for the minimum interference frequency assignment problem (MI-FAP) in

mobile telecommunications networks. The SEMA is a multi-agent orientated design. The SEMA is based on

the stigmergy concept. The stigmergy concept allows the actual changes in the environment made by

entities in a swarm to act as a source of information that aids the swarm entities when making further

changes in the environment. The entities do not blindly control the changes in the environment the actual

changes guide the entities. The SwarmAFP is tested against the COST 259 Siemens bench marks as well as

tested in a commercial mobile telecommunications network and the results are presented in this paper.

1 INTRODUCTION

The frequency assignment problem (FAP) is a daily

occurrence in second generation (2G) mobile

telecommunications networks. A large saving in

revenue could be made by mobile network operators

if a model were presented that could improve

optimization of the FAP more efficiently and in less

time. The FAP focused on in this paper is the

minimum interference frequency assignment

problem (MI-FAP) with a fixed spectrum. The FAP

is a NP-complete problem (Grotschel 2000,

Eisenblätter 2000). There are a number of

techniques that have been used to try and optimize a

solution in an NP-complete problem to a level that is

acceptable (Eberhart et al., 2001, Bonabeau et al.,

1999, Dorigo et al., 1999). The success of these

techniques is measured by the time it took to reach

an acceptable solution as well as the efficiency of

the acceptable solution. The FAP is practically

unsolvable for real mobile telephone networks and

approximate algorithmic methods that obtain

solutions close the absolute minimum in a

reasonable time frame need to be used. It is beyond

the scope of this paper to give a detailed discussion

on all the proposed optimization algorithms for FAP.

However, a survey of all the optimization algorithms

and additional references can be found (Aardal et

al., 2001, Eisenblatter and Koster, 2007).

In this paper the swarm effect minimization

algorithm (SEMA) will be presented and discussed.

SEMA is an algorithm based on stigmergy.

The

SEMA is a multi-agent orientated application

design. The SEMA was utilized to try and improve

the optimization of the minimum interference

frequency assignment problem (MI-FAP). The

results produced by the SEMA were compared to the

COST 259 Siemens bench marks (Eisenblatter and

Koster, 2007). The SEMA was also applied to a

commercial, operational mobile telephone network

and the results are presented in this paper.

2 STIGMERGY

Stigmergy is the coordination of tasks and regulation

of constructions (e.g. a termite mound in a termite

colony) in an environment that depends not on the

entities, but on the constructions themselves

(Kristensen 2000, Valckenaers et al., 2001). The

entities do not direct the work but are guided by it.

In the swarm effect, stigmergy is defined as the

influence the changing environment has on the

entities in the environment. The constructions

created by the entities in the environment are

assumed to form part of the environment. These

constructions change the environment and the

changing environment stimulates a certain response

in the agents. In stigmergy the fundamental

mechanism is the ability to use the environment as a

397

Blaise O’Reilly G. and Ehlers E. (2008).

THE SWARM EFFECT MINIMIZATION ALGORITHM - Utilized to Optimise the Frequency Assignment Problem.

In Proceedings of the Tenth International Conference on Enterprise Information Systems - AIDSS, pages 397-402

DOI: 10.5220/0001671803970402

 SciTePress

shared medium for storing information so that other

individuals can interpret it (Heylighen, 1999).

3 THE SWARM EFFECT

MINIMIZATION ALGORITHM

The swarm effect minimization algorithm (SEMA)

is based on a swarm of agents making changes in the

environment in which they exist. The continual

changes induced in the environment act as a growing

information base which the agents utilize to make

further more informed changes. When applying the

SEMA to the FAP, in particular the MI-FAP, the

environment will represent the mobile telephone

network. The cells in the network will represent the

swarm agents and will be referred to as cell agents.

Each cell agent will contain a list of its channels and

each channel will require a carrier i.e. frequency.

The environment will be represented by the

collective memory map. The collective memory map

is a data structure containing information on all the

cell agents. The cell agents in the cellular network

make localized changes that result in a globalized

effect.

