Design of Distributed OpticalFiber Raman Amplifiers using Multiobjective Particle Swarm Optimization
ABSTRACT A novel method is presented to design the configuration of pumping lasers of Raman amplifiers using a multiobjective particle swarm optimizer. The goal is to obtain the pump laser wavelengths and powers that maximize the amplifier onoff gain, while maintaining the flatness of the gain over the used bandwidth. We used an algorithm called Multiple Objective Particle Swarm Optimization with Crowding Distance and Roulette Wheel to generate the nondominated solutions, considering the average onoff gain and the ripple of the amplifier over the transmission bandwidth as the objectives in the optimization process. We designed amplifiers using three, four and five pump lasers. The experimental results showed that our proposal was able to design Raman amplifiers with a gain ripple lower than 0.2 dB and with an average onoff gain around 16.7 dB, when 20 signal channels and a total pump power of 1 W were considered. Moreover, we demonstrated that it is possible to allow the decision maker to choose among many possible nondominated solutions depending on the application requirements.

Conference Paper: Combining a MultiObjective Optimization Approach with MetaLearning for SVM Parameter Selection
[Show abstract] [Hide abstract]
ABSTRACT: Support Vector Machine (SVM) is a supervised technique, which achieves good performance on different learning problems. However, adjustments on its model are essentials to the SVM work well. Optimization techniques have been used to automatize this process finding suitable configurations of parameters which attends some learning problems. This work utilizes Particle Swarm Optimization (PSO) applied to the SVM parameter selection problem. As the learning systems are essentially a multiobjective problem, a multiobjective PSO (MOPSO) was used to maximize the success rate and minimize the number of support vectors of the model. Nevertheless, we propose the combination of MetaLearning (ML) with a modified MOPSO which uses the crowding distance mechanism (MOPSOCDR). In this combination, solutions provided by ML are possibly located in good regions in the search space. Hence, using a reduced number of successful candidates, the search process would converge faster and be less expensive. In our work, we implemented a prototype in which MOPSOCDR was used to select the values of two SVM parameters for classification problems. In the performed experiments, the proposed solution (MOPSOCDR using ML) was compared to the MOPSOCDR with random initialization, obtaining pareto fronts with higher quality on a set of 40 classification problems.SMC2012; 01/2012  SourceAvailable from: Rajesh KumarTransactions on Combinatorics. 08/2013; 2(1):89101.
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Abstract— A novel method is presented to design the configuration
of pumping lasers of Raman amplifiers using a multiobjective
particle swarm optimizer. The goal is to obtain the pump laser
wavelengths and powers that maximize the amplifier onoff gain,
while maintaining the flatness of the gain over the used bandwidth.
We used an algorithm called Multiple Objective Particle Swarm
Optimization with Crowding Distance and Roulette Wheel to
generate the nondominated solutions, considering the average on
off gain and the ripple of the amplifier over the transmission
bandwidth as the objectives in the optimization process. We
designed amplifiers using three, four and five pump lasers. The
experimental results showed that our proposal was able to design
Raman amplifiers with a gain ripple lower than 0.2 dB and with an
average onoff gain around 16.7 dB, when 20 signal channels and a
total pump power of 1 W were considered. Moreover, we
demonstrated that it is possible to allow the decision maker to
choose among many possible nondominated solutions depending
on the application requirements.
Index Terms— Optical Amplifiers, Raman Amplification, Multiobjective
Optimization, Particle Swarm Optimization.
I. INTRODUCTION
The deployment of Wavelength Division Multiplexing (WDM) systems resulted in a huge demand
to develop broadband devices. Besides, the ever increasing traffic demand generated by the new
Internet and videobased services has driven the telecommunication market to expand the systems in
order to use other transmission bands [1]. Although ErbiumDoped Fiber Amplifiers (EDFA) have
been successfully used in WDM systems since the 1990’s, EDFAs cannot provide flat gain over the
entire S+C+L transmission bands (1460nm − 1610nm).
Optical Raman Fiber Amplifiers (RFA) have been widely investigated because of some promising
features, such as low noise figure, wide and tunable amplification bandwidth, and low nonlinearity [2]
[3]. Moreover, RFAs can allow Raman amplification through the entire transmission fiber [4].
