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1644 IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART C: APPLICATIONS AND REVIEWS, VOL. 42, NO. 6, NOVEMBER 2012
A Comparative Study on Multiobjective Swarm
Intelligence for the Routing and Wavelength
Assignment Problem
´
Alvaro Rubio-Largo, Miguel A. Vega-Rodr´
ıguez, Juan A. G´
omez-Pulido, and Juan M. S´
anchez-P´
erez
Abstract—The future of designing optical networks is focused
on the wavelength division multiplexing (WDM) technology. This
technology divides the huge bandwidth of an optical fiber into
different wavelengths, providing different available channels per
link of fiber. However, when it is necessary to establish a set of
demands, a problem comes up. This problem is known as a rout-
ing and wavelength assignment (RWA) problem. Depending on
the traffic pattern, two varieties of a RWA problem have been
considered in the literature: static and dynamic. In this paper, we
present a comparative study among three multiobjective evolution-
ary algorithms (MOEAs) based on swarm intelligence to solve the
RWA problem in real-world optical networks. Artificial bee colony
(ABC) algorithm, gravitational search algorithm (GSA), and firefly
algorithm (FA) are the selected evolutionary algorithms, but
are adapted to multiobjective domain (MO-ABC, MO-GSA, and
MO-FA, respectively). In order to prove the goodness of the swarm
proposals, we have compared them with a standard MOEA: fast
nondominated sorting genetic algorithm. Finally, we presenta com-
parison among the metaheuristics based on swarm intelligence and
several techniques published in the literature, coming to the con-
clusion that swarm intelligence is very suitable to solve the RWA
problem, and presumably that it may obtain such quality results
not only in diverse telecommunication optimization problems, but
also in other engineering optimization problems.
Index Terms—Multiobjective optimization, routing and wave-
length assignment (RWA) problem, swarm intelligence, wavelength
division multiplexing (WDM) optical networks.
I. INTRODUCTION
IN PAST decades, optical fiber was considered as a prototype.
However, this technology is getting increasingly important
nowadays; therefore, the challenge is to make it into a reality.
The number of users that use the Internet has grown exponen-
tially over the past years, as well as the bandwidth requirements
Manuscript received January 11, 2012; revised May 18, 2012 and July 31,
2012; accepted August 5, 2012. Date of current version December 17, 2012.
This work was supported in part by the Spanish Ministry of Science and Inno-
vation and in part by the European Regional Development Fund (ERDF) under
Contract TIN2008-06491-C04-04 (the M* project). The work of ´
A. Rubio-
Largo was supported in part by the Gobierno de Extremadura (Consejer´
ıa de
Econom´
ıa, Comercio e Innovaci´
on) under research grant PRE09010 and in part
by the European Social Fund. This paper was recommended by Associate Editor
J. Lazansky.
The authors are with the Department of Computer and Communications
Technologies, University of Extremadura, Escuela Polit´
ecnica, Campus Uni-
versitario s/n, Caceres 10003, Spain (e-mail: arl@unex.es; mavega@unex.es;
jangomez@unex.es; sanperez@unex.es).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TSMCC.2012.2212704
Fig. 1. WDM technology.
of users’ devices. Unfortunately, our current data networks are
not ready for this exponential growth because their bandwidth is
understaffed. This way, the usage of optical fiber is very suitable
to tackle this problem.
The bandwidth of an optical fiber link is around 50 Tb/s;
however, end users are constrained by the maximum speed of
their devices (a few gigabytes per second). In order to fix this
drawback, the wavelength division multiplexing (WDM) tech-
nology appears. This technology multiplexes transmissions of
data with the aim to exploit the huge bandwidth of an optical
fiber link; see Fig. 1.
Since WDM uses several wavelengths to multiplex multiple
signals, the transmitters operate in different wavelengths in order
to add their own optical signal into the optical fiber. A WDM
coupler allows separating optical signal streams wavelengths to
be combined and/or divided, for transmission on a single fiber.
A WDM optical link consists of WDM transmitters, WDM
multiplexers, optical preamplifiers, postamplifiers, WDM de-
multiplexers, and WDM receivers [1].
Currently, there exist several relevant telecommunication
companies in the U.S., Europe, and Japan that are testing and
using several prototypes of WDM optical networks. Therefore,
everything pointing to the future of the Internet will be based
on WDM.
In WDM networks, a problem comes up when it is necessary
to interconnect a set of connection requests. This problem is
known in the literature as a routing and wavelength assignment
(RWA) problem. On the one hand, the choice of the physical
route of a connection is based on some cost criterion such as
hop length. On the other hand, the wavelength is chosen based
on the wavelength usage factor in the entire network [2].
A connection request carried end to end from a source node
to a destination node over a wavelength on each intermediate
optical fiber link is known as lightpath. Furthermore, an inter-
mediate node in the network and the lightpath are routed and
switched from one link to another. However, it is very com-
mon that lightpaths may be converted from one wavelength to
another wavelength as well along their route.
1094-6977/$31.00 © 2012 IEEE
RUBIO-LARGO et al.: COMPARATIVE STUDY ON MULTIOBJECTIVE SWARM INTELLIGENCE 1645
Depending on the traffic pattern, the RWA problem can be
classified into two varieties.
1) Static-RWA problem: The entire set of requests is known
in advance; therefore, the aim is to establish all demands
trying to minimize the usage of network resources.
2) Dynamic-RWA problem: A lightpath is set up for each
demand request. This request is erased after a finite period
of time.
Since wide area networks (WANs) are oriented to precon-
tracted services [3], in this paper we focus on solving the static-
RWA problem. This problem is NP-hard; therefore, it is very
common the use of heuristics to tackle it [4], [5].
In this paper, we present a comparative study among three
multiobjective evolutionary algorithms (MOEAs) based on
swarm intelligence to solve the RWA problem in real-world
optical networks. We apply three innovative swarm approaches:
artificial bee colony (ABC) [6], gravitational search algorithm
(GSA) [7], and firefly algorithm (FA) [8], but adapt them to
the multiobjective domain and refer to them as MO-ABC,
MO-GSA, and MO-FA, respectively. Furthermore, we have in-
cluded in the study the well-known fast nondominated sorting
genetic algorithm (NSGA-II) [9] in order to ensure the good-
ness and accuracy of the swarm proposals. Finally, we present
a comparison with other approaches that are published in the
literature.
The rest of this paper is organized as follows. In Section II, we
present how other authors have tackled the RWA problem before.
The RWA problem in a formal way is presented in Section III.
A brief description of the MOEAs based on swarm intelligence
appears in Section IV. In Section V, we include the analysis of
the experiments that are carried out as well as a comparison with
other approaches that are published in the literature. Finally, in
Section VI, we summarize the conclusions of this study and
discuss possible lines of future work.
