FREQUENCY ASSIGNMENT OPTIMIZATION USING THE
SWARM INTELLIGENCE MULTI-AGENT BASED ALGORITHM
(SIMBA)
Grant Blaise O’Reilly
Academy for Information Technology, University of Johannnesburg, Auckland Park, Johannesburg, South Africa
Keywords: Swarm intelligence, Stigmergy, Multi-agent system, Frequency assignment problem.
Abstract: The swarm intelligence multi-agent based algorithm (SIMBA) is presented in this paper. The SIMBA
utilizes swarm intelligence and a multi-agent system (MAS) to optimize the frequency assignment problem
(FAP). The SIMBA optimises by considering both local and global i.e. collective solutions in the
optimization process. Stigmergy single cell optimization (SSCO) is also used by the individual agents in
SIMBA. SSCO enables the agents to recognize interference patterns in the frequency assignment structure
that is being optimized and to augment it with frequency selections that minimized the interference. The
changing configurations of the frequency assignment structure acts as a source of information that aids the
agents when making further decisions. Due to the increasing demand of cellular communication services
and the available frequency spectrum optimal frequency assignment is necessary. The SIMBA was used to
optimize the fixed-spectrum frequency assignment problem (FS-FAP) in cellular radio networks. The results
produced by the SIMBA were benchmarked against the COST 259 Siemens scenarios. The frequency
assignment solutions produced by the SIMBA were also implemented in a commercial cellular radio
network and the results are presented.
1 INTRODUCTION
The demand for cellular communication services is
constantly growing. However, due to the limited
frequency spectrum available to cellular network
operators the efficiency in which the frequency
spectrum is utilized is a very important issue. This is
the reason why the frequency assignment problem
has attracted a large amount of interest. The efficient
use of radio spectrum and the minimization of
interference is the main goal of any frequency
assignment algorithm.
The frequency assignment problem (FAP) in its
simplest form is equivalent to the generalized graph-
colouring problem (Hale, 1980). Thus it is also an
N-P complete problem (Hale, 1980). Searching for a
solution to the frequency assignment problem
increases exponentially with the number of cells in
the radio network. In this paper the swarm
intelligence multi-agent based algorithm (SIMBA)
will be presented and discussed. SIMBA is an
algorithm inspired by swarm intelligence. The
SIMBA was implemented using a multi-agent
system (MAS). Agents in the multi-agent system of
SIMBA consider both local and global solutions
when optimizing the fixed spectrum frequency
assignment problem (FS-FAP). The local solution is
the frequency assignment solution produced by the
individual agent. The global solution is the best
frequency assignment solution (solution with the
least interference) produced by the collective. The
design of the SIMBA as well as the MAS supporting
the SIMBA will be described in depth. The results
produced by the SIMBA will be compared to the
COST 259 Siemens bench marks (Eisenblätter and
Koster, 2008). The frequency assignment solutions
produced by SIMBA were implemented in a
commercial, operational cellular radio network and
the results are presented in this paper.
Stigmergy single cell optimization (SSCO) was
utilised by the individual agents in the SIMBA in
order to make intelligent decisions on the next
frequency that needed to be selected. SSCO is based
on stigmergy. The actual structure that the agents are
working on actually guides the agents on their future
decisions. SSCO enables the agents to recognize
interference patterns in the frequency assignment
structure that is being optimized. These interference
25
Blaise O’Reilly G. (2009).
FREQUENCY ASSIGNMENT OPTIMIZATION USING THE SWARM INTELLIGENCE MULTI-AGENT BASED ALGORITHM (SIMBA).
In Proceedings of the 11th International Conference on Enterprise Information Systems - Artificial Intelligence and Decision Support Systems, pages
25-32
DOI: 10.5220/0001857600250032
Copyright
c
SciTePress
patterns then stimulate the agent to select a
frequency that minimises this interference pattern.
The SIMBA has shown promising improvements
both in the efficiency of the resultant solution and
the time it took to find an acceptable solution. The
efficiency of the resultant solutions has been tested
against a number of cellular radio network
measurement parameters. These parameters
indicated the quality in a cellular radio network after
a frequency assignment solution is implemented.
These parameters will also be discussed briefly.