However, different channels in a WDM system can be amplified by different gain due to the flatless
nature of the Raman gain spectrum. This effect can be mitigated using multiple pumps lasers at
Design of Distributed OpticalFiber Raman
Amplifiers using Multiobjective Particle
Swarm Optimization
Carmelo J. A. BastosFilho and Elliackin M. N. Figueiredo
Polytechnic School of Pernambuco, University of Pernambuco, Recife, Brazil, Email: carmelofillho@ieee.org
Joaquim F. MartinsFilho and Daniel A. R. Chaves
Department of Electronics and Systems, Federal University of Pernambuco, Recife, Brazil, Email: jfmf@ufpe.br
Marcelo E. V. Segatto, S. Cani and Maria J. Pontes
Electrical Engineering Department, Federal University of Espírito Santo, Vitória, Brazil, Email:
segatto@ele.ufes.br
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slightly different wavelengths. In this case, each pump provides a nonuniform gain, but the gain
spectra for different pumps can overlap partially. Therefore, a suitable choice of the wavelength and
of the power of each pump laser can generate a nearly flat gain profile over a wide wavelength range
[5]. In order to provide a wide and flat gain bandwidth, the power and the wavelength of each pump
must be carefully chosen [2].
In 1999, for example, an amplification bandwidth of 100 nm with a ripple lower than 1 dB, using
12 pump lasers was demonstrated [6]. However, the complex nonlinear interaction caused by the
Raman effect among pumps and signals over a distributed RFA employing multiplepumps turns the
adjustment of the powers and the wavelengths of the pumps a difficult task [3]. Because of this, some
global optimization methods have been proposed to solve this problem such as: simulated annealing
[2]; neural networks [7]; particle swarm optimization and genetic algorithm [8]. However, despite the
conflicting nature between gain and ripple, to the best of our knowledge, no multiobjective
optimization approach was applied to solve this problem so far.
Here we propose a multiobjective particle swarm optimizer to proper select the wavelengths and
the powers of the pumps, in order to balance the tradeoff between gain and ripple. We propose to use
the Multiple Objective Particle Swarm Optimization approach using Crowding Distance and Roulette
Wheel (MOPSOCDR) [9]. We considered counterpumped distributed Raman amplifiers since they
can improve the noise characteristics, mitigate fiber nonlinear effects and improve the optical signal
tonoise ratio (OSNR) [1].
The rest of this paper is organized as follow. In Section II some Raman amplifier concepts are
presented. In Section III, the MOPSOCDR algorithm is briefly described, while in Sections IV and V
the simulation setup and the results are presented. Finally, we give our conclusions in Section VI.
II. RAMAN FIBER AMPLIFIERS
Optical Raman Fiber Amplifiers present several merits such as wider amplification bandwidth, low
noise, flexible center wavelength, and higher power budget capacity, when compared to doped fiber
amplifiers. Although multiple pumps are necessary to allow spectral flattened gain amplification, the
technological advances in highpower laser diodes allow the implementation of such amplifiers at
competitive prices.
RFAs are commonly designed as lumped Raman amplifier or distributed Raman amplifier
configurations [10]. Pumping schemes in those amplifiers can go forward and/or backward in relation
to the propagating signals. One advantage of implementing lumped over distributed amplifiers is to
avoid the downsides of high pump powers propagating in the transmission fiber, which results from
the pump power extending along the entire fiber link in the distributed configuration [4; 5].
Theoretical Raman gain as well as noise impairments are ordinarily evaluated using numerical
simulation methods. A closed analytical solution to this problem is therefore a contribution in its own
right since it provides insights into the gain dependence on the physical parameters of the Raman
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amplifier. Moreover, approximated analytical expressions may allow to obtain accurate results in a
reduced computation time. Such analytical expressions are of particular interest in the intricate
optimization of broadband Raman amplifiers, where several pumps have to be properly selected,
regarding their wavelengths and intensities, so as to achieve multiobjective functions such as
minimal ripple and maximal gain.
The evolution of the powers of the signals and pumps are governed by the nonlinear coupled
equations described in [4], [10]. In this paper we will use the analytical simulator developed by Cani
et al. [10] and presented in Section IV.D.
III. MULTIOBJECTIVE PARTICLE SWARM OPTIMIZATION WITH CROWDING DISTANCE
AND ROULETTE WHEEL
The Multiple Objective Particle Swarm Optimization with Crowding Distance and Roulette Wheel
(MOPSOCDR) algorithm was proposed by Santana et al. in 2009 [9] and is based on a well known
optimization technique called Particle Swarm Optimization (PSO) [11].