II. STATE OF THE ART
In [10], the authors suggest dividing the RWA problem into
two subproblems: on the one hand, the routing of the connection
requests over a given topology, and on the other hand assigning
an available wavelength to each link of each path established.
They propose mixed-integer linear programming to solve each
subproblem separately.
In the literature [11]–[14], the first subproblem (routing) has
been tackled by using several well-known methods, such as:
1) Fixed routing: It does not consider traffic or efficient paths.
2) Fixed-alternate routing: It is an extension of fixed-path
routing; instead of having just one fixed route for a given
source and destination pair, several routes are stored.
3) Adaptive routing: It offers a tradeoff between complexity
and performance.
Furthermore, in [15]–[21], the authors suggest several meth-
ods to solve the second subproblem (wavelength assignment),
such as Random Wavelength Assignment,First Fit,Least
Used/SPREAD,Most Used/PACK,Min-Product,Least Loaded,
MAX-SUM,Relative Capacity Loss,Wavelength Reservation,
and Protecting Threshold.
Zang et al. propose [22] a heuristics for the wavelength as-
signment subproblem: distributed relative capacity loss as well
as a review of several RWA approaches.
Due to the prohibitive computational efforts that are required
to solve the RWA problem, several metaheuristics have been
applied in the literature, such as Tabu search (TS) [23]–[25],
simulated annealing (SA) [5], [26], and genetic algorithm (GA)
[4], [27]–[31]. Furthermore, in [32], the authors make a com-
parison between a GA approach and a SA approach, concluding
that the GA obtains better performance than SA.
In [33], Varela and Sinclair propose different varieties of ant
colony optimization (ACO) algorithms to solve the static-RWA
problem. However, they use ACOs only to solve the routing sub-
problem; therefore, the second subproblem is tackled by using a
greedy method to solve the wavelength assignment subproblem.
All the previous proposals consider the RWA as a monob-
jective problem, tackling both subproblems (routing and wave-
length assignment) separately. However, in more recent liter-
ature, the RWA problem has been tackled as a multiobjective
optimization problem (MOOP). In this way, with multiobjective
optimization, we are looking for a solution for which each ob-
jective has been optimized to the extent that if we try to optimize
it any further, then the other objective will worsen as a result.
Two multiobjective ACOs are proposed in [34]: on the one
hand, a multiobjective ant colony system (MOACS), and on the
other hand, a multiobjective max–min ant system (M3AS).
In [35], the authors make a comparison among these multiob-
jective varieties of ACO algorithms (MOACS and M3AS), typi-
cal RWA heuristics in the telecommunication field, and their own
varieties, which are Multiobjective Ant Q algorithm (MOAQ),
Bicriterion Ant (BIANT),Pareto Ant Colony Optimization
(PACO),COMPETants (COMP),Multiobjective Omicron ACO
(MOA), and Multiobjective Ant System (MAS).
Finally, in [36] and [37], Rubio-Largo et al. present two mul-
tiobjective metaheuristics to solve the RWA problem. On the one
hand, in [36], a differential evolution with Pareto tournaments
(DEPT) is suggested. On the other hand, a trajectory-based al-
gorithm is presented in [37]. It is a multiobjective variety of the
variable neighborhood search algorithm (MO-VNS).
The major differences and contributions of this study are
the comparative study on multiobjective swarm intelligence to
solve a large number of datasets over three real-world optical
network topologies and a complete statistical study on the re-
sults obtained. Furthermore, with the aim of demonstrating the
efficiency of the swarm intelligence to solve the RWA problem,
we present a comparison between the proposed swarm heuris-
tics and several approaches published in the literature, including
previous work (DEPT and MO-VNS).
III. ROUTING AND WAVELENGTH ASSIGNMENT PROBLEM
In this section, we present the problem formulation and the
objective functions. At the end of the section, we explain the
static-RWA problem by using an example.
1646 IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART C: APPLICATIONS AND REVIEWS, VOL. 42, NO. 6, NOVEMBER 2012
A. Problem Formulation
In this paper, an optical network is modeled as a direct graph
G=(V,E,C), where Vis the set of nodes, Eis the set of links
between nodes, and Cis the set of available wavelengths for
each optical link in E.
1) (i, j)∈E:Optical link from node ito node j.
2) cij ∈C:Number of channels or different wavelengths at
link (i, j).
3) u=(su,d
u): Unicast request uwith source node suand
a destination node du, where su,d
u∈V.
4) U:Set of unicast requests, where U={u|uis an unicast
request}. Note that |U|is the number of unicast requests.
5) uλ
i,j :Wavelength λassigned to the unicast request uat
link (i, j).
6) lu:Lightpath or set of links between a source node suand
a destination node du, with the corresponding wavelength
assignment in each link (i, j).
7) LU:Solution of the RWA problem considering the set of
Urequests.
Note that LU={Lu}is the set of links with their corre-
sponding wavelength assignment. Using the aforementioned
definitions, the RWA problem may be stated as a MOOP [38],
searching the best solution LUthat simultaneously minimizes
the following two objective functions.
1) Number of hops (y1): It is the number of routers traversed
by a packet between its source and destination:
y1=
u∈U
(i,j)∈E
Φu
(i,j)
where Φu
(i,j)=1 if (i, j )∈lu
Φu
(i,j)=0 otherwise .(1)
2) Number of wavelength (λ) conversions (y2): A wavelength
conversion occurs when the input wavelength in a WDM
router must be converted into another wavelength of light:
y2=
u∈U
i∈V
ϕu
i
where ϕu
i=1 if i∈Vswitches λ
ϕu
i=0 otherwise .(2)
Furthermore, we have to fulfill the wavelength conflict con-
straint: Two different unicast transmissions must be allocated
with different wavelengths when they are transmitted through
the same optical link (i, j).
B. Example of the RWA problem
In order to facilitate the RWA problem formulation (see
Section III-A), in this section we present an illustrative example
that helps to understand the formulation as well as the objective
functions of the RWA problem.
Statement: Given the optical network topology of Fig. 2, we
will suppose the following set of demands (U) and number of
different wavelengths at link (cij):
U={(5,1) (3,5) (2,3) (1,4)}cij =2.
Fig. 2. Illustrative example of the RWA problem.
As we can see in Fig. 2, the demands (5,1), (3,5), and (2,3)
do not present any wavelength switching; however, the demand
(1,4) presents one wavelength conversion in node 3. Therefore,
the solution has eight hops (y1=8) and one wavelength con-
version (y2=1).
The solution presented for this specific topology could not be
the best one; this example only tries to help to understand the
problem formulation and the objective functions.