2 THE FIXED-SPECTRUM
FREQUENCY ASSIGNMENT
PROBLEM
The FS-FAP can be represented by a weighted,
undirected graph G with a set of vertices V and a set
of edges E (Montemanni et al., 2003). Formally, it is
a quadtuple FS-FAP = {V, E, D, P} with
Every transceiver in the frequency
assignment problem is represented by a
vertex v where v Є V. Every vertex
represents a transmitter of the original
frequency assignment problem
(Montemanni et al., 2003).
Interference between two transceivers is
represented by an edge. Edges will be
written as {v, u} (Montemanni et al., 2003).
A label on the edges will be described by D
such that the edge {v, u} is mapped to d
vu
Є
N where N={x|x is a positive integer or
zero}. d
vu
will be defined as the highest
separation that may cause unacceptable
interference between frequencies assigned
to transceivers u and v. The frequency
assigned to transceiver v is denoted by f(v)
and similarly the frequency assigned to
transceiver u is denoted by f(u). If |f(v) –
f(u)|> d
vu
, then the interference between the
frequencies on transceiver v and u is
acceptable (Montemanni et al., 2003).
A label on the edges will be described by P
such that the edge {v, u} is mapped to p
vu
Є
N where N={x|x is a positive integer or
zero}. p
vu
is defined as the cost to be paid if
the separation between the frequencies
assigned to transmitters v and u is less than
or equal to d
vu
(Montemanni et al., 2003).
The cost of the total interference in the
frequency assignment problem is given by
the following cost function:
=
d
vu
ufvf
Euv
vu
p
SCos
t
|)()(|
;},{
)(
(1)
where the solution representation of a
frequency assignment S will be represented
by using a list
<f
s
(0), f
s
(1), f
s
(2),…, f
s
(v),…, f
s
(|V|-1)>
where the v
th
element contains the frequency
assigned to transceiver v.
The objective of the FS-FAP is to find an
assignment that minimizes the sum of p
vu
over all
pairs for which |f(v) – f(u)| d
vw
(Montemanni et al.,
2003).
3 STIGMERGY SINGLE CELL
OPTIMIZATION
In a cellular network each cell is served by a small
number of transmitters (usually 1-9). With exception
of the broadcast control channel (BCCH) the
constraints applied to the frequency assignment of
each transceiver (TRX) in the cell may be identical.
Due to the BCCH being a critical channel the
constraints (frequency separation or penalties)
associated with this channel are usually very high.
Thus, stigmergy single cell optimization (SSCO) is
an appropriate technique that can be used only in
cellular telecommunication networks.
Stigmergy single cell optimization (SSCO)
allows one to fix all the frequencies assigned to a
single cell’s interferers. The frequencies of this
single cell’s transceivers can then be optimized
according to the interference patterns that emerge
when certain frequencies are selected. If large
interference patterns emerge when a frequency is
selected then the frequency is discarded. If no
interference or minimal interference patterns are
experienced by the selection of a frequency then the
frequency is accepted. The actual structure of the
frequency assignments and the interference patterns
created by the frequency selections is constantly
influencing the decision of the agent. It is proposed
that an agent will change the frequencies on the
transceivers according to the structure of the current
interference pattern in the frequency assignment
structure. The frequency assignment working
solution will represent the structure the agent is
building. The agent will approach each transceiver
and change its frequency to the current best
frequency. The current best frequency has the least
amount of interference. Once the new frequency has
been assigned to the transceiver the cost of the
frequency assignment solution is calculated using
ICEIS 2009 - International Conference on Enterprise Information Systems
26
equation 1. The agent will be stimulated to accept a
configuration change where the interference pattern
(i.e. cost) was decreased and repel a change that
increased the interference.
The analogy to stigmergy comes from the fact
that 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 and Valckenaers et al., 2001). The
entities do not direct the work but are guided by it.
Structure construction e.g. nest building in social
wasps is an example of this form of communication.
Agents recognize patterns in a structure that is being
built and are able to augment it with new
components. The changing configurations of the
structure act as a source of information that aids the
agents when making further decisions. The agents
are stimulated by the change in the configuration of
the structure and respond accordingly (Bonabeau et
al., 1999). Social wasps have the ability to build
highly organized construction i.e. nests. These
structures can range from a few cells to millions of
cells packed in stacked combs. Studies have shown
that these building characteristics consist of a series
of if-then decision loops (Bonabeau et al., 1999).
