Genetic Fuzzy Rule-Based meta-scheduler for Grid computing

Abstract

The growing interest in grids technologies for the solving of large-scale computational problems leads related framework improvement. One of the challenging problems in Grid computing is the efficient resources utilization and allocation of tasks, i.e. scheduling problem. Fuzzy Rule-Based Systems (FRBSs) have recently proved to be a competitive alternative for the development of scheduling systems, outperforming extensively used scheduling strategies such as EASY Backfilling or Greedy. However, FRBSs-based schedulers performance strongly depends on their data bases quality and a major effort is still required for the knowledge acquisition process improvement. This paper presents a fuzzy rule-based meta-scheduler incorporating a new genetic approach for the learning process. Concretely, the suggested learning strategy is inspired by classical rule evolution strategies, Pittsburgh and Michigan approaches. Experimental results show that further accuracy in the learning process of fuzzy meta-schedulers can be achieved without significantly increasing the associated computational effort.

Full text

Genetic Fuzzy Rule-Based Meta-Scheduler
for Grid Computing
R. P. Prado, S. García-Galán, A. J. Yuste, J. E. Muñoz Expósito and S. Bruque
Telecommunication Engineering Department.
University of Jaén. Alfonso X el Sabio, 28 Linares, Jaén. Spain.
Abstract—The growing interest in grids technologies for the
solving of large-scale computational problems leads related
framework improvement. One of the challenging problems in
Grid computing is the efficient resources utilization and allocation
of tasks, i.e. scheduling problem. Fuzzy Rule-Based Systems
(FRBSs) have recently proved to be a competitive alternative for
the development of scheduling systems, outperforming extensively
used scheduling strategies such as EASY Backfilling or Greedy.
However, FRBSs-based schedulers performance strongly depends
on their data bases quality and a major effort is still required
for the knowledge acquisition process improvement. This paper
presents a fuzzy rule-based meta-scheduler incorporating a
new genetic approach for the learning process. Concretely, the
suggested learning strategy is inspired by classical rule evolution
strategies, Pittsburgh and Michigan approaches. Experimental
results show that further accuracy in the learning process of fuzzy
meta-schedulers can be achieved without significantly increasing
the associated computational effort.
Index Terms—Grid Computing, Scheduling, Fuzzy Rule-Based
Systems, Genetic Fuzzy Systems.
I. INTRODUCTION
Grid computing is an emergent platform for the solving of
large-scale computational problems in wide range of science
and engineering fields [1]. It is characterized by the coopera-
tion of heterogeneous and geographically distributed resources
interconnected through high speed networks. Further, these
resources are located under different resources domains (RDs)
considering their own access and sharing policies [2]. One of
the main challenges facing Grid computing is given by the
efficient submission of tasks and resources management or
grid scheduling, which is known to be a NP-hard problem
[3]. Generally, the scheduling problem on grids is classified
into two categories attending to a two-level grid structure,
the meta-scheduling and local scheduling problem [4]. A
meta-scheduler is responsible for the tasks distribution to the
participating RDs, whereas local schedulers or Local Resource
Management Systems (LRMSs) carry out tasks allocation to
machines within its own domain. Concretely, in this work
we focus our attention on the improvement of grids meta-
scheduling systems based on Fuzzy Rule-Based Systems
(FRBSs).
FRBSs are knowledge-based systems increasingly used in
the grid research community for the scheduling problem [5],
[6]. In the light of the high dependence of FRBSs performance
with theirs knowledge bases (KBs) quality, the knowledge
acquisition problem arises as a relevant issue. It is to be
noticed that the incorporation of expert knowledge is not
possible in the vast majority of application fields of FRBSs
and thus, an automatic learning of KBs is pursued. There
exist several learning strategies for the learning of fuzzy
rules. Genetics Algorithms (GAs) are evolutionary techniques
which have demonstrated its efficiency in the learning of KBs
[7], [8], [9]. Specifically, two successful strategies must be
pointed out, namely, Pittsburgh [10] and Michigan approach
[11], that mainly differentiate in the level of application of
the genetic operators. Pittsburgh approach considers a whole
rule set or rule base (RB) as an individual or chromosome.
In contrast, population in Michigan approach is made up of
rules as individuals. On the one hand Pittsburgh is known to
achieve more accurate results than Michigan approach. On the
other hand, Michigan approach requires much reducer com-
putational effort and has high search ability for finding good
rules than Pittsburgh approach [12]. However, considering the
learning process relevance for the whole scheduling strategy
performance, new approaches have been suggested [9].
In this work, a meta-scheduler for grid computing con-
sidering a novel strategy for the learning of fuzzy rules is
introduced. Concretely, the genetic strategy is inspired by the
dual consideration of RBs and rules as individuals, resulting
in a hybrid Pittsburgh-Michigan approach. The combination
of Pittsburgh and Michigan approaches has been addressed
before. Ishibuchi et al. [12], [13] proposed to harness the
advantages of each classical strategy by the incorporation
of a Michigan-style step at every generation of Pittsburgh
approach. However, in this work it is suggested to improve
Pittsburgh approach final accuracy by the analysis and modifi-
cation of rules as individuals, in a Michigan-style strategy, in a
way that no significant increment of the overall computational
cost is necessary. Thus, the proposed learning strategy do
not consider Pittsburgh approach alteration and deals with
the further examination of the obtained rules. Hence, the
approach in this work is to automatically finding high quality
RBs that allow optimums schedules in terms of response
time and resource utilization. Simulation results show that the
proposed schema is able to achieve a greater accuracy with
a reduced computational effort than the classical approaches.
Therein, this paper is a major effort of the authors towards
the development of new schemas allowing more efficient
scheduling strategies for grids [14], [15].
The rest of the paper is organized as follows. First, Section
II deals with previous works on scheduling on grids and the
role of FRBSs within this platform. The proposed learning
Fourth International Workshop on Genetic and Evolutionary Fuzzy Systems. Mieres, Spain, March 2010
978-1-4244-4622-3/10/$25.00 ©2010 IEEE
51