IV. MULTIOBJECTIVE OPTIMIZATION ALGORITHMS
In this section, we briefly describe the individual encoding and
the three MOEAs based on swarm intelligence (MO-ABC, MO-
GSA, and MO-FA) that we have considered in this comparative
study, as well as the standard NSGA-II.
A. Representation of Individuals
The individual encoding is the main issue to determine how
the problem is structured in the algorithms. It provides us with
the necessary information to understand the behavior of each
algorithm. In Fig. 3, the representation of an individual is shown.
As we may observe in Fig. 3, the solution of the presented
individual corresponds with the solution shown in the illustrative
example (see Fig. 2). For each demand (s,d)ofthesetU,werun
Yen’s algorithm [39], with the aim to obtain the kshortest paths
from the source node sto the destination node d—in Fig. 3, we
have supposed k=4. For each shortest path, we generate a list
with all possible combinations with the available wavelengths;
RUBIO-LARGO et al.: COMPARATIVE STUDY ON MULTIOBJECTIVE SWARM INTELLIGENCE 1647
Fig. 3. Representation of an individual.
therefore, if the shortest path consists of nhops, and we have
cij available wavelengths per link, then we generate cn
ij possible
lightpaths.
For example, the shortest path, 5−2−1, consists of two
hops; thus, supposing cij =2, we generate 22possible light-
paths:
5−λ1−2−λ1−1
5−λ1−2−λ2−1
5−λ2−2−λ1−1
5−λ2−2−λ2−1.
To generate a random individual, we choose randomly a possi-
ble lightpath (fulfilling the wavelength conflict constraint) from
the generated list of each demand of the set Uand store a pointer
to the entry of the list in the chromosome of the individual. Note
that the set of lists is only calculated once, at the beginning of
the execution of the algorithm.
Since the considered algorithms work with continuous values
in the reproduction operators, the genes of the chromosome
are also continuous. This way, when we need to calculate the
objective functions of an individual, we truncate each gene of the
chromosome. For simplicity, in Fig. 3 we present the truncated
values in the chromosome.
B. Multiobjective Artificial Bee Colony
In [6], Karaboga proposes a new population-based evolution-
ary algorithm that is based on the intelligent behavior of honey
bees, the ABC. The well-known concept of population is de-
fined in [6] as a colony. This colony consists of three varieties
of artificial bees. The onlooker bee waits on the dance area to
make decision to choose a food source, and a bee going to the
food source visited by itself previously is an employed bee. The
scout bees carry out random searches.
A multiobjective version of the ABC appears in [40]. For
further information about MO-ABC, see [40].
C. Multiobjective Gravitational Search Algorithm
In [7], Rashedi et al. present a new population-based evolu-
tonary algorithm that is based on the law of gravity and mass
interactions, the GSA. In the GSA, the members of the popula-
tion are named searcher agents. They are a collection of masses
that interact with each other based on the Newtonian gravity
laws of motion.
In [41], a MO-GSA is proposed. See [41] for a detailed ex-
planation of MO-GSA.
D. Multiobjective Firefly Algorithm
In [8], Yang proposes an innovative population-based evo-
lutionary algorithm that is inspired by the flash pattern and
characteristics of fireflies, the FA. The fireflies are characterized
by their bioluminescent aptitudes. A firefly uses its luminescent
flash pattern to attract other fireflies that are flying around.
In this study, we adapt the FA to multiobjective problems
(MO-FA).
A pseudocode of MO-FA is shown in Algorithm 1. As we
can see, we start by generating SwarmSize fireflies in a random
way in order to fill the population P(lines 2–5). Then, we
initialize the absorption coefficient in the media (γ) and the
control parameter αto make the search space exploration more
efficient (lines 6 and 7). Afterward, we initialize the ParetoFront
as empty (line 8).
The most important issues of the FA are the variation of light
intensity and formulation of the attractiveness. The author pos-
tulates that, in a monoobjective problem, fireflies with a better
value of fitness are considered more attractive; therefore, the
other ones will move toward them. In the MO-FA, we have used
1648 IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART C: APPLICATIONS AND REVIEWS, VOL. 42, NO. 6, NOVEMBER 2012
the well-known dominance () multiobjective concept [38] in
order to compare a pair of fireflies (line 12).
In the case of a firefly, Xjattracts (dominates) other firefly
Xi(lines 13–18), and then Ximoves toward Xjin each po-
sition of its chromosome. To move a firefly, we calculate the
Euclidean distance between both fireflies (line 14) and apply
the attractiveness equation (line 16). In this equation, the sec-
ond term corresponds with the attraction and the third term with
the control parameter α(adding dispersion). In this paper, we
have established the attractiveness β0as in [8] (β0=1). Finally,
we update the Pareto front (line 22).
E. Fast Nondominated Sorting Genetic Algorithm
In [9], Deb et al. propose the NSGA-II, which is a revised
version of NSGA [42].
NSGA-II tries to obtain a new population (offspring popula-
tion Q) from an original one (parent population P) by applying
classical genetic operators, such as selection, crossover, and
mutation. For further information about NSGA-II, see [9].
V. EXPERIMENTAL RESULTS
In this section, we present a comparative study among three
MOEAs based on swarm intelligence to solve the RWA problem.
Furthermore, with the aim to ensure the goodness of the swarm
proposals, we include in the study the well-known NSGA-II.
Finally, we present a comparison with other approaches that are
published in the literature.
A. Previous Considerations
In this section, we present the methodology and statistical
procedure followed in order to conduct the comparative study.
In this study, we compare three MOEAs based on swarm in-
telligence (MO-ABC, MO-GSA, and MO-FA) and the standard
NSGA-II. This way, we have made the comparison by using
three real-world optical network topologies.
The first real-world optical network is the well-documented
pan European network (COST239, Europe), which consists of
11 nodes and 52 links of fiber. The second one is the National
Science Foundation network (NSF, U.S.), which consists of 14
nodes and 42 links. Finally, the last optical network corresponds
with the Nippon Telegraph and Telephone (NTT, Japan), which
consists of 55 nodes and 144 links.
We have chosen a gravity demand model [43] to create the
datasets. As we can see in (3), the gravity-based model assumes
that the number of demands exchanged between two nodes is
proportional to the product of the degrees of the two nodes
and is inversely proportional to the Euclidean distance between
them. In (3), the constant is simply a uniform scaling factor
to adjust the traffic to the desired volume level. This way, we
have generated 12 datasets for each optical topology, a total of
36 problem datasets. The three optical network topologies and
the 36 datasets are available for downloading in [44]:
demands(a, b)=nodal degreea∗nodal degreeb
distancea−b∗constant .