Each stage of the nest stimulates the wasps to
respond in a certain manner.
3.1 Implementing the Stigmergy Single
Cell Optimization
The list of fixed frequencies in the network’s
allocated spectrum will be represented by L. Each
frequency is tested using the SSCO. A priority queue
will be created with the priority ranked according to
the frequency causing the least amount of
interference. When a frequency is requested from
the priority queue the frequency with the least
amount of interference is returned. This is the best
current frequency that can be used.
The priority queue calculates the priority of the
frequencies with minimum interference by taking as
input the transceiver T. Through an iterative process
the transceiver T will be set to each frequency in the
fixed frequency list L, respectively. For each
frequency in the list L that is set to the transceiver T
the cost of the total interference is calculated i.e. an
interference pattern is determined. Thus each
frequency in L will have an associated interference
cost. The list L is then sorted in a descending order
with the frequency with the lowest interference cost
at the top of list L. When requested the priority
queue will return the top element or highest priority
element from the list L i.e. the frequency with the
lowest interference cost.
When the agent is executing the algorithm it will
iterate through every transceiver in the FAP. When a
certain transceiver v is selected by the agent it will
select the best current frequency. The agent does this
by requesting the frequency from the priority queue.
The frequency is then removed from the priority
queue. This process is repeated until a frequency is
found that does not cause any violations (i.e.
minimizes the interference pattern) and is not in the
pheromone list (see section 3.2). Once a frequency is
found it is assigned to the transceiver v. The cost is
then calculated for the new solution S i.e. Cost(S). If
the Cost(S) is less than the previous cost i.e.
Cost(S
prev
) plus a threshold value i.e. Cost(S) –
Cost(S
prev
) threshold then the frequency assigned
to v is accepted. However, if Cost(S) – Cost(S
prev
) >
threshold then the frequency assigned to v is rejected
and the transceiver v reverts back to its previous
frequency.
3.2 The Analogy to Stigmergy
The structure of the frequency assignment solution
influences how the agent assigns frequencies to the
different transceivers. The structure seems to
provide enough constraints to direct the selection of
frequencies. Frequencies are not just added or
changed randomly. The agent is influenced by
previous frequency assignments. Assignment
decisions seem to be made locally on perceived
configurations in a way that possibly constrains the
assignment dynamics.
The second type of stigmergy built into the
algorithm is short term memory via pheromones.
This is very similar to a dynamic tabu list which has
been used successfully in a number of optimization
algorithms (Montemanni et al., 2003, Hao et al.,
1998). Each time a frequency is assigned to a
transceiver a pheromone is created and added to the
pheromone list. A pheromone is a structure
containing the transceiver identity, the frequency
and a duration variable. The pheromone list is a
first-in-first-out queue of pheromones. The time the
pheromone resides in the pheromone list is
equivalent to the time it would take for the
pheromone to dissolve. The pheromone is constantly
dissolving in nature. To model this behavior the
duration variable in the pheromone is incremented
every time a frequency is assigned to a transceiver.
The pheromone list is a fixed size M. If the duration
variable is greater than M then the pheromone is
removed from the pheromone list i.e. it has
dissolved.
FREQUENCY ASSIGNMENT OPTIMIZATION USING THE SWARM INTELLIGENCE MULTI-AGENT BASED
ALGORITHM (SIMBA)
27
When the current best frequency is selected it is
also checked against the pheromone list. If the
current best frequency and transceiver that is busy
being changed are matched against an existing
pheromone in the pheromone list then that current
best frequency is ignored and the next best
frequency is selected from the priority queue. This
technique allows the search to explore new areas in
the search space and to escape local minima
(Michalewicz et al., 2007). The general idea behind
pheromones in the algorithm is to ensure that certain
changes made in the assignment solution are
undisturbed for a certain amount of time or future
iterations. This forces the algorithm to explore other
parts of the search space and after a certain amount
of time or after a number of iterations have elapsed
these frequencies would become available again
(Michalewicz et al., 2007). A β variable was also
introduced into the algorithm to reduce the size of
the pheromone list M. The pheromone list will
reduce over time by setting the size of the
pheromone list T
M
= β* T
M
. The longer the
algorithm executes the shorter the dissolve period
for a pheromone. The reason for the reduction of the
pheromone dissolve period is that the closer the
algorithm moves to an optimized solution the more
focused the search should be.