strategy for the fuzzy rule-based meta-scheduler is introduced
in Section III. In Section IV simulation results and comparative
results are presented. Finally, Section V concludes the paper.
II. B
ACKGROUND
Scheduling is a long-standing problem in grid computing.
From the point of view of scheduling, computational grids
can be considered a hierarchical structure considering two-
levels, the RD level and the Virtual Organization (VO) level
[4], [16]. The grid is made up of different RDs, making up a
global virtual entity or VO. Each RD comprises a given set of
heterogeneous resources and imposes its management policies.
Scheduling within a RD is performed by a local scheduler
which is responsible for the allocation of tasks within its
associated domain. On the other hand, it is the meta-scheduler
which distributes tasks among the different RDs and so drives
the whole VO scheduling process.
A wide range of heuristics have been suggested to improve
the scheduling process in high-demanding and distributed
environments such as grids. Typically, heuristics are classified
into dynamic and static [17]. These categories differ in the
number of tasks that are considered at every scheduling step
or the fixing of objective tasks set. Static heuristics for hetero-
geneous computing environment include OLB (Opportunistic
Load Balancing), MET (Minimum Execution Time) and MCT
[17], [18]. In contrast, some instances of dynamic heuristics
are Min-Min , Max-min, RR (Round Robin), DFPLTF (Dy-
namic FPLTF) and WQ (Work Queue) [19]. It is to be noted
that these strategies basically found their decisions on the
estimation of resources performance and tasks requirements.
However, given the changing and dynamic nature of grids,
more flexible strategies are pursued. In this sense, the role of
FRBSs must be pointed out.
FRBSs are expert systems that have recently attracted the
grid community for the solving of scheduling problems [20].
However, since the quality of the fuzzy rule-based scheduler
is subject to the quality of its KB, the automatic knowledge
acquisition is a relevant process. As stated before, GAs have
proved to be one of the best option for the evolution of
fuzzy knowledge, as it is the case of Pittsburgh and Michigan
approaches [7]. The main challenge for Michigan approach
is given by the Competition vs Cooperation Problem (CPP)
[21]. That is, within Michigan approach, rules are encoded
as individual that competes as to be selected for the next
generation. However, a rule success may also depends on the
cooperation with other rules, and thus, the process is driven
by a conflict of interests. In contrast, Pittsburgh approach
considers a whole RB as an individual and so competition is
exercised among RBs, that is, with independence of competi-
tors cooperation. However, crossover in Pittsburgh approach,
can dramatically affect the RB performance, since this operator
does not consider any dependence among rules within the
mixing of RBs. In fact, the little reinforcement informa-
tion in the Pittsburgh approach generally leads to a higher
computational cost. Thus, with the aim of benefiting both
from Pittsburgh and Michigan advantages, a hybrid strategy
D^͗DĞƚĂ^ĐŚĞĚƵůĞƌ
<͗<ŶŽǁůĞĚŐĞ ĂƐĞ
>ŽĐĂů^ĐŚĞĚƵůĞƌ Ϯ
>ŽĐĂů^ĐŚĞĚƵůĞƌ ũ
>ŽĐĂů^ĐŚĞĚƵůĞƌ ϭ
D^
ƌĚϭ͕ϭ
ƌĚϮ͕Ŭ
ƌĚϭ͕ϯ
ƌĚϭ͕Ŭ
ƌĚϮ͕ϭ
ƌĚϭ͕Ϯ
ƌĚũ͕ϭ
ƌĚũ͕Ϯ
ƌĚũ͕Ŭ
ƌĚϭ
ƌĚϮ
'ƌŝĚ hƐĞƌ ϭ
'ƌŝĚ hƐĞƌ Ϯ
'ƌŝĚ hƐĞƌ Ŷ
ƌĚũ
ZD
Zd
&W
Wd
W^
Z^
Z
<
'ƌŝĚ ƐƚĂƚĞ ĨĞĂƚƵƌĞƐ
Figure 1. Fuzzy meta-scheduler structure within grid environment.
is suggested in this work. Concretely, attending to Genetic
Fuzzy Systems classification trends [22], the proposed learning
strategy can be categorized into Pittsburgh learning strategies
with a Cooperative-Competitive final stage.
III. P
ROPOSED SCHEMA
The proposed meta-scheduler or resource broker structure
within the grid environment is shown in Figure 1. The classical
schema of Fuzzy Logic Systems can be distinguished for the
meta-scheduler; Fuzzification, Inference and Defuzzification
systems and its associated Knowledge base. The basic opera-
tion can be summarized as follows. At every scheduling step
the meta-scheduler analyze RD availability (i.e. as stated in
[23] a grid is a fully dynamic environment with uncertainty
where resources may fall down, become reserved, change their
access policies or join the system over time) update each
cooperating RD state information offered by their the local
schedulers and feature their conditions by means of limited
and normalized set of variables. The meta-scheduler initialize
the process of transforming the RD state into a resource
domain selector index it showing the suitability level for being
selected in the next schedule. First, the Fuzzification system is
responsible for obtaining a fuzzy value from the crisp value
obtained for each grid state variable in a way that the obtained
information is associated a linguistic label representing a
vagueness level of relevance. Then, in the Inference system a
fuzzy output is obtained through the application of the system
knowledge (rules) to finally derive a crisp value that represent
fuzzy RD selector in the Defuzzification system. Concretely,
“center of gravity” is selected as the defuzzification method.
This way, the distribution of tasks among RDs is faced on
the basis of the grid state and acquired knowledge. The grid
state, or VO state as mentioned before, is characterized though
seven dynamic inputs. They are described in Table I.
Note that the selected input variables contemplate both cur-
rent conditions (FPE and RE) and resource domain utilization
52