The algorithm utilizes a heuristic cost function to

determine the minimum interference or network

quality due to interference (NQI) (see equation 1

(Eisenblätter 2000)). The first step in the algorithm

is to load the interference matrix. An interference

matrix (IM) is a model of all the interference in the

network, i.e. it describes how the cell’s frequencies

are interfering with the neighbouring cell’s

frequencies. Each row in the IM represents a cell in

the cellular network while each column represents

an interfering cellular network cell.

Mobile measurement reports (MMRs) are used

to generate an interference matrix (Eisenblätter

2000). MMR data can be extracted from the base

station controller (BSC) in the network. This data is

utilized to build up the cell agents. From this data

each cell agent is able to build up a list of interferers,

neighbours and transceivers (TRX). Interference

between two cells in the IM is measured by the

frame erasure rate (FER). To calculate the FER the

frame erasure probability (FEP) is needed. The FEP

is calculated for all the measurements collected on

the specific cell and its interferers. These

measurements are summed and then divided by the

total number of MMRs as in equation 2 (Kuurne,

2001). The FEP is defined in equation 4. The

constants a and b are used to fit the curve to actual

broad casting control channel (BCCH) FEP and

traffic channel (TCH) FEP measurements in the

network. To calculate the FEP the carrier to

interference ratio (CIR) is needed. The CIR is

defined in equation 3. The CIR is calculated using

the data in the MMR, namely the BSPower,

rxlevelsub for the serving cell (i.e cell agent) and the

rxlevel for all the potential interferers. The BSPower

indicates the reduction from nominal power in steps

of 2dB emitted by the channel used by the call that

originated the MMR. To eliminate the effect of

power control the BSPower*2 needs to be added to

the carrier power level in an MMR. The rxlevelsub

is actually the carrier power level measured on the

slow associated control channel (SACCH). The

rxlevel reports the average signal strength during a

measurement period.

∑

∈

=−

∈

Evw

wyvy

adj

Evw

wyvy

vwcvwcNQI

feasibley

1|)()(|)()(

min

)()(

where

• v,w are carriers and represent transceivers (TRX).

• c

(vw) and c

(vw) denote the co-channel and

adjacent channel respectively, which may occur

between v and w

• y(v) Є C where C= all available channels at

carrier v\

• |y(v) - y(w)|

≥

d(vw) where d(vw) gives the

separation necessary between channels assigned

to v and w

(1)

FER = ∑

i,j

FEP/ (Total number of MMRs)

(2)

CIR

i,j

= C – I

i,j

where

• C=BSPower*2 + rxlevelSubservercell.

• Ii,j=Potential interferer’s rxlevel (dBm).

• Each MMR contains up to six I-values.

(3)

bCIRa

FEP

(4)

All the cell agents are referenced from the

collective memory map. Once all the cell agents

have been created the process begins. The swarm of

agents is created by iterating through the collective

memory map and spawning each cell agent. Each

cell agent then determines its interference. An

important rule is that a cell agent is only allowed to

adjust its own channels. The cell agent cannot adjust

its interferer’s or neighbour’s channels. A cell agent

will adjust its own channels depending on how the

channels interferer with other cell agents’ channels

(i.e. the cell agent’s interferers and neighbours

channels). Weights are assigned to each channel

depending on the amount of interference that

channel is experiencing. Thus a channel with a large

ICEIS 2008 - International Conference on Enterprise Information Systems

398

amount of interference will have a large weighting.

If a certain channel of the cell agent interferes with a

channel from one of the cell agent’s interferers or

neighbours then that specific channel is weighted

accordingly.

If the interference is co-channel i.e. the channels

have the same frequency values then the channel is

weighted for co-channel interference. Similarly, if

the interference is adjacent channel interference i.e.

the channels are adjacent to each other (separated by

one) then the channel is weighted for adjacent

channel interference. The weightings are found in

the interference matrix. Channels are also checked

against locally blocked channels, handovers, co-site

and co-cell separation. Channels violating these

checks are weighted heavily i.e. a large value

typically 1000. Thus channels with the lowest

weighting are queued to the front of the selection

queue while the highest weighted channels are

queued at the back. Once the cell agent has picked

the channels with the least interference from the

selection queue (i.e. the best channels) it will update

its channels with these selections.