4 SWARM INTELLIGENCE
MULTI-AGENT BASED
ALGORITHM (SIMBA)
The pseudo code below describes the spectrum
priority queue used in the algorithm. The purpose of
the spectrum priority queue was to produce a
priority queue with the best current frequencies to
use. The pseudo code utilizing the spectrum priority
queue would remove the first element in the priority
queue to find the current best frequency to use.
PriorityQueue
spectrumPriorityQ(transceiver v)
begin
Instantiate PriorityQueue PQ
foreach frequency f do
begin
oldFreq = v.getFrequency
v.setFrequency(f)
cost = Cost(S)
PQ.add(KeyValuePair<f,cost>)
end
v.setFrequency(oldFreq)
return PQ.sorted
end.
The allow assignment pseudo code described
below determines whether the current best frequency
selected from the priority queue will be used or not.
If the frequency is in the pheromone list then it is not
allowed to be used. Similarly, if the frequency
causes violating transceivers i.e. the transceivers
does not obey co-site and co-cell separation
constraints it is not allowed to be used. Violating
transceivers cause an increase in the interference
pattern. Co-site is defined as transceivers sharing the
same site and co-cell is defined as transceivers
sharing the same cell. The allow assignment method
returns the frequency that does not cause any
violating transmitters or that does not reside in the
pheromone list otherwise it returns -1.
int AllowAssignment(transceiver v,
PriorityQueue PQ)
begin
while (not PQ.isEmpty)
begin
KeyValuePair<frequency,cost>KVP =
PQ.getFirst()
PQ.removeFirst()
if(not inPheromoneList
(v,KVP.frequency))
AND
(not violatingTransmitter
(v,KVP.frequency))
return KVP.frequency
end
return -1
end.
The multi-agent framework for the SIMBA is
comprised of the agents executing the SIMBA and a
repository for the global best solution found (see
figure 1). Each agent contains a working solution S
for the frequency assignment problem as well as a
local best solution. The local best solution is the best
solution found by the individual agent. The working
solution S is the solution that is constantly changing
as the search is taking place. Each agent is able to
access the repository for the best global solution. If
at any time during the execution of the algorithm an
agent’s local best solution is better than the global
best solution i.e. the total interference in the local
best solution is less than the total interference in the
global best solution then the global best solution is
replaced with the agent’s local best solution. At this
point in time the remainder of the agents in the
system excluding the agent that found the new
global best solution will perform a transformation on
their working solutions (see figure 1). The
transformation process performed by the agent
merges its current locally best solution with the new
global best solution. The merge is dependent on two
variables Φ
l
and Φ
g
. Φ
l
is the percentage of the local
ICEIS 2009 - International Conference on Enterprise Information Systems
28
solution that will be merged into the new working
solution and similarly Φ
g
is the percentage of the
global solution that will be merged into the agent’s
new working solution. Selecting Φ
g
> Φ
l
allows the
merge to put more trust in the global solution i.e. it
places more trust in the swarm solution than its own
local solution. In this case more of the merged
solution will be made up of the global solution than
the previous local solution.
Figure 1: Multi-agent system supporting SIMBA.
The merge method in the swarm interaction takes
as input parameters the local and global frequency
assignment solutions as well as the two variables Φ
l
and Φ
g
. N
local
= Φ
l
*(total number of TRXs) and
N
global
= Φ
g
*(total number of TRXs). N
local
will be
the number of transceivers (including the set
frequency) selected from the local solution.
Similarly, N
global
will be the number of transceivers
(including the set frequency) selected from the
global solution. A transceiver selected into N
local
cannot be selected into N
global
and similarly a
transceiver selected into N
global
cannot be selected
into N
local
. The new merged solution is N
global
+N
local
.
The Swarm Intelligence Multi-agent Based
Algorithm (SIMBA) is described below.