Feature Description
Number of free processing elements (FPE) Number of free processing element within RD
i
.
Previous Tardiness (PT) Sum of tardiness of all finished jobs.
Resource Makespan (RM) Current makespan for RD
i
.
Resource Tardiness (RT) Current tardiness of jobs within RD
i
.
Previous Score (PS) Previous deadline score of already finished jobs in RD
i
.
Resource Score (RS) Number of non delayed jobs so far in RD
i
.
Resources In Execution (RE) Number of resources currently executing jobs within RD
i
.
Table I
I
NPUTS FEATURES FOR THE FUZZY META-SCHEDULER.
history (PT, RM, RT, PS and RS) in terms of processing
elements and resources state, tardiness, makespan and jobs
deadlines. The selection of this variables is founded on the
achievement of an adaptive scheduling [24]. As stated in [23]
any scheduling strategy aiming to offer a certain level of
QoS must consider a more or less precise environment. In
this sense adaptive scheduling suggest the consideration of
both current and past conditions and it has been taken into
account in the selection of the grid variables. Moreover, these
input features are considered to be enough representative to
describe the system state without requiring a high increment
in the search space complexity. Their associated membership
functions are depicted in Figure 2. Variables are represented
by three gaussian shaped sets corresponding to low, medium
and high levels.
Hence, rules in this work follow the Mamdani-type encod-
ing where the antecedent part is made up of seven features and
the consequent part consists of a single output or RD selector
factor. Also, the antecedents connector must be distinguished
and weight of the rule. Two possibilities are considered for
the connector: “1” represents AND and “2” represents OR
operators. A rule expression and its associated linguistic and
numeric encoding are represented as follows,
R
i
= if ω
1
is A
1n
and/or...ω
m
is A
mn
then y is B
n
: w
i
(1)
R
i
:[a
1
... a
m
b
n
c
n
w
i
] (2)
where A
mn
, B
n
, and/or, denote the fuzzy set for input
variable ω
m
, output set and associated connector, and a
m
, b
n
and c
n
represents its numeric encoding, respectively. Also, w
i
indicates rule i corresponding weight.
As stated before, a decisive factor for the fuzzy meta-
scheduler success is given by the quality of this fuzzy knowl-
edge. Thus, we seek to improve the RB quality by means of
a learning process. Concretely, the initial evolution of rules
is driven by a genetic process where RBs act as individuals
or chromosome. That is, we suggest the application of a
Pittsburgh based strategy for knowledge acquisition. How-
ever, since a Pittsburgh based strategy does not differentiate
individual contribution or cooperation of every rule within
a RB, it is suggested here to further enlarge the learning
process as to increase the accuracy of the obtained RB by
the considerations of rules as individuals. Thus, a Michigan-
approach style strategy is suggested to analyze a previous
evolved RB without a significant increment in the number of
RB evaluations. With this aim, a performance index must be
specified to evaluate each RB. In this work, we suggest the
utilization of Response Time (RT).
Hence, the learning strategy is divided into two phases.
Initially, a set of RB are generated randomly, in a way that no
previous knowledge is required, and evolution is achieved by
the application of genetic factors at the level of fuzzy RBs.
Once the Pittsburgh stage has concluded, the selected RB rules
undergo an analysis to test its role in its RB success. Firstly,
rules contribution to the scheduler output is obtained and those
rules presenting a significant relevance in the contribution,
given by index α, are subject to an increase in its weight,
w
i
.
w
i
=