If the cost value or NQI (defined in equation 1

(Eisenblätter 2000)) is greater than the previous cost

value then the localized adjustments made by the

cell agent are not beneficial to the collective. Non

beneficial adjustments are dropped and the old

channels of the cell agent are reloaded. The cost

value is then assigned to the previous cost value. In

the case where the cost value is equal to the previous

cost then no adjustment has been made i.e. the cell

agent is content with its current channel settings.

If the cost is less than the lowest cost then the

cell entities have made a localized adjustment to

their channels that have benefited the collective. In

this scenario the global interference is lower than it

was previously and the adjustment is accepted. The

lowest cost is then set to the current cost and the

collective memory map is update with the recent

changes. The process is terminated by the user once

a satisfactory cost value is achieved.

Predators are introduced into the system when

trying to break a local minimum. A local minimum

can be defined as a minimum found by the system

but that minimum is not a global minimum.

Predators are used to cause perturbations in the

collective by randomly selecting a cell agent and

then randomly changing the cell agent’s channels. If

the cell agents are randomly changed this will cause

a major perturbation in the interference resulting in a

change in the cost value or NQI. If the change

caused by the predators is within a certain threshold

value then the change is allowed otherwise the

change is dropped and another attack by the

predators is allowed. Each predator will only select

and attack a single cell agent out of the collective. A

beta parameter is used to reduce the number of

predators every time a new lowest cost is found. An

alpha parameter is used to reduce the threshold value

as time progresses.

At startup the threshold value will be set large

enough so that the system will accept many of the

changes made by the predators i.e. the system is very

volatile allowing a greater search space. However, as

the process matures the selection on changes caused

by the predators will become more conservative.

Thus, allowing the process to be less volatile as it

matures. As the process matures the threshold value

will grow smaller allowing the process to settle into

a more stable state.

4 COST 259 BENCHMARK

The effectiveness of the swarm effect algorithm is

demonstrated by applying the algorithm to the

COST 259 benchmarks (Eisenblatter and Koster,

2007). These instances are widely used in the mobile

telephone industry. The best cost values found by

the SEMA for the Siemens instances were compared

to the following: DTS (Glamorgan) a dynamic tabu

search method (Eisenblatter and Koster, 2007),

KTHIN a simulated annealing combined with

dynamic programming to compute local optima

method (Mannino et al., 2002),, TUHH a simulated

annealing (Beckmann and Killat, 1999). RWTH a

threshold accepting method (Hellebrandt and Heller,

2000) TA a threshold accepting method (Hellebrandt

and Heller, 2000) and U(Siemens) an unknown

method (Eisenblatter and Koster, 2007). The COST

259 scenarios used are described in Table 1.

The results from these methods were obtained

from the FAP website (Eisenblatter and Koster,

2007) and are presented in Table1. The comparison

of these results and the results obtained with the

SEMA are also presented in Table 1. The columns

described in table 1 are the total cost, the maximum

co-channel, adjacent channel and TRX values as

well as the total number TRX pairs exceeding an

interference of x where xЄ(0.01, 0.02, 0.03, 0.04).

The emphasis was on the ultimate quality of the

solution so the SEMA solutions did not take time

into consideration i.e. the application was run until

an acceptable solution was found. However, it

should be emphasized that the SEMA can produce

satisfactory results in times that range from 45

minutes to several hours. These times are acceptable

THE SWARM EFFECT MINIMIZATION ALGORITHM - Utilized to Optimise the Frequency Assignment Problem

399

in a commercial environment. For example a cost

minimization value of 3.21 was achieved in 45

minutes for the Siemens 1 scenario utilizing ten

predators, alpha = 0.95 and beta = 0.99. Best results

were found when using less than twenty predators,

0.9≤alpha≤0.99 and 0.9≤beta≤0.999 in all the COST

259 scenarios.

Table 1: COST 259 Siemens scenarios.