SIMBA
begin
N
it
= 0; T
M
= 500; I
reduce
= 5*10
4
;
Φ
l
= 30 40; Φ
g
= 60 70;
Threshold = 1 10; alpha = 0.99;
beta =0.999;
S = randomly generate solution for
FAP
foreach transceiver v do
begin
newFreq = AllowAssignment
(v,spectrumPriorityQ(v))
if (newFreq not equal to -1) then
begin
oldFreq = v.getFrequency()
prevCost = Cost(S)
v.setFrequency(newFreq)
UpdatePheromoneList
(new Pheromone(newFreq,v,0))
if ((Cost(S) – prevCost)
> Threshold) then
v.setFrequency(oldFreq)
else
begin
if(Cost(S) < Cost(localBest))
localBest = S
SwarmInteraction(this,Φ
l
,Φ
g
)
end
end
end
N
it
++;
If (I
reduce
equals N
it
) then
begin
N
it
= 0;
T
M
= T
M
*beta;
Threshold = Threshold*alpha
end
end.
The multi-agent system is based on a social
model that is based on swarm intelligence. Each
agent is making use of its own local search
knowledge as well as knowledge from the swarm as
a whole to find an optimized solution.
void SwarmInteraction
(SIMBAAgent agent, Φ
l
, Φ
g
)
begin
if (Cost(agent.localBest) <
Cost(globalBest)) then
begin
globalBest = agent.localBest
GlobalBest.setFound(TRUE);
end
if (GlobalBest.getFound())
begin
agent.S = Merge(agent.localBest,
globalBest,Φ
l
,Φ
g
)
end
end.
5 COST 259 BENCHMARKS
AUTHOR(S)
The effectiveness of the SIMBA is demonstrated by
applying the SIMBA to the COST 259 benchmarks
FREQUENCY ASSIGNMENT OPTIMIZATION USING THE SWARM INTELLIGENCE MULTI-AGENT BASED
ALGORITHM (SIMBA)
29
(Eisenblätter and Koster, 2008). These instances are
widely used in the mobile telephone industry. The
largest problem considered (Siemens 4) had 2780
transceivers. The best cost values found by the
SIMBA for the Siemens instances were compared to
the following:
DTS (Glamorgan) a dynamic tabu search method
(Eisenblätter and Koster, 2008).
K-THIN(UR1) a simulated annealing combined with
dynamic programming to compute local optima
method (Mannino et al., 2000).
SA(TUHH) a simulated annealing (Beckmann and
Killat, 1999).
TA(RWTH) a threshold accepting method
(Hellebrandt and Heller, 2000).
TA(Siemens) a threshold accepting method
(Hellebrandt and Heller, 2000).
U(Siemens) an unknown method (Eisenblätter and
Koster, 2008).
SEMA, the Swarm Effect minimization algorithm
(O’Reilly and Ehlers, 2008)
Table 1: 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.
App Cost Co Adj TRX
TRX pairs exceeding
.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
SIMBA 2.26 0.03 0.03 0.05 39 7 1 0
Table 2: 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.
App Cost Co Adj TRX
TRX pairs exceeding
.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
SIMBA 14.34 0.08 0.02 0.20 360 77 33 13
The results from these methods were obtained
from the FAP website (Eisenblätter and Koster,
2008) and are presented in tables 1 to 4. The
comparison of these results and the results obtained
with the SIMBA are also presented in tables 1 to 4.
The columns described in tables 1 to 4 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 that SIMBA produced within
limited time constraints. The time constraints set for
SIMBA were 24 hours where many of the other
algorithms ran for several days.
Table 3: 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.
App Cost Co Adj TRX
TRX pairs exceeding
.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
SIMBA 5.24 0.03 0.03 0.08 83 11 3 0
Table 4: 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.