In general, PSO algorithms are suitable to tackle problems with continuous decision variables in
high dimensional spaces, as is the present case, where we are dealing with many lasers and the
wavelengths and powers can vary continuously. This particular algorithm has been chosen because it
led to a better performance than other PSObased approaches [9].
MOPSOCDR uses a diversity mechanism called crowding distance to select the social leader (gBest)
and the cognitive leader (pBest) to guide the particles during the search process. pBest and gBest are the
best positions obtained by the particle and the swarm during the search process so far. The same
mechanism is used to remove solutions from the external archive. The pseudocode of the MOPSO
CDR is presented in Algorithm I. The following subsections show the main features of the MOPSO
CDR.
A. External Archive (EA)
The External Archive (EA) is a repository to store the nondominated solutions found during the
search process so far. A solution a dominates another solution b, if a presents a better fitness values
for all the objective functions than b. If a is better in one objective function and is not worse in the
others, we say a weakly dominates b.
The MOPSOCDR has to decide whether a certain solution should be added to the EA or not. At
each iteration, nondominated solutions of the swarm population are compared with the solutions of
the EA. The candidate solutions that are not dominated by the current solutions within the EA must be
included in the EA. After this, the dominated solutions within the EA must be removed. Besides, the
EA has a maximum number of solutions. If the size of the EA is exceeded at the end of the iteration,
solutions in more crowded regions are removed from the EA using the crowding distance criterion.
B. Selection of the Social Leader
In the MOPSOCDR, the candidates to be a social leader are the current solutions stored in the EA.
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The probability to choose a solution stored in the EA is proportional to its crowding distance. The
crowding distance of a solution corresponds to the semiperimeter of the rectangle that connects the
neighbor solutions within the EA. After this, the solutions of the EA are sorted by using crowding
distance (CD) before the next iteration. For each particle, a social leader is selected for each iteration
by applying a roulette wheel in the EA considering the CD. One can note that the solutions in less
crowded regions have more chance to be selected.
C. Updating the Cognitive Leader
In the MOPSOCDR, the cognitive leader of each particle is updated if the new position of the
particle dominates the current pBest. If the new position and the pBest are incomparable, the choice is
made using the EA. The MOPSOCDR searches for solutions in the EA with minimum Euclidean
distance for the pBest and for the new position. If the closer solution to the new position in the EA is in
a less crowded region than the closer solution to the pBest in the EA, the pBest will be updated with the
new position of the particle. Otherwise, the old pBest remains.
D. Turbulence Operator
The turbulence operator of MOPSOCDR is the same used in the MOPSO [12] and it is applied at
each iteration with a bounded influence. The turbulence operator performs a local search toward the
current position of the particle. If the new position dominates the position before the turbulence, the
position is updated. Otherwise, the old position remains.
In the beginning of the algorithm execution, all particles of the swarm are affected by this operator.
As the number of iterations increases, the percentage of affected particles decreases.
ALGORITHM I. PSEUDOCODE OF THE MOPSOCDR ALGORITHM.
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IV. EXPERIMENTAL SETUP
In order to allow the MOPSOCDR to be used to design Raman amplifiers, we had to define the
input parameters (decision variables) and the objectives of the problem. The wavelengths and the
power of the pump lasers were defined as input parameters. The selected objectives were the average
onoff gain and the ripple of the gain over the transmission bandwidth. An analytical simulator was
used to evaluate the average onoff gain and the ripple. This simulation tool is based on the analytical
model for the evolution of signal and pump powers along the optical fiber. The details are described
in Section IVD. Fig. 1 illustrates the communication between the MOPSOCDR optimizer and the
Analytical Simulator.
Fig. 1. Communication between the MOPSOCDR algorithm and the Analytical Simulator.
We performed experiments to design Raman amplifiers with 3, 4 and 5 pump lasers. All the
amplifiers are distributed and use a counterpropagating pump scheme in a singlemode fiber with a
length of 75 km. The total pump power must be equal or below 1 W. Other aspects concerning the
experimental setup are detailed below.
A. The Selection of the Objectives
We used two goals in our experiments: minimize the ripple and maximize the average onoff gain.