w
i
+Δw
i
if α
i
 α
w
i
if α
i
<α
(3)
Rules are modified individually and its cooperation with the
rest of original rules is examined. This way, if a relevant rule
weight it is increased and its interaction with the rest of rules
improves the response of the fuzzy system within the grid
environment, a positive influence is considered for the rule.
Analog reasoning can be followed for a deterioration in system
performance. This operation is repeated for all the relevant
rules as to infer its influence polarity. All the rules whose
weight increment derives in a performance improvement are
incorporated in the candidate RB preserving this modification.
If the overall contribution is favorable, rules keep their weight.
In other case, only the rule presenting the major contribution
preserves its modification,
w
i
=
⎧
⎪
⎨
⎪
⎩
w
i
+Δw
i
if α
i
 α, P I
i
<PI
o
and (PI
sim
<PI
imax
or P I
imax
= PI
i
)
w
i
if α
i
<α
(4)
where PI
o
, PI
sim
, PI
imax
and PI
i
represent the original
performance index for the RB, PI for the RB with simultane-
ous weight modification, best individual weight resulting RB
after a rule weight increment and RB
i
, respectively.
Secondly, those relevant rules deteriorating the RB per-
formance in the face of a weight increment are analyzed.
As stated before, these rules contribution to the scheduler
output is significant, but it is considered to be a negative
contribution. Hence, it is tested here whether the modification
of its consequent polarity contributes to a RB improvement.
53