App Cost Co Adj
TR
X
TRX pairs exceeding
.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 105.8 0.27 0.04 0.53 2644 1286 798 562
SEMA 81.96 0.21 0.05 0.48 2181 991 549 353
SIMBA 81.91 0.21 0.05 0.48 2178 990 549 353
6 CELLULAR RADIO NETWORK
PARAMETER DESCRIPTION
The SIMBA was tested on a commercial mobile
telecommunications network in South Africa. The
frequency assignment solution produced by SIMBA
was applied to an operational base station controller
(BSC). There were 349 cells with an average of 3
transmitters per cell on the BSC. The available
spectrum consisted of two blocks containing 24 and
31 frequencies, respectively. In order to appreciate
the results produced in this paper a brief explanation
needs to be given of the mobile telecommunications
parameters utilized.
ICEIS 2009 - International Conference on Enterprise Information Systems
30
The %DROP (percent drop) parameter
represents the percentage of abnormal
disconnections (drop calls) on the BSC in a mobile
cellular network. Clearly, from the description of the
%DROP, a decrease in the %DROP would be very
advantageous to the network, as the number of
abnormal disconnections would decrease.
The idle channel measurement (ICM) was also
used as an interference indicator. 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 2, 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 2: Interference bands 1 to 5, each interference band
ends at a limit.
7 RESULTS OF
IMPLEMENTATION INTO A
CELLULAR RADIO NETWORK
The frequency assignments produced by the SIMBA
took on average 24 hours to produce. The frequency
assignment produced by the SIMBA was
implemented in a cellular radio network. From
figure 3 it is clear that there was a decrease in the
%DROP on the BSC after the frequency assignment
solution was implemented. This can be seen by
studying the %DROP before and after the vertical
black broken line. The vertical black broken line
depicts the point at which the SIMBA frequency
assignment solution was implemented into the BSC.
Figure 3: %DROP before and after the SIMBA frequency
assignment solution was implemented.
The decrease in the %DROP was a substantial
0.2 in figure 3 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 0.2 is amazing. An
improvement of 0.2 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 0.2 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 3 it can be seen that the erlang rate remained
constant while there was a distinct decrease in the
%DROP after the SIMBA frequency assignment
solution was implemented.
Figure 4 depicts the actual idle channel
measurements for the BSC before and after the
SIMBA frequency assignment solution was
implemented. Remember that the vertical black
broken line represents the point at which the
frequency assignments were implemented. It is
apparent from the measurements in figure 4 that
there was a drastic drop in ICM5 and ICM4
parameter values after the SIMBA frequency
assignment solution was implemented. There was
also an extensive improvement in ICM2 after the
implementation. These results prove that the SIMBA
frequency assignment solution has made
FREQUENCY ASSIGNMENT OPTIMIZATION USING THE SWARM INTELLIGENCE MULTI-AGENT BASED
ALGORITHM (SIMBA)
31
considerable improvements to the quality on the
BSC. The BSC was optimized to the ideal situation
with regard to the ideal channel measurements (see
section 6) as the number of points has decreased in
the ICM4 and ICM5 bands, while the ICM2 band
has increased considerably (see figure 4).
Figure 4: ICM interference bands 2, 4 and 5 before and
after the SIMBA frequency assignment solution was
implemented.
8 CONCLUSIONS
An engineering problem of high practical relevance
has been addressed in this paper. An algorithm based
on swarm intelligence that utilizes a multi-agent
system has been proposed. The SIMBA also
includes a stigmergy single cell optimization
(SSCO) approach which is used during selection of
the best frequencies that minimize interference
patterns. This approach has a strong analogy to
natural stigmergy in natural. One of the most
important characteristics of the SSCO was that
agents recognize interference patterns in the
changing structure of the frequency assignment
solution and are able to augment it with new
components that minimize the interference pattern.
The agents are able to make these decisions as the
changing configuration of the structures acts as a
source of information that aids the agents.
Another important aspect of the SIMBA was the
social model created by the multi-agent system.
Each agent was able to make local changes to its
own local knowledge; however the agent also could
gain addition knowledge from the collective giving
the SIMBA its swarm intelligence characteristics.
The SIMBA was benchmarked against the
COST 259 benchmarks, in particular the Siemens set
of problems and the SIMBA closely match some of
the best results with a search time of 24 hours. The
frequency assignment solutions produced by SIMBA
were also implemented into a commercial cellular
radio network with good results.
ACKNOWLEDGEMENTS
The authors wish to thank the University of
Johannesburg and the Academy for Information
Technology at the University of Johannesburg.
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