(3)
TAB L E I
BEST CONFIGURATION FOUND OF EACH MOEA FOR RWA PROBLEM
In the parameter tuning of each MOEA, we have used the
NSF and NTT topologies, and six datasets for each one, a total of
twelve datasets. For each parameter in each experiment, we have
performed 30 independent runs obtaining a Pareto front in each
run. This way, we select the value of a parameter basing on the
quality of the Pareto fronts produced in the 30 runs. In Table I,
we present the values that were tested for each parameter, as
well as the best configuration found of each MOEA for the
RWA problem.
To measure the quality of a Pareto front, we have used two
well-known multiobjective indicators.
1) Hypervolume (HV) [45] measures the volume (in objec-
tive function space) that is covered by members of a
nondominated set of solutions. In a MOOP with dmini-
mization objective functions, we calculate the size of the
region of the objective space (HV) of a nondominated
set of solutions A={a1,...,a
n}bounded by a refer-
ence point r=(r1,...,r
d). The corresponding hyper-
cube for each member aiof set Ais calculated as follows:
h(ai)=[ai1,r
1]×···×[aid ,r
d]. This way, as is shown
in (4), the HV of Ais computed by the union of these
|A|hypercubes, with repeatedly covered hypercubes be-
ing counted once; note that in (4), Lrefers to the Lebesgue
measure [46]:
HV (A, r)=L⎛
⎝|A|
i=1
h(ai)|ai∈A⎞
⎠.(4)
Note that this metrics is not free from arbitrary scaling
of objectives; that is to say, the value of this metrics may
be distorted if the range of each objective function is dif-
ferent. Thus, before calculating the HV of A,wehave
to normalize the objective function values. This way, the
reference point to calculate the HV metrics in this study
is r=(0,0) for all datasets, since y1and y2are for mini-
mizing; therefore, the normalization point will be different
depending on the dataset.
2) Set Coverage (SC) [47]: If we suppose two sets of
nondominated solutions A={a1,...,a
n}and B=
RUBIO-LARGO et al.: COMPARATIVE STUDY ON MULTIOBJECTIVE SWARM INTELLIGENCE 1649
Fig. 4. Statistical analysis schema.
{b1,...,b
m}, the SC measures the fraction of non-
dominated solutions in B, which are covered by the
nondominated solutions in A[see (5)]:
SC(A, B)= |{bi∈B;∃ai∈A:aibi}|
|B|.(5)
If SC(A, B)=1, all points in Bare dominated by or
equal to points in A, whereas SC(A, B)=0 means that
none of the points in Bare covered by the set of A.As
the dominance operator is not symmetric, it is necessary to
calculate both SC(A, B)and SC(B,A), since SC(B,A)
is not necessarily equal to 1 −SC(A, B).
In order to make a study among the MOEAs with a certain
level of confidence, and because evolutionary algorithms are
stochastic, we have performed a statistical analysis of the ob-
tained results. In Fig. 4, we present a schema of the statistical
analysis that we have applied in this study [48].
As we can see in Fig. 4, in the first place, a test to calcu-
late residual normality is applied; in our case, Kolmogorov–
Smirnov. The main objective of this test is to check whether the
values of the results follow a Gaussian distribution or not. For
non-Gaussian distributions, we perform a nonparametric anal-
ysis, such as Kruskal–Wallis. However, if the values follow a
Gaussian distribution, a test to check the homogeneity of the
variances (Levene test) is also carried out. Finally, if this is
positive, we apply an ANOVA analysis (parametric analysis);
otherwise, we perform the Kruskal–Wallis analysis.
The confidence level that is considered in this study is always
95% in the statistical tests (a significance level of 5% or p-value
under 0.05), which means that the differences are unlikely to
have occurred by chance with a probability of 95%.
B. Pan European Optical Network—COST239
In the first place, we start with the pan European optical Net-
work (COST239, Europe), which consists of 11 nodes and 52
optical links. In Table II, we show the physical topology of
COST239. Furthermore, we present for each dataset, the corre-
sponding runtime, the normalization points that are required to
calculate the HV metrics, and the value of the constant used in
(3) to calculate the number of demands.
On the one hand, we compare the swarm proposals and
NSGA-II by using the average HV of 30 independent runs.
As we can see in Table III, all approaches obtain similar val-
TAB L E II
COST239: SPECIFICATIONS OF DATASETS
TABLE III
AVERAGE HYPERVOLUME OF 30 RUNS OBTAINED BY MO-ABC, MO-GSA,
MO-FA, AND NSGA-II (COST239)
TAB L E IV
RESULTS FROM STATISTICAL ANALYSIS OF THE COMPARISON AMONG
APPROACHES BY USING HYPERVOLUME INDICATOR (COST239)
ues of HV for those datasets with a lower number of de-
mands (COST239#01-COST239#06). As we can observe in
Table IV, there are no relevant statistical differences among the
approaches in the majority of these datasets.
However, in datasets COST239#07–COST239#12, we can
notice that differences of HV are remarkable. As we can observe
in Fig. 5, when the number of demands is over 100 (|U|>100),
MO-FA obtains higher values of hypervolume than MO-ABC,
MO-GSA, and NSGA-II.
1650 IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART C: APPLICATIONS AND REVIEWS, VOL. 42, NO. 6, NOVEMBER 2012
Fig. 5. Comparison among MO-ABC, MO-GSA, MO-FA, and NSGA-II by
using the average HV of 30 runs (COST239).
TAB L E V
SET COVER AGE AB(COST239)
Furthermore, if we focus on the last row of Table III, we can
see that the average hypervolume values obtained by MO-ABC
and MO-GSA (69.24% and 68.16%, respectively) are greater
than the average value obtained by the well-known NSGA-II
(66.93%).
On the other hand, we have made a comparison among the
MOEAs by using the SC indicator. In Table V, we present
a comparison by pairs of MOEAs in order to determine the
coverage relation of each one with the rest. As we can see,
MO-ABC covers at least a half of nondominated solutions that
are obtained by MO-GSA, MO-FA, and NSGA-II. In the case
of MO-GSA, we can observe that it only covers a quarter of
nondominated solutions from MO-FA, but it is able to cover
49.03% and 58.33% of nondominated solutions from MO-ABC
and NSGA-II, respectively. The nondominated solutions that
are achieved by MO-FA in each dataset of COST239 clearly
cover the nondominated solutions obtained by MO-ABC, MO-
GSA, and MO-FA (100% in all cases). Finally, if we check the
coverage relation obtained by NSGA-II with MO-ABC, MO-
GSA, and MO-FA, we may observe that it obtains a low coverage
percentage: 37.50%, 52.08%, and 25%, respectively.