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.2
0.4
0.6
0.8
1
RECURS OS
Degree of membership
BAJO MEDIO ALTO
D/> ,/',
&W
Wd
ZD
Zd
W^
Z^
Z
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.2
0.4
0.6
0.8
1
SALIDA
Degree of membership
MUYBAJO BAJO MEDIO ALTO MUYALTO
sZz>KtD/> ,/', sZz,/',>Kt
>Kt
Z^ĞůĞĐƚŝŽŶ &ĂĐƚŽƌ
Figure 2. Membership functions for the meta-scheduler inputs and output.
Algorithm 1 Genetic learning strategy
Initialization. Pittsburgh-based stage.
1. Random generation of
RB
pop
rules bases.
Do
1. Evaluate RB i generation.
2. RB Selection: Elitism(λ).
3. RB Crossover: Two point crossover.
4. Mutation. Decreasing exponential mutation. Eq 6.
j++
While(stopping condition j ≤ N)
Select best individual: RB
b
.
Michigan-based stage.
1. Retrieve RB
b
rules contribution α
i
.
for (rules in RB
b
)
Increment i rule weight. Eq 3; RB

b
.
Evaluate RB

b
end
2. Evaluate overall weight increment result. Select best weight increment
behaviour. Eq 4.
3. Consequent inversion. Eq 5. RB

b
.
Return: Final Rule Base: RB

b
.
However, as in the weight increment process, these rules
behaviour are individually and jointly tested and the best
configuration is kept.
c
i
=

−c
i
if α
i
 α, P I
i
>PI
o
c
i
i.o.c
(5)
Note that the learning strategy does not only consider
rules weight adjustment but also the alteration of their con-
sequent polarity and thus it is classified into a Pittsburgh and
Competitive-Cooperative hybrid approach [22]. The learning
strategy is summarized in Algorithm 1. Note that tuning of
fuzzy sets is not considered here. Thus, rules interpretability
does not change through the whole process.
It is worth mentioning here, that the suggested Michigan-
style testing process computational effort is bounded to (2 ·
RB
size
+2) RB evaluations, corresponding to the case when
all rules are relevant with a negative evaluation in the face of
a weight increment. It can be inferred that extra computational
effort is negligible in this process in comparison to the
Pittsburgh-based stage. Thus, the suggested learning strategy
for the learning of the fuzzy meta-scheduler it is intended
Cluster CPUs
clrlcgce01 112
clrlcgce02 84
clrlcgce03 186
iut15 38
obc 55
Table II
A
UVERGRID SCENARIO MACHINES COMPOSITION.
to further increase the accuracy of Pittsburgh process, in a
confined number of RB evaluations.
IV. S
IMULATION RESULTS
In order to test the proposed fuzzy-meta-scheduler, a grid
scenario based on GridSim toolkit is simulated [25]. GridSim
allows the utilization of traces and grid configuration from
existing installations obtained from the Grid Workload Archive
(GWA) [26]. Concretely, the proposed grid scenario is inspired
by AuverGrid. AuverGrid is a production grid platform made
up of five clusters situated in the Auvergne, France. The Au-
verGrid project represents a sub-project of the EGEE project
(Enabling Grids for E-science in Europe) that uses the LCG
(Large hadron collider Computing Grid project) middleware
as grid framework (being biomedical and high-energy physics
research its main application areas). Table II summarizes the
AuverGrid-based scenario where clusters consists of a set of
computing resources executing Scientific Linux (dual 3GHz
Pentium-IV Xeons). Also, workload is bounded to 3000 tasks
for this simulation.
Moreover, the learning strategy configuration is presented.
Initially, in the Pittsburgh-based learning stage, the candidate
population consists of 10 randomly generated RBs and the
maximum RB size is set to 10 rules. Also, two-point crossover
and elitist selection is considered with a selection rate λ of 0.8.
Further, mutation following a decreasing exponential function
is applied in a way that local minimums are avoided,
M(n)=M
o
exp
(−n/N)c
(6)
where M
o
represents the initial mutation (0.1), n is the
considered generation, N is the number of iterations set as
54