The onoff gain is the gain provided by the amplifier to the signal when the pumps are turned on after
subtracting the fiber link attenuation. The average onoff gain is simply the arithmetic mean value of
the onoff gains for each signal. The ripple is the difference between the maximum onoff gain and
minimum onoff gain, considering all the transmission signals.
B. The Representation of the Particles
Each particle consists of a vector containing the wavelengths and powers of the pumps. Considering
an amplifier with n pumps, the particle has 2n positions, where the n first elements correspond to the
wavelengths, while the remaining elements correspond to the power levels. Table I shows an example
of representation for a particle when three pumps are considered. As shown in this table, the first
pump has wavelength equal to λ1 and power equal to P1, the second pump has wavelength equal to λ2
and power equal to P2, and so on. The wavelengths can vary continuously within the interval from
1410 nm to 1470 nm, while the powers can vary between 100 mW and 1000 mW per pump laser.
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TABLE I. EXAMPLE OF REPRESENTATION FOR A PARTICLE WHEN THREE PUMPS ARE CONSIDERED.
λ1
λ2
λ3
P1
P2
P3
1444 nm 1447 nm 1454 nm 333 mW 270 mW 297 mW
C. Parameters for the MOPSOCDR
In the simulations, we used 20 particles, mutation rate equal to 0.5 (the mutation is used to perform
a local search around gbest), maximum number of solutions in the EA equal to 200, c1 and c2 are the
acceleration constants of the cognitive and the social terms of the velocity equation, respectively, and
are equal to 1.49445. ω is the inertia factor and weights the previous value of the velocity in the
velocity equation. ω decreases linearly from 0.4 to 0 along the iterations. The maximum number of
iterations is 1000. These values were defined based on the previous experiments in benchmark
functions [9].
D. Analytical Simulator
The Analytical Simulator is a computational simulation tool for the analysis of multichannel optical
communication systems with Raman amplifiers with multiple pumps. The simulator is based on an
approximate analytical model of the evolution of pumps and signals along the optical link proposed
by Cani et al. [10]. The objective of this simulator is to evaluate the gain achieved by the signal
channel due to the presence of a distributed Raman amplifier in a singlemode fiber with one or more
pumps.
The input parameters of the simulator are:
• The number of laser pumps with the respective wavelengths and powers. The wavelengths can
vary between 1430 nm and 1470 nm and the power can vary between 0 W and the total maximum
power divided by the number of laser pumps;
• The number of signal channels with the respective wavelengths. In the experiments, we used 20
WDM signal channels with 100 GHz of separation in the C band between 1545.32 nm and 1560.61
nm;
• The Polarization Factor of the pump lasers (PF). The gain provided by the Raman effect depends
on the polarizations of the signal and the pumps. For long optical fibers typically used in transmission
systems, the polarization between pump and signal can vary arbitrarily between parallel and
perpendicular. In the Analytical Simulator, PF = 1 if the polarization between pump and signal is
maintained, and PF = 2 if the polarization varies as the signals and the pumps propagate through the
optical fiber [10]. In the experiments, we assumed PF = 2.
The outputs provided by the simulator are:
• Average onoff gain: The onoff gain is defined as the ratio between the signal power at the end of
the link with pump and without pump. The average onoff gain is the mean of the onoff gains for all
the signal channels;
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• Ripple: Each signal has an onoff gain, which is evaluated by considering the other signals and the
pumps. The Ripple is the difference between the maximum onoff gain and the minimum onoff gain
achieved by the signal channels.
E. Metrics to Evaluate the Quality of the Pareto Fronts
There are some metrics that can be used to measure the quality of the Pareto Fronts. The Pareto
Front is the set of the obtained nondominated solutions. The following metrics are used in this paper:
Spacing, Maximum spread and Coverage. Each metric highlights a different aspect of the Pareto
Front.
1) Spacing (S): Proposed by Schott in [13], it estimates the diversity for the achieved Pareto Front.
S is evaluated by computing the relative distance between adjacent solutions of the Pareto Front, as
follows,
(1)
where n is the number of nondominated solutions, di is the distance between adjacent solutions to the
solution i, andd is the average distance between the adjacent solutions. S=0 means that all the
solutions of the Pareto Front are equally spaced.