Siemens 1: GSM 900 network with 179 active sites, 506 cells, and an average of

1.84 TRXs per cell. The available spectrum consists of two blocks containing 20

and 23 frequencies, respectively

TRX pairs exceeding App Cost Co Adj TRX

.01 .02 .03 .04

K-THIN 2.20 0.03 0.03 0.05 33 4 1 0

TUHH 2.78 0.04 0.04 0.08 60 14 6 0

RWTH 2.53 0.03 0.03 0.06 48 11 3 0

TA 2.30 0.03 0.03 0.05 43 7 2 0

U 3.36 0.05 0.04 0.12 78 25 10 3

SEMA 2.35 0.03 0.03 0.06 44 9 2 0

Siemens 2: GSM 900 network with 86 active sites, 254 cells, and an average of

3.85 TRXs per cell. The available spectrum consists of two blocks containing 4

and 72 frequencies, respectively

TRX pairs exceeding App Cost Co Adj TRX

.01 .02 .03 .04

DTS 14.28 0.11 0.02 0.20 343 89 24 18

K-THIN 14.27 0.07 0.02 0.16 359 71 27 17

TUHH 15.46 0.07 0.02 0.18 404 109 42 20

RWTH 14.75 0.06 0.02 0.17 268 91 34 13

TA 15.05 0.11 0.02 0.20 381 92 37 15

U 17.33 0.08 0.02 0.20 462 148 47 18

SEMA 14.86 0.08 0.02 0.17 364 87 41 14

Siemens 3: GSM 900 network with 366 active sites, 894 cells, and an average of

1.82 TRXs per cell. The available spectrum comprises 55 contiguous frequencies.

TRX pairs exceeding App Cost Co Adj TRX

.01 .02 .03 .04

DTS 5.19 0.04 0.03 0.07 88 14 3 0

K-THIN 4.73 0.03 0.02 0.08 80 6 0 0

TUHH 6.75 0.05 0.03 0.11 137 31 9 2

RWTH 5.63 0.03 0.03 0.07 103 15 3 0

TA 5.26 0.04 0.03 0.07 87 10 3 0

U 8.42 0.05 0.04 0.12 188 47 18 6

SEMA 5.76 0.03 0.03 0.08 101 28 3 0

Siemens 4: GSM 900 network with 276 active sites, 760 cells, and an average of

3.66 TRXs per cell. The available spectrum comprises 39 contiguous frequencies

TRX pairs exceeding App Cost Co Adj TRX

.01 .02 .03 .04

DTS 81.88 0.20 0.05 0.43 2161 971 547 344

K-THIN 77.25 0.19 0.05 0.36 2053 871 445 282

TUHH 89.15 0.24 0.03 0.53 2350 1056 591 368

RWTH 83.57 0.18 0.04 0.35 2251 1006 540 343

TA 80.97 0.17 0.03 0.36 2143 933 502 328

U 105.82 0.27 0.04 0.53 2644 1286 798 562

SEMA 81.96 0.21 0.05 0.48 2181 991 549 353

5 RESULTS OF

IMPLEMENTATION

The SEMA was tested on a commercial mobile

telecommunications network in South Africa,

namely MTN. The SEMA was applied to one

operational base station controller (BSC). There

were 349 cells with an average of 3 transmitters per

cell in the BSC. The available spectrum consisted of

two blocks containing 24 and 31 frequencies,

respectively. The frequency plan produced by the

SEMA took on average several days to produce. The

frequency plan produced by the SEMA was also

implemented into the mobile telephone network. The

%DROP (percent drop) parameter represents the

percentage of abnormal disconnections (drop calls)

on the BSC in a mobile cellular network. From

figure 1 it is clear that there was a decrease in the

%DROP on the BSC after the SEMA frequency plan

was implemented. This can be seen by studying the

%DROP before and after the vertical yellow broken

line. The vertical yellow broken line depicts the

point at which the SEMA was implemented into the

BSC (see the label “Swarm AFP run in”). Swarm

AFP stands for the Swarm automatic frequency

planner that implements SEMA. The measurement

before this mark depicts the initial network

measurements while all measurements after the

mark depict the network after the SEMA frequency

plan was implemented. The decrease in the %DROP

was a substantial 0.4 on the %DROP scale. This may

not seem significant, but in terms of the %DROP on

a cellular network that prides itself on its low

%DROP, a decrease of 0.4 is amazing. An

improvement of 0.4 on the %DROP scale on a BSC

carrying a large amount of traffic can equate to a

large addition in revenue. To substantiate the actual

decrease of a 0.4% on the %DROP scale, the traffic

(erlang rate) would have to have remained constant,

since a decrease in the erlang rate would also cause a

decrease in the %DROP. However, by studying

figure 1 it can be seen that the erlang rate remained

constant (see the horizontal black broken line which

represents the erlang gradient), while there was a

distinct decrease in the %DROP after the SEMA

was implemented. Usually when a frequency plan is

implemented an increase in the %CFAIL is

experienced. The %CFAIL (percent channel failure)