Results Average awrt (fitness) Improvement % (Michigan/Pittsburgh) Worst solution Best improvement Average Runtime
Pittsburgh-stage 3.7086e+004 - 3.7620974e+004 - 38199.62
Michigan-stage 3.6636e+004 1.21% 3.6599808e+004 2.71% 1991.91
Table III
S
IMULATIONS RESULTS FOR THE LEARNING STRATEGY.
0 10 20 30 40 50 60 70
3.65
3.7
3.75
3.8
3.85
3.9
3.95
4
x 10
4
Generation
Fitness
PITTSBURGH
Figure 3. Convergence behaviour of the learning strategy initial stage.
stopping condition (70) and c is a constant fixed to 5 in
this experiment. On the other hand, the Michigan-approach
learning stage is configured considering a relevance factor α
fixed to 0.8.
Figure 3 presents the convergence behaviour of the initial
learning stage for 40 experiments where fitness represent av-
erage weighted response time. It is shown that the Pittsburgh-
based stage reaches its final result in approximately 50 gener-
ations. This process is translated in (RB
pop
· λ · 50) number
of RBs evaluations.
Table III shows simulation results for both strategies in
terms of the learning index and runtimes. The first column rep-
resent (Average awrt -fitness) the average final fitness obtained
though Pittsburgh and Michigan learning stages and the second
one (Improvement % -Michigan/Pittsburgh). It is observed,
that the second stage of the learning strategy improves the final
result of the Pittsburgh stage in 1.21%. Further, response time
is reduced in 2.71% in the most favorable simulation (worst
solution for Pittsburgh-based stage shown in third column of
Table III). Note this result is obtained in a reduced number
of RB evaluations, representing a maximum of 5.36% of
the whole computational effort in the presented simulations
(2· RB
size
+2) in front to (RB
pop
· λ· N ). Average runtimes for
both Pittsburgh and Michigan strategies are presented in Table
III. Moreover, it must be pointed out, that an improvement over
the first learning stage is achieved in 96% of the experiments,
proving the strategy ability to differentiate rules role in the
RB success, reward positive contributions and conveniently
modify rules polarity.
Further, the fuzzy meta-scheduler is analyzed from both
the perspective of users and administrator QoS criteria. Con-
cretely, the scheduler performance is evaluated considering
average makespan, classic and machine usage, flow time,
tardiness, slowdown, average weighed slowdown (awsd) be-
sides average weighed response time (awrt) that was selected
as training index in this work. Figure IV shows the fuzzy
scheduler simulation results for a set of configurations for
the fuzzy scheduler. The first two columns present the fuzzy
scheduler results when considering the proposed hybrid learn-
ing approach and Pittsburgh approach, respectively, where
results are the average results of 40 experiments. Therein,
40 evolved RB are used with fuzzy scheduler to test its
efficiency in several criteria. It is observed that machine and
classic usage do not present any significant difference for both
configurations. This was expected since these criteria may
present conflicting interests with the selected learning index,
awrt. On contrary, it is observed that flow time and tardiness
are improved on average with the fuzzy scheduler with the
hybrid learning strategy.
Moreover, the best obtained RB with the proposed approach
is tested within the grid environment and results are presented
in Table IV. Also, results are compared with a widely extended
scheduling strategy in distributed system, Min-Min [19]. It
is shown that the fuzzy meta-scheduler outperforms Min-
Min strategy in 11.91% and 12.09% in awrt, on average
and considering the best RB, respectively. Despite, the fuzzy
scheduling strategy improving the classical approach in other
considered metrics such as flow time it is to be noted that the
fuzzy scheduler learning strategy is successful in providing
successful results in the training index. Furthermore, it is
observed that the considered approaches require approximately
the same time for its execution as shown by runtimes results.
This shows that the fuzzy scheduling strategy does not present
higher computational effort than other scheduling strategies
such as Min-Min.
V. C
ONCLUSIONS
Designing efficient scheduling strategies is critical for the
harnessing of the high potential of grids. Due to the inher-
ent distributed and changing environment of grids, dynamics
models are increasingly attracting grids researchers attention.
Concretely, in this work, a meta-scheduler based on dynamic
FRBSs has been suggested. In previous works [14] authors
have previously studied the efficiency of grid fuzzy schedulers
in comparison to widely used scheduling systems. Further,
the dependence with the learning process was analyzed and a
classical learning strategy, Pittsburgh approach was employed
as to evolute the scheduler knowledge. However, in the light
of the high dependence of the fuzzy system with the quality
of it RB, more efficient learning processes are required and
55