2) Maximum Spread (MS): Proposed by Zitzler et al. [14], it evaluates the maximum extension
covered by the nondominated solutions in the Pareto front. MS is evaluated by
(2)
where n is the number of solutions in the Pareto front and M is the number of objectives.
3) Coverage (C): Proposed by Zitzler et al. [15], it is evaluated by
(3)
where A and B are two sets of nondominated solutions. The value C(A,B)=1 means that all solutions
in B are weakly dominated by A. On the other hand, C(A, B)=0 means that none of the solutions in B
are weakly dominated by A.
One should note that both C(A, B) and C(B, A) have to be evaluated, since C(A,B) is not
necessarily equal to 1−C(B,A). If 0<C(A,B)<1 and 0<C(B,A)<1, then neither A weakly dominates B
nor B weakly dominates A. In this case, the sets A and B are incomparable, thus meaning that A is not
worse than B and viceversa.
V. SIMULATION RESULTS
In this section we present some simulation results considering 3 pump lasers (subsection VA), 4
pump lasers (subsection VB) and 5 pump lasers (subsection VC).
A. Results for 3 pump lasers
We first run the MOPSOCDR algorithm in order to optimize the Raman amplifier with 3 pumps.
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Fig. 2 illustrates the evolution of Pareto Fronts for the iterations 50, 100, 500 and 1000. One can
notice that the Pareto Fronts are quite close to each other for the iterations 500th and 1000th.
Table II shows the metrics used to compare the Pareto Fronts. We ran 30 trials and presented the
mean value and standard deviation (in parenthesis) for each case. The Coverage was evaluated in
relation to the previously collected Pareto Front, i.e. the Coverage at the 100th iteration was compared
to the Pareto front at the 50th iteration. The high values for the Coverage indicate that the algorithm
evolved along the iterations.
TABLE II. METRICS FOR THE PARETO FRONT FOR RAMAN AMPLIFIERS WITH 3 PUMP LASERS FOR THE ITERATIONS 50TH, 100TH,
500TH AND 1000TH.
Iteration
50
100
500
1000
Spacing
0.832 (0.819)
0.582 (0.492)
0.246 (0.209)
0.150 (0.132)
Maximum Spreading
7.666 (3.273)
7.361 (3.450)
7.367 (3.668)
7.366 (3.549)
Coverage
0.991 (0.044)
0.559 (0.173)
0.779 (0.164)
0.589 (0.126)
Fig. 2. Evolution of Pareto Fronts for the Raman amplifier with 3 pump lasers.
We chose the solution pointed at in Fig. 2 to design the Raman amplifier with 3 pump lasers. This
solution represents an amplifier with average onoff gain around 16.86 dB and ripple around 0.141
dB. Table III presents the wavelengths and the powers for the pump lasers.
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TABLE III. WAVELENGTHS AND POWERS FOR THE RAMAN AMPLIFIER WITH 3 PUMP LASERS.
Wavelength (nm) Power (mW)
1444.378
1447.535
1454.585
333
333
333
After that, we performed a simulation using the Analytical Simulator for an optical link with 20
WDM signal channels considering the Raman amplifier with the pumps showed in Table III. Fig. 3
shows the onoff gains achieved by the Analytical Simulator for all signal channels. As one can see,
Ripple < 0.2 dB, which means that all signal channels achieved almost the same onoff gain, all of
them exceeding 16.5 dB.
We also performed a test rounding the wavelengths to integer numbers in order to check the
sensibility of the result. We observed that by doing this that the ripple is not affected significantly.
Fig. 3. Onoff gain for the Raman amplifier with 3 pumping lasers.
B. Results for 4 pump lasers
Now we apply the same methodology to design of the amplifier with 4 pump lasers. The evolution
of the Pareto Front is shown in Fig. 4. As in the previous experiment, we evaluated the metrics for the
Pareto Fronts and the results are summarized in Table IV.
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Fig. 4. Evolution of Pareto Fronts for the Raman amplifier with 4 pump lasers.
TABLE IV. METRICS FOR THE PARETO FRONT FOR RAMAN AMPLIFIERS WITH 4 PUMP LASERS FOR THE ITERATIONS 50TH, 100TH,
500TH AND 1000TH.