TAB L E VI
NSF: SPECIFICATIONS OF DATASETS
TAB L E VII
AVERAGE HV OF 30 RUNS OBTAINED BY MO-ABC, MO-GSA, MO-FA,
AND NSGA-II (NSF)
In summary, we can conclude that MO-FA is the MOEA that
obtains better results, followed by MO-ABC, MO-GSA, and
NSGA-II.
C. National Science Foundation Network
In this section, we present a comparison among the MOEAs
by using the real-world optical network topology National Sci-
ence Foundation (NSF, U.S.), which consists of 14 nodes and 42
optical links. The NSF physical topology and all specifications
about those datasets used in this subsection are presented in
Table VI. Note that those datasets in which there is no constant
value is due to the fact that they were not calculated by using
equation (3), but they were obtained from [49].
First, we present a comparison among MO-ABC, MO-GSA,
MO-FA, and NSGA-II by using the HV indicator. As we can
see in Table VII, when the datasets contain a low number of de-
mands (less than or equal to 30 demands), there are no statistical
differences of HV among the MOEAs (see Table VIII).
However, we can observe in Fig. 6 how the differences of HV
among the MOEAs increase when the number of demands is
RUBIO-LARGO et al.: COMPARATIVE STUDY ON MULTIOBJECTIVE SWARM INTELLIGENCE 1651
TABLE VIII
RESULTS FROM STATISTICAL ANALYSIS OF THE COMPARISON AMONG
APPROACHES BY USING HV METRICS (NSF)
Fig. 6. Comparison among MO-ABC, MO-GSA, MO-FA, and NSGA-II by
using the average HV of 30 runs (NSF).
higher. Furthermore, we can see that MO-FA clearly overcomes
the value of HV achieved by MO-ABC, MO-GSA, and NSGA-II
in datasets with a large number of demands (NSF#07–NSF#12).
Next, we compare the MOEAs by using the SC metrics. As
we can see in Table IX, all algorithms obtain 100% of coverage
relation with the rest of MOEAs in datasets with a low num-
ber of demands; however, it is not applicable to those datasets
in which the number of demands is higher. The set of non-
dominated solutions that are generated by MO-ABC obtains a
good average coverage relation, since it covers 100%, 50%, and
83.33% of nondominated solutions achieved by MO-GSA, MO-
FA, and NSGA-II, respectively. Following with MO-GSA, we
can notice that their nondominated solutions cover a great part
of the solutions obtained by MO-ABC and NSGA-II; however,
it is only able to cover 41.67% of the nondominated solutions
from MO-FA. The results that are obtained by MO-FA are the
best ones; it is able to cover all nondominated solutions (100%)
that are obtained by MO-ABC, MO-GSA, and NSGA-II. Fi-
nally, NSGA-II is the worst MOEA; it covers 38.33%, 55%,
and 33.33% of nondominated solutions achieved by MO-ABC,
MO-GSA, and MO-FA, respectively.
For the NSF topology, we conclude that the best MOEA is
MO-FA. It obtains higher quality Pareto fronts than MO-ABC,
MO-GSA, and NSGA-II. As occurred with the pan European
optical network (COST239), the second best algorithm is MO-
ABC, followed by MO-GSA, and finally NSGA-II.
TAB L E IX
SET COVER AGE AB(NSF)
TAB L E X
NTT: SPECIFICATIONS OF DATASETS
D. Nippon Telegraph and Telephone Network
The Nippon Telegraph and Telephone Network (NTT, Japan)
is a large optical network that consists of 55 nodes and 144 opti-
cal links. In Table X, we present the NTT physical topology and
all specifications about those datasets used in our experiments.
Note that those datasets in which there is no constant value is
due to the fact that they were obtained from [50].
We start comparing the MOEAs by using the HV indicator
(see Table XI). Since the NTT network topology is larger than
the previous ones (COST239 and NSF), in Table XII we can see
how differences of HV among the MOEAs are not statistically
significant in many of the datasets with a lower number of
demands (NTT#01–NTT#06).
1652 IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART C: APPLICATIONS AND REVIEWS, VOL. 42, NO. 6, NOVEMBER 2012
TAB L E XI
AVERAGE HV OF 30 RUNS OBTAINED BY MO-ABC, MO-GSA, MO-FA,
AND NSGA-II (NTT)
TAB L E XII
RESULTS FROM STATISTICAL ANALYSIS OF THE COMPARISON AMONG
APPROACHES BY USING HV METRICS (NTT)
Fig. 7. Comparison among MO-ABC, MO-GSA, MO-FA, and NSGA-II by
using the average HV of 30 runs (NTT).
In Fig. 7, we can observe that MO-FA presents better results
of HV than MO-ABC, MO-GSA, and NSGA-II. Furthermore,
we can check that there exist remarkable differences of HV
among MO-FA and the rest of MOEAs when the number of
demands increases.
In Table XIII, we present a comparison by pairs of MOEAs by
using the SC metrics. As we can see, all swarm proposals (MO-
ABC, MO-GSA, and MO-FA) obtain a set of nondominated so-
lutions that is able to cover 100% of the nondominated solutions
obtained by NSGA-II in all datasets. However, NSGA-II only
covers 33.33%, 41.67%, and 16.67% of the nondominated so-
lutions that are obtained by MO-ABC, MO-GSA, and MO-FA,
respectively. If we focus on studying the behavior of the swarm
proposals, we notice that MO-FA is the algorithm that obtains
better coverage relation, followed by MO-ABC and MO-GSA.
To summarize, we can say that the usage of swarm intelli-
gence to deal with a large real-world optical network, such NTT,
is very suitable. As occurs with COST239 and NSF, the MOEA
TABLE XIII
SET COVER AGE AB(NTT)
TAB L E XIV
LIST OF APPROACHES PUBLISHED IN THE LITERATURE WHICH DEAL WITH THE
RWA PROBLEM
that is based on fireflies behavior (MO-FA) obtains better Pareto
fronts than the other MOEAs in terms of quality.
E. Comparison With Other Approaches
In this section, we present a comparison between our best
proposal based on swarm intelligence (MO-FA) and other ap-
proaches published in the literature.
In Table XIV, we present a great variety of heuristics and
metaheuristics to solve the RWA problem published in the liter-
ature. In the first place, in [35], the authors suggest eight typical
heuristics in the telecommunication field, formed by combin-
ing two routing methods (3-Shortest-Paths and Shortest-Path-
Dijsktra) and four wavelength assignment techniques (First
Fit,Least Used,Most Used, and Random). Second, in [34]
and [35] several multiobjective ant colony optimization algo-
rithms (MOACOs) are presented. Finally, two recent multiob-
jective metaheuristics to solve the RWA are presented in [36]
and [37]. For further information about them, see the references
that are shown in Table XIV.