parameter represents the percentage failure rate in

the ability to seize a traffic channel. The reason for

this is that most frequency plans relax the adjacent

channel rule for the traffic channels, as the major

concern is to minimize co-channel interference on

the TCHs and to ensure that there is absolutely no

co-channel or adjacent channel interference between

the BCCH and TCHs. Again, an encouraging feature

noted in figure 1 is that the BSC did not suffer from

an increase in the %CFAIL. The %CFAIL remained

fairly constant after the SEMA implementation. This

indicates that the actual frequency planning that was

taking place by the SEMA was of good quality.

Overall the SEMA frequency plan performed fairly

well by decreasing the %DROP by 0.4% on the

%DROP scale and did not cause the %CFAIL to

fluctuate in an increasing way after the frequency

plan was implemented.

ICEIS 2008 - International Conference on Enterprise Information Systems

400

%DROP and %CFAIL

1 16 31 46 61 76 91 106 121 136 151 166 181 196 211 226 241 256 271 286 301 316 331 346 361 376 391 406 421 436 451 466 481

Hours

Erlan

%DROP, %CFAIL

Erlang %DROP %CFAIL Linear (Erlang)

Swarm AFP run in

Figure 1: %DROP and %CFAIL for the operational BSC

before and after the Swarm AFP run.

Figure 2: Interference bands 1 to 5.

ICM

1 19 37 55 73 91 109 127 145 163 181 199 217 235 253 271 289 307 325 343 361 379 397 415 433 451 469

Hours

ICM 2,ICM 3

ICM 4,ICM 5

ICM2 ICM3 ICM4 ICM5

Swarm AFP run in

Figure 3: ICMs for operational BSC.

The idle channel measurement (ICM) parameter is

explained with the use of figure 2. There are five

interference bands, each marked by a limit. For

example, interference band 1 ends at limit 1 and

interference band 2 ends at limit 2. This continues

up to interference band 5, which is the last

interference band. The limits 1 to 5 are represented

by the ICM parameters, namely ICM1 to ICM5,

respectively. The ICM band parameters provide an

indication of the level of interference in the cell.

A large number of points in the ICM4 and ICM5

bands indicates a large amount of interference in the

BSC and is a very unfavourable situation. From

figure 3, it can be seen that the more points in band

5, the more the interference (~-47dBm), while

interference band 1 has much less interference

(~110dBm). Thus ICM5 is worse than ICM4 and

similarly ICM4 is worse than ICM3 and so on. The

ideal situation in a mobile cellular network BSC is to

have all points located in ICM1 and ICM2, a smaller

number of points in ICM3 and virtually no points in

ICM4 and ICM5.

Figure 3 depicts the actual idle channel

measurements for the BSC before and after the

SEMA frequency plan was implemented. Remember

that the vertical yellow broken line represents the

point at which the frequency plan was implemented

into the BSC. It is apparent from the measurements

in figure 3 that there was a drastic drop in ICM5 and

ICM4 parameter values after the SEMA was

implemented into the BSC. There was also an

extensive improvement in ICM2 after the

implementation of the SEMA frequency plan. This

again proves that the SEMA frequency plan has

made considerable improvements to the BSC. The

BSC was optimized to the ideal situation with regard

to the ideal channel measurements. The number of

points has decreased in the ICM4 and ICM5 bands,

while the ICM2 band has increased considerably.