Metric/Strategy Hybrid Average Pittsburgh Average Hybrid Best Min-Min
Average Makespan 272691.015 272691.015 272691.015 273296.015
Classic Usage 6.05 5.77 5.77 5.75
Flow Time 1914.380 2337.983 1866.721 6515.479
Machine Usage 6.06 5.77 6.04 6.03
Tardiness 15.0232 326.7426 0.1016 4109.3788
Slowdown 1.2696 4.1166 1.0073 27.586
Awrt 36636.594 370861.086 36563.870 41591.697
Awsd 1.0258 1.2528 1.0003 3.4914
Runtime 35 39 34 38
Table IV
S
CHEDULING STRATEGIES SIMULATION RESULTS COMPARATIVE.
a novel strategy for the knowledge acquisition process of the
fuzzy scheduler has been presented in the work. Specifically,
the learning strategy takes advantage of both classical Pitts-
burgh and Michigan approaches strengths and improves the
classical rule evolution strategy, Pittsburgh approach, accuracy
in 1.12%. In spite of being a reduced improvement over
the genetic strategy, its relevance resides in the insignificant
increment of computational effort in comparison to the whole
learning strategy. Further, it is to highlighted here the simple
implementation of the Competitive-Cooperative stage. Hence,
this work contributes to the specification of more effective
scheduling strategies for the emerging Grid computing plat-
forms.
A
CKNOWLEDGMENT
This work has been financially supported by the Andalusian
Government (Research Project P06-SEJ-01694).
R
EFERENCES
[1] I. Foster and C. Kesselman, “The grid: Blueprint for a new computing
infrastructure,” USA, 2004.
[2] J. M. Marín and S. B. Cámara, Las Tecnologías Grid de la Informa-
ción como Nueva Herramienta Empresarial. Jaén (España): Septem
Ediciones, 2008.
[3] M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide
to the Theory of NP-Completeness. New York, NY, USA: W. H.
Freeman & Co., 1979.
[4] K. Christodoulopoulos, V. Sourlas, I. Mpakolas, and E. Varvarigos, “A
comparison of centralized and distributed meta-scheduling architectures
for computation and communication tasks in grid networks,” Computer
Communications, vol. 32, no. 7-10, pp. 1172 – 1184, 2009.
[5] H. Liu, A. Abraham, and A. E. Hassanien, “Scheduling jobs on com-
putational grids using a fuzzy particle swarm optimization algorithm,”
Future Generation Computer Systems, June 2009.
[6] J. Zhou, K.-M. Yu, C.-H. Chou, L.-A. Yang, and Z.-J. Luo, “A dynamic
resource broker and fuzzy logic based scheduling algorithm in grid
environment,” in ICANNGA ’07: Proceedings of the 8th international
conference on Adaptive and Natural Computing Algorithms, Part I.
Berlin, Heidelberg: Springer-Verlag, 2007, pp. 604–613.
[7] O. Cordon, F. Herrera, and P. Villar, “Generating the knowledge base
of a fuzzy rule-based system by the genetic learning of the data base,”
Fuzzy Systems, IEEE Transactions on, vol. 9, no. 4, pp. 667–674, Aug
2001.
[8] S. García, A. Fernández, J. Luengo, and F. Herrera, “A study of statis-
tical techniques and performance measures for genetics-based machine
learning: accuracy and interpretability,” Soft Comput., vol. 13, no. 10,
pp. 959–977, 2009.
[9] C. Franke, F. Hoffmann, J. Lepping, and U. Schwiegelshohn, “Devel-
opment of scheduling strategies with genetic fuzzy systems,” Appl. Soft
Comput., vol. 8, no. 1, pp. 706–721, 2008.
[10] S. F. Smith, “A learning system based on genetic adaptive algorithms,”
Ph.D. dissertation, Pittsburgh, PA, USA, 1980.
[11] L. B. Booker, D. E. Goldberg, and J. H. Holland, “Classifier systems and