RUBIO-LARGO et al.: COMPARATIVE STUDY ON MULTIOBJECTIVE SWARM INTELLIGENCE 1653
TAB L E XV
COMPARISON AMONG MO-FA AND OTHER APPROACHES PUBLISHED IN THE
LITERATURE BY USING HV METRICS
Fig. 8. Comparison among DEPT, MO-VNS, MO-FA, the best typical heuris-
tics, and the best MOACO by using the HV indicator.
TABLE XVI
COMPARISON AMONG SEVERAL APPROACHES AND MO-FA
BY USING SC AB
Unfortunately, in [34] and [35] the authors do not provide
enough information to make a comparison with them using
their methodology. However, they present for each dataset the
best Pareto front obtained by the best typical heuristics and best
MOACO; therefore, we can perform comparison with these data.
In Table XIV, we have highlighted which are the best typical
heuristics and best MOACO for each dataset.
To make the comparison, we use the same multiobjective in-
dicators as those used in previous sections: HV and SC. Further-
more, we have used the same network topology (NTT) as well
as datasets (NTT#01–NTT#06) that are presented in [34]–[37].
The specifications of datasets are presented in Table X.
In Table XV, we show a comparison among the best typi-
cal heuristics, the best MOACO, DEPT, MO-VNS, and MO-
FA. Note that for the best two typical heuristics and the
best MOACO, no data are available for datasets NTT#01 and
NTT#06. As may be observed, MO-FA obtains a value of HV
better than or equal to the rest of approaches in all datasets.
Those datasets in which all approaches obtain identical value
consist of a low number of demands (|U|=10). In the rest of
the datasets, MO-FA clearly obtains better value of HV than the
best typical heuristics, the best MOACO, DEPT, and MO-VNS
(see Fig. 8).
In the second place, we present a comparison by pairs of
approaches using the SC metrics. In Table XVI, the nondomi-
nated solutions that are obtained by the MO-FA are only covered
33.33%, 33.33%, 25%, and 25% (in average) by DEPT, MO-
VNS, the best typical heuristics, and the best MOACO, respec-
tively. However, MO-FA is able to cover 100% of nondominated
solutions that are obtained by any approach published in the lit-
erature in all datasets.
VI. CONCLUSION AND FUTURE WORK
In this paper, we have presented a comparative study on
swarm intelligence to solve the RWA problem. We have evalu-
ated three multiobjective metaheuristics based on the behavior
of honey bees (MO-ABC), on the law of gravity and mass in-
teractions (MO-GSA), as well as on the flash pattern of fireflies
(MO-FA). In order to study the goodness of these algorithms,
we have evaluated their capabilities to solve the RWA problem
over three real-world optical networks, comparing their results
with those obtained by a well-known multiobjective approach
(NSGA-II). The optical networks that are used in this paper
correspond with the pan European optical network, COST239,
Europe (11 nodes and 52 links), the NSF network, U.S. (14
nodes and 42 links), and the NTT, Japan (55 nodes and 144
links). For each optical network, we have designed 12 datasets
with a different number of demands, therefore a total of 36
datasets.
Our study has revealed that the usage of swarm intelligence
to solve the RWA problem is very suitable. More concretely,
there exist remarkable differences in the quality of the solutions
between the swarm proposals and the standard NSGA-II. This
may be due to the fact that the NSGA-II uses crossover operators
to produce new individuals from the present ones; however,
swarm approaches do not. The swarm approaches generate new
individuals taking not only parts from its parent, but also from
the rest of the population, increasing the richness of search
as a result. We have also concluded that—in this particular
telecommunication problem—the usage of swarm intelligence
is specially advisable when the number of demands increases. At
this point, we have to highlight that MO-FA is a very promising
approach to deal with this telecommunication problem.
Finally, we present a comparison among the best swarm meta-
heuristics (MO-FA) and diverse techniques published in the
literature. After performing an exhaustive comparison among
MO-FA and nearly 20 approaches (including previous work
DEPT and MO-VNS), we can conclude that MO-FA is a very
suitable approach to solve the RWA problem. From the posi-
tive results that are obtained in this study, it seems reasonable
to think that the multiobjective proposals of this manuscript
1654 IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART C: APPLICATIONS AND REVIEWS, VOL. 42, NO. 6, NOVEMBER 2012
could be applied not only in other telecommunication problems
that involve routing [51], [52], but also in diverse engineering
multiobjective problems [53], [54].
The next step would be applying other metaheuristics to the
RWA problem in order to make a comparison between those
MOEAs presented in this study and the new ones. Another re-
search line would be designing a parallel cooperative team to
study the behavior of MO-ABC, MO-GSA, and MO-FA work-
ing together to solve the RWA problem.
REFERENCES
[1] A. Wason and R. Kaler, “Routing and wavelength assignment in
wavelength-routed all-optical WDM networks,” Optik—Int. J. Light Elec-
tron. Optics., vol. 121, no. 16, pp. 1478–1486, 2010.
[2] C. Siva Ram Murthy and M. Gurusamy, WD Optical Networks Concepts,
Design and Algorithms: NJ: Prentice-Hall, 2002.
[3] A. M. Hamad and A. E. Kamal, “A survey of multicasting protocols for
broadcast-and-select single-hop networks,” IEEE Netw., vol. 16, no. 4,
pp. 36–48, Jul./Aug. 2002.
[4] M. Saha and I. Sengupta, “A genetic algorithm based approach for static
virtual topology design in optical networks,” in Proc. IEEE Indicom Conf.,
2005, pp. 392–395.
[5] B. Mukherjee, D. Banerjee, S. Ramamurthy, and A. Mukherjee, “Some
principles for designing a wide-area WDM optical network,” IEEE/ACM
Trans. Netw., vol. 4, no. 5, pp. 684–696, 1996.
[6] D. Karaboga, “An idea based on honey bee swarm for numerical opti-
mization,” in Comput. Eng. Dept., Eng. Faculty, Erciyes Univ., Kayseri,
Turkey, Tech. Rep. tr06, 2005.
[7] E. Rashedi, H. Nezamabadi-pour, and S. Saryazdi, “GSA: A gravitational
search algorithm,” Inf. Sci., vol. 179, no. 13, pp. 2232–2248, 2009.
[8] X. S. Yang, “Firefly algorithms for multimodal optimization,” in Proc. 5th
Int. Conf. Stochastic Algorithms: Found. Appl., 2009, pp. 169–178.
[9] K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast elitist multi-
objective genetic algorithm: NSGA-II,” IEEE Trans. Evolutionary Com-
put., vol. 6, no. 2, pp. 182–197, Apr. 2002.
[10] R. Ramaswami and K. N. Sivarajan, “Routing and wavelength assignment
in all-optical networks,” IEEE/ACM Trans. Netw., vol. 3, no. 5, pp. 489–
500, Oct. 1995.