6 CONCLUSIONS

In this paper an engineering problem of high

practical relevance has been addressed, a relatively

simple optimization approached based on a

particular search scheme, namely the swarm effect

minimization algorithm (SEMA) has been designed

and implemented using a multi-agent model. The

SEMA was benchmarked against the COST 259

benchmarks, in particular the Siemens set of

problems. The SEMA was then implemented into a

commercial mobile telephone network in South

Africa, namely MTN. It was shown that the SEMA

produced encouraging results when applied to the

COST 259 Siemen’s problems. The results were

compared to the current results published on the

FAP website (Eisenblatter and Koster, 2007) and the

SEMA closely match some of the best results. One

of the most important characterizing aspects

produced in the swarm effect minimization

algorithm is the use of the stigmergetic model of

communication. This allows the cell agents to be

directed by the formation of the ever changing

assignments of frequencies in the network. The cell

THE SWARM EFFECT MINIMIZATION ALGORITHM - Utilized to Optimise the Frequency Assignment Problem

401

agents form the swarm. This novel approach of

allowing the changes in the structure of the network

frequencies (i.e. the environment) to guide the actual

selection and determination of assigned frequencies

is the main reason for the improvements displayed

by the SEMA.

ACKNOWLEDGEMENTS

The authors wish to thank the University of

Johannesburg and the Academy for Information

Technology at the University of Johannesburg and

MTN (SA).

REFERENCES

Grotschel, M., 2000. Frequency Assignment in Mobile

Phone Systems, ZIB-Report 00-58, December.

Eisenblätter, A., 2000. Frequency Assignment in GSM

Networks: Models, Heuristics and Lower Bounds, PhD

Thesis, TU Berlin.

Eberhart, R.C., Kennedy K., and Shi, Y., 2001. Swarm

Intelligence (The Morgan Kaufmann Series in

Artificial Intelligence), Academic Press.

Bonabeau, E., Dorigo, M., and Theraulaz, G., 1999.

Swarm Intelligence: From Natural to Artificial

Systems (Santa Fe Institute Studies in the Sciences of

Complexity Proceedings), Oxford University Press.

Dorigo, M., and di Caro, G., 1999. The ant colony

optimization meta-heuristic, New Ideas in

Optimization, D. Corne, M. Dorigo and F. Glover,

eds., McGraw-Hill, pp.11-32.

Eisenblatter A. And Koster A. 2007. FAP website

http://fap.zib.de

Aardal, K. I., van Hoesel, S. P. M. , Koster, A. M. C. A.,

Mannino, C. , and Sassano, A., 2001. Models and

Solution Techniques for Frequency Assignment

Problems, Berlin, Germany, ZIB-Rep. 01–40.

Montemanni, R., Moon, J.N.J., Smith, D.H., 2003. An

improved tabu search algorithm for the fixed spectrum

frequency assignment problem, IEEE Transactions on

Vehicular Technology, vol 52, no.3, pp.891–901,

May.

Maniezzo, V., and Carbonaro, A., 2000. An ANTS

heuristic for the frequency assignment problem, Future

Generation Computer Systems 16, pp. 927-935, 2000.

Kristensen, L.K. 2000. Aintz: Collective Problem Solving

by Artificial Ants,

http://www.evalife.dk/publications2.php.

Valckenaers, P., Kollingbaum, M., van Brussel, K.,

Bochmann, O., and Zamfirescu, C., 2001. The Design

of Multi-Agent Coordination and Control Systems

using Stigmergy, Proc. of the IWES'01 Conference.

Heylighen, F., 1999. Collective intelligence and its

implementation on the Web: algorithms to develop a

collective mental map, Computational and

Mathematical Organizational Theory, vol. 5, no. 3,

pp.253-280.

Kuurne A., 2001. Mobile Measurement based frequency

planning in GSM Networks, M.Sc. dissertation,

Department of Engineering Physics and Mathematics,

University of Helsinki.

Mannino, C., Oriolo G., and Ricci f., 2002. Solving

Stability Problems on a Superclass of Interval Graphs,

26-02,Universit'a di Roma La Sapienza, Dipartimento

di Informatica e Sistemistica,

Beckmann, D., and Killat U., 1999. Frequency Planning

with respect to Interference Minimization in Cellular

Radio Networks, TD(99)032, COST 259, Vienna,

Austria", January, 1999.

Hellebrandt, M., and Heller, H., 2000. A new heuristic

method for frequency assignment TD(00)003", COST

259, Valencia, Spain, January.

ICEIS 2008 - International Conference on Enterprise Information Systems

402