genetic algorithms,” Artif. Intell., vol. 40, no. 1-3, pp. 235–282, 1989.
[12] H. Ishibuchi, T. Yamamoto, and T. Nakashima, “Hybridization of fuzzy
gbml approaches for pattern classification problems,” Systems, Man, and
Cybernetics, Part B: Cybernetics, IEEE Transactions on, vol. 35, no. 2,
pp. 359–365, April 2005.
[13] H. Ishibuchi, T. Nakashima, and M. Nii, Classification and Modeling
with Linguistic Information Granules: Advanced Approaches to Linguis-
tic Data Mining (Advanced Information Processing). Secaucus, NJ,
USA: Springer-Verlag New York, Inc., 2004.
[14] R. P. Prado, S. G. Galán, A. J. Yuste, J. E. M. Expósito, A. J. S. Santiago,
and S. Bruque, “Evolutionary fuzzy scheduler for grid computing,” ser.
Lecture Notes in Computer Science, vol. 5517. Springer, 2009, pp.
286–293.
[15] A. J. S. Santiago, A. J. Yuste, J. E. M. Expósito, S. G. Galán, J. M. M.
Marín, and S. Bruque, “A dynamic-balanced scheduler for genetic
algorithms for grid computing,” W. Trans. on Comp., vol. 8, no. 1, pp.
11–20, 2009.
[16] S. Phatanapherom, P. Uthayopas, and V. Kachitvichyanukul, “Dynamic
scheduling ii: fast simulation model for grid scheduling using hypersim,”
in WSC ’03: Proceedings of the 35th conference on Winter simulation.
Winter Simulation Conference, 2003, pp. 1494–1500.
[17] L. Tseng, Y. Chin, and S. Wang, “The anatomy study of high perfor-
mance task scheduling algorithm for grid computing system,” Computer
Standards and Interfaces, vol. 31, no. 4, pp. 713 – 722, 2009.
[18] H. S. T.D. Braun and N. Beck, “A comparison of eleven static heuristics
for mapping a class of independent tasks onto heterogeneous distributed
computing systems,” Journal of Parallel and Distributed Computing,
vol. 61, pp. 810–837, 2001.
[19] N. Fujimoto and K. Hagihara, “A comparison among grid scheduling
algorithms for independent coarse-grained tasks,” in SAINT-W ’04:
Proceedings of the 2004 Symposium on Applications and the Internet-
Workshops (SAINT 2004 Workshops). Washington, DC, USA: IEEE
Computer Society, 2004, p. 674.
[20] C. Franke, J. Lepping, and U. Schwiegelshohn, “Genetic fuzzy systems
applied to online job scheduling,” in Fuzzy Systems Conference, 2007.
FUZZ-IEEE 2007. IEEE International, July 2007, pp. 1–6.
[21] O. Cordón, F. Herrera, F. Hoffmann, and L. Magdalena, Genetic fuzzy
systems: Evolutionary tuning and learning of fuzzy knowledge bases
.
World Scientific Pub Co Inc, 2001.
[22] F. Herrera, “Genetic fuzzy systems: taxonomy, current research trends
and prospects,” Evolutionary Intelligence, vol. 1, no. 1, pp. 27–46, 2008.
[23] D. Klusacek, “Dealing with Uncertainties in Grids through the Event-
based Scheduling Approach,” in Fourth Doctoral Workshop on Math-
ematical and Engineering Methods in Computer Science (MEMICS
2008), vol. 1. Ing. Zden
ˇ
ek Novotn
`
y CSc., Ondrá
ˇ
ckova 105, 628 00
Brno Further information, 2008, pp. 978–80.
[24] F. Xhafa and A. Abraham, “Meta-heuristics for grid scheduling prob-
lems,” Metaheuristics for Scheduling: Distributed Computing Environ-
ments, Studies in Computational Intelligence, Springer Verlag, Germany,
ISBN, pp. 978–3, 2008.
[25] A. Sulistio, G. Poduval, R. Buyya, and C.-K. Tham, “On incorporating
differentiated levels of network service into gridsim,” Future Gener.
Comput. Syst., vol. 23, no. 4, pp. 606–615, 2007.
[26] T. U. Delft, “The grid workloads archive,” 2007. [Online]. Available:
http://gwa.ewi.tudelft.nl/pmwiki/pmwiki.php?n=Workloads.Gwa-t-4
56