[11] K. Chan and T. P. Yum, “Analysis of least congested path routing in
WDM lightwave networks,” in 13th Proc. IEEE INFOCOM’94, 1994,
vol. 2, pp. 962–969.
[12] H. H. Masayuki, M. Murata, and H. Miyahara, “Performance of alter-
nate routing methods in all-optical switching networks,” in Proc. IEEE
INFOCOM’97, 1997, pp. 9–17.
[13] L. Li and A. K. Somani, “Dynamic wavelength routing using congestion
and neighborhood information,” IEEE/ACM Trans. Netw., vol. 7, no. 5,
pp. 779–786, Oct. 1999.
[14] R. Ramamurthy and B. Mukherjee, “Fixed-alternate routing and wave-
length conversion in wavelength-routed optical networks,” IEEE/ACM
Trans. Netw., vol. 10, no. 3, pp. 351–367, Jun. 2002.
[15] I. Chlamtac, A. Ganz, and G. Karmi, “Purely optical networks for terabit
communication,” in Proc. IEEE INFOCOM’89, Apr. 1989, vol. 3, pp. 887–
896.
[16] R. Barry and S. Subramaniam, “The max sum wavelength assignment
algorithm for WDM ring networks,” in Proc. Opt. Fiber Commun., 1997,
pp. 121–122.
[17] A. Birman and A. Kershenbaum, “Routing and wavelength assignment
methods in single-hop all-optical networks with blocking,” in Proc. IEEE
INFOCOM’95, 1995, pp. 431–438.
[18] G. Jeong and E. Ayanoglu, “Comparison of wavelength-interchanging
and wavelength-selective cross-connects in multiwavelength all-optical
networks,” in Proc. IEEE INFOCOM’96, Mar. 1996, vol. 1, pp. 156–163.
[19] E. Karasan and E. Ayanoglu, “Effects of wavelength routing and selection
algorithms on wavelength conversion gain in WDM optical networks,”
IEEE/ACM Trans. Netw., vol. 6, no. 2, pp. 186–196, Apr. 1998.
[20] S. Subramaniam and R. Barry, “Wavelength assignment in fixed routing
WDM networks,” in Proc. IEEE Int. Conf. Commun., Jun. 1997, vol. 1,
pp. 406–410.
[21] X. Zhang and C. Qiao, “Wavelength assignment for dynamic traffic in
multi-fiber WDM networks,” in Proc. 7th Int. Conf. Comput. Commun.
Netw., 1998, pp. 479–585.
[22] H. Zang, J. P. Jue, and B. Mukherjee, “A review of routing and wavelength
assignment approaches for wavelength-routed optical WDM networks,”
Opt. Netw. Mag., vol. 1, pp. 47–60, 2000.
[23] G. D. Morley and W. D. Grover, “Tabu search optimization of optical ring
transport networks,” in Proc. IEEE GLOBECOM, 2001, pp. 2160–2164.
[24] A. Grosso, E. Leonardi, M. Mellia, and A. Nucci, “Logical topology design
over WDM wavelength routed networks robust to traffic uncertanities,”
IEEE Commun. Lett., vol. 5, no. 4, pp. 172–174, Apr. 2001.
[25] S. Yan, M. Ali, and J. Deogun, “Route optimization of multicast sessions
in sparse light-splitting optical networks,” in Proc. IEEE GLOBECOM,
2001, pp. 2134–2138.
[26] R. Rodriguez-Dagnino, E. Lopez-Caudana, H. Martinez-Alfaro, and
J. Gonzalez-Velarde, “Simulated annealing and stochastic ruler algorithms
for wavelength assignment planning in WDM optical networks,” in Proc.
IEEE Int. Conf. Syst., Man, Cybern., 1999, vol. 6, pp. 1015–1020.
[27] R. Inkret, B. Mikac, and I. Podnar, “A heuristic approach to wavelength
assignment in all-optical network,” in Proc. 9th Medit. Electrtech. Conf.,
1998, vol. 2, pp. 759–763.
[28] M. Ali, B. Ramamurthy, and J. Deogun, “Routing algorithms for all-optical
networks with power considerations: The unicast case,” in Proc. 8th Int.
Conf. Comput. Commun. Netw., 1999, pp. 237–241.
[29] S. Shiann-Tsong, C. Yue-Ru, C. Yu-Jie, and T. Hsuen-Wen, “A novel
optical ip router architecture for WDM networks,” in Proc. 15th Int. Conf.
Inf. Netw., 2001, p. 335.
[30] L. Zong and B. Ramamurthy, “Optimisation of amplifier placement in
switch-based Optical Network,” in Proc. IEEE Int. Conf. Commun., 2001,
vol. 1, pp. 224–228.
[31] V. Banerjee, N. Metha, and S. Pandey, “A genetic algorithm approach
for solving the routing and wavelength assignment problem in WDM
network,” in Proc. 3rd IEEE/IEE Int. Conf. Netw., 2004, pp. 70–78.
[32] D. Thompson and G. Bilbro, “Comparison of a genetic algorithm and
simulated annealing algorithm for the design of an ATM network,” IEEE
Commun. Lett., vol. 4, no. 8, pp. 267–269, Aug. 2000.
[33] G. N. Varela and M. C. Sinclair, “Ant colony optimisation for virtual-
wavelength-path routing and wavelength allocation,” in Proc. Congr. Evo-
lutionary Comput., 1999, pp. 1809–1816.
[34] C. Insfr´
an, D. Pinto, and B. Bar´
an, “Dise˜
no de topolog´
ıas virtuales en
redes ´
opticas. un enfoque basado en colonia de hormigas,” in Proc. XXXII
Latin-Amer. Conf. Inf. 2006—CLEI2006, 2006, vol. 8, pp. 173–195.
[35] A. Arteta, B. Bar´
an, and D. Pinto, “Routing and wavelength assignment
over WDM optical networks: A comparison between MOACOs and clas-
sical approaches,” in Proc. 4th Int. IFIP/ACM Latin Amer. Conf. Netw.,
2007, pp. 53–63.
[36] A. Rubio-Largo, M. A. Vega Rodr´
ıguez, J. A. G´
omez-Pulido, and
J. M. S´
anchez-P´
erez, “A differential evolution with Pareto tournaments
for solving the routing and wavelength assignment problem in WDM
networks,” in Proc. IEEE Congr. Evolutionary Comput., 2010, vol. 10,
pp. 129–136.