Iteration
50
100
500
1000
Spacing
0.710 (0.723)
0.476 (0.341)
0.224 (0.187)
0.092 (0.0076)
Maximum Spreading
6.541 (2.598)
6.309 (2.668)
5.456 (2.321)
5.213 (2.296)
Coverage
0.982 (0.068)
0.558 (0.284)
0.901 (0.132)
0.682 (0.155)
Though most of the comments done for the case with 3 pump lasers can be extended to here, one
can notice that the Pareto Fronts achieved for 4 pump lasers are quite better than the ones achieved for
3 pump lasers, mainly in the kink.
We chose the solution pointed at in Fig. 4 to design the Raman amplifier with 4 pump lasers. This
solution represents an amplifier with average onoff gain around 16.8 dB and ripple around 0.089 dB.
Table V presents the wavelengths and the powers for the pump lasers.
TABLE V. WAVELENGTHS AND POWERS FOR THE RAMAN AMPLIFIER WITH 4 PUMP LASERS.
Wavelength (nm) Power (mW)
1442.890
1446.545
1448.670
1455.986
250
250
250
250
Fig. 5 shows the onoff gains achieved by the Analytical Simulator for all signal channels.
Furthermore, all signal channels achieved almost the same onoff gain, all of them exceeding 16.5 dB.
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Fig. 5. Onoff gain for the Raman amplifier with 4 pumping lasers.
C. Results for 5 pump lasers
We performed the optimization to design the amplifier with 5 pump lasers. The evolution of the
Pareto Front is shown in Fig. 6. As in the previous experiment, we evaluated the metrics for the
Pareto Fronts and the results are summarized in Table VI.
TABLE VI. METRICS FOR THE PARETO FRONT FOR RAMAN AMPLIFIERS WITH 5 PUMP LASERS FOR THE ITERATIONS 50TH, 100TH,
500TH AND 1000TH.
Iteration
50
100
500
1000
Spacing
0.533 (0.334)
0.429 (0.407)
0.236 (0.238)
0.131 (0.136)
Maximum Spreading
4.905 (2.152)
5.114 (2.312)
4.894 (2.133)
4.644 (2.079)
Coverage
0.991 (0.044)
0.621 (0.229)
0.891 (0.101)
0.721 (0.146)
We chose the solution pointed in Fig. 6 to design the Raman amplifier with 5 pump lasers. This
solution represents an amplifier with average onoff gain around 16.73 dB and ripple around 0.15 dB.
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Fig. 6. Evolution of Pareto Fronts for the Raman amplifier with 5 pump lasers.
Table VII presents the wavelengths and the powers for the pump lasers. Fig. 7 shows the onoff
gains achieved by the Analytical Simulator for all signal channels.
TABLE VII. WAVELENGTHS AND POWERS FOR THE RAMAN AMPLIFIER WITH 5 PUMP LASERS.
Wavelength (nm) Power (mW)
1444.198
1446.016
1447.553
1452.093
1456.884
200
200
200
200
193
Finally, we increased the number of channels to analyze the scalability of the algorithm. We
performed the optimization to design the amplifier with 5 pump lasers for 40 signal channels covering
the entire C band. The evolution of the Pareto Front is shown in Fig. 8. The ripple was slightly
increased, as expected.
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Fig. 7. Onoff gain for the Raman amplifier with 5 pumping lasers.
Fig. 8. Evolution of Pareto Fronts for the Raman amplifier with 5 pump lasers for 40 channels.
VI. CONCLUSIONS
We proposed in this paper a novel method to define the pump specifications for Raman fiber
amplifiers. We used a multiobjective particle swarm optimization algorithm known as MOPSOCDR
to design the Raman amplifier. Configurations of Raman fiber amplifiers with 3, 4 and 5 pump lasers
were generated and demonstrated. This method allows one to design high performance Raman
amplifiers with high gain, low ripple, and wide bandwidth for WDM systems. One should notice that
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better results could be achieved if more pump lasers are used, but it will also increase the total cost of
the amplifier. The method achieved better results in terms of ripple when compared to a simple
genetic algorithm, which achieved a ripple around 1 dB for similar conditions [16]. One can observe
that the MOPSOCDR is suitable for this type of application since it presents a fast convergence and
can easily deal with more than one objective function. Besides, as future work, one can add a third
objective in order to minimize the number of required pump lasers.
ACKNOWLEDGMENT
The authors thank the University of Pernambuco, Federal University of Pernambuco, Federal
University of Espírito Santos, FACEPE, FAPES, CAPES and CNPq.
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