[37] A. Rubio-Largo, M. A. Vega-Rodr´
ıguez, J. A. G´
omez-Pulido, and
J. M. S´
anchez-P´
erez, “Solving the routing and wavelength assignment
problem in WDM networks by using a multiobjective variable neighbor-
hood search algorithm,” in Proc. 5th Int. Workshop Soft Comput. Models
Ind. Environmental Appl., 2010, vol. 73, pp. 47–54.
[38] C. A. Coello, C. Dhaenens, and L. Jourdan Eds., Advances in Multi-
Objective Nature Inspired Computin. (Studies in Computational Intel-
ligence vol. 272) New York: Springer, 2010.
[39] J. Y. Yen, “Finding the k shortest loopless paths in a network,” Manag.
Sci., vol. 17, no. 11, pp. 712–716, 2003.
[40] A. Rubio-Largo, M. A. Vega-Rodr´
ıguez, J. A. G´
omez-Pulido, and
J. M. S´
anchez-P´
erez, “Tackling the static RWA problem by using a mul-
tiobjective artificial bee colony algorithm,” in Proc. 11th Int. Work Conf.
Artif. Neural Netw.—Volume Part II, 2011, pp. 364–371.
[41] A. Rubio-Largo, M. A. Vega-Rodr´
ıguez, J. A. G´
omez-Pulido, and
J. M. S´
anchez-P´
erez, “A multiobjective gravitational search algorithm
applied to the static routing and wavelength assignment problem,” in
Proc. 2011 Int. Conf. Appl. Evolutionary Comput.—Vol. Part II, 2011,
pp. 41–50.
[42] N. Srinivas, K. Deb, “Multiobjective optimization using nondominated
sorting in genetic algorithms,” Evolut. Comput., vol. 2, pp. 221–248,
1994.
[43] D. Leung and W. D. Grover, “Capacity planning of survivable mesh-
based transport networks under demand uncertainty,” Photonic Network
Commun., vol. 10, pp. 123–140, 2005.
[44] A. Rubio-Largo and M. A. Vega-Rodr´
ıguez. (2012, May). Optical Net-
work Topologies and Data Sets for the RWA Problem [Online]. Available:
http://mstar.unex.es/mstar_documentos/RWA/RWA-Instances.html
RUBIO-LARGO et al.: COMPARATIVE STUDY ON MULTIOBJECTIVE SWARM INTELLIGENCE 1655
[45] A. Auger, J. Bader, D. Brockhoff, and E. Zitzler, “Theory of the hyper-
volume indicator: Optimal n-distributions and the choice of the reference
point,” in Proc. 10th ACM SIGEVO Workshop Foundations Genetic Algo-
rithms, 2009, pp. 87–102.
[46] R. M. Solovay, “A model of set-theory in which every set of reals is
Lebesgue measurable,” Ann. Math., vol. 92, no. 1, pp. 1–56, 1970.
[47] E. Zitzler, L. Thiele, M. Laumanns, C. Fonseca, and V. da Fonseca, “Perfor-
mance assessment of multiobjective optimizers: An analysis and review,”
IEEE Trans. Evolut. Comput., vol. 7, no. 2, pp. 117–132, Apr. 2003.
[48] D. J. Sheskin, Handbook of Parametric and Nonparametric Statistical
Procedures. 4th ed., New York: Chapman & Hall/CRC Press, 2007.
[49] D. Pinto and B. Bar´
an, “Solving multiobjective multicast routing problem
with a new ant colony optimization approach,” in Proc. 3rd Int. IFIP/ACM
Latin Amer. Conf. Netw., 2005, pp. 11–19.
[50] M. Schaerer and B. Bar´
an,, “A multiobjective ant colony system for vehicle
routing problem with time windows,” in Proc. IASTED Int. Conf. Appl.
Inf., 2003, pp. 97–102.
[51] Y.-J. Gong, J. Zhang, O. Liu, R.-Z. Huang, H.-H. Chung, and Y.-H. Shi,
“Optimizing the vehicle routing problem with time windows: A discrete
particle swarm optimization approach,” IEEE Trans. Syst., Man, Cybern.
C, Appl. Rev., vol. 42, no. 2, pp. 254–267, Mar. 2012.
[52] A. Vasilakos,M. Saltouros, A. Atlassis, and W. Pedrycz, “Optimizing QoS
routing in hierarchical ATM networks using computational intelligence
techniques,” IEEE Trans. Syst., Man, Cybern. C, Appl. Rev., vol. 33,
no. 3, pp. 297–312, Aug. 2003.
[53] G. Ewald, W. Kurek, and M. Brdys, “Grid implementation of a parallel
multiobjective genetic algorithm for optimized allocation of chlorination
stations in drinking water distribution systems: Chojnice case study,”
IEEE Trans. Syst., Man, Cybern. C, Appl. Rev., vol. 38, no. 4, pp. 497–
509, July 2008.
[54] F. Xue, A. Sanderson, and R. Graves, “Multiobjective evolutionary deci-
sion support for design supplier manufacturing planning,” IEEE Trans.
Syst., Man Cybern. A, Syst., Humans, vol. 39, no. 2, pp. 309–320, Mar.
2009.
´
Alvaro Rubio-Largo received the M.S. degree
in computer science from the University of
Extremadura, Caceres, Spain, in 2009, where he
is currently working toward the Ph.D. degree in
computer science under the direction of Dr. Vega-
Rodr´
ıguez.
His current research interests include the design
and implementation of multiobjective metaheuristics
and their application to NP-hard problems in the field
of telecommunications.
Miguel A. Vega-Rodr´
ıguez received the Ph.D. de-
gree in computer science from the University of
Extremadura, Caceres, Spain.
He is a professor of Computer Architecture with
the Department of Computer and Communications
Technologies, University of Extremadura. He has
authored or coauthored more than 400 publications
including journal papers, book chapters, and peer-
reviewed conference proceedings. In addition, he is
an editor and reviewer of several international JCR
journals. His main research interests include par-
allel and distributed computing, reconfigurable computing, and evolutionary
computing.
Juan A. G´
omez-Pulido received the Ph.D. degree in
computer science from the Complutense University
of Madrid, Madrid, Spain, in 1993.
He is a professor of Computer Architecture with
the Department of Computer and Communications
Technologies, University of Extremadura, Caceres,
Spain. He has authored or coauthored 35 ISI journals,
as well as many book chapters and peer-reviewed
conference proceedings. His current research interest
includes the application of high-performance recon-
figurable computing to speed up EA in large opti-
mization problems.
Juan M. S ´
anchez-P´
erez received the Ph.D. degree in
physics from the Complutense University of Madrid,
Madrid, Spain, in 1976.
He is a Professor of Computer Architecture
with the Department of Computer and Communi-
cations Technologies, University of Extremadura,
Caceres, Spain. His research interests include artifi-
cial intelligence, logic design, and modern computer
architectures.
