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CHAPTER 6

HYBRID METHODS FOR MINING ASSOCIATION RULES

6.1 GENERAL

This chapter reviews the necessity of hybridizing GA and PSO methods,

salient aspects of GA and PSO hybrid methods as available in published

literature, and proposes a new hybrid methodology of GA and PSO for AR !

As the main drawbac" of PSO being wea" local search, it is overcome by

proposing Shuffle #rog $eaping Algorithm for the local search to mine ARs!

The e%perimental results of both proposals are also presented, and discussed

along with the salient inferences there from!

6.2 NEED FOR HYBRIDIZATION

The PSO was inspired by insect swarms and has been proven as a

competitor to the standard GA for function optimization! Since then several

researchers have analyzed the performance of the PSO with different settings,

e!g!, neighborhood settings &'ennedy()))* Suganthan()))+! omparisons

between PSOs and the standard GA were done analytically in &-berhart and

Shi()).+ and also with regard to performance in &Angeline ()).+! /t has been

pointed out that the PSO performs well in the early iterations, but has problems

reaching a near optimal solution in several real0valued function optimization

problems &Angeline ()).+! 1oth -berhart and Angeline conclude that hybrid

models of standard GA and PSO could lead to further advances!

6.3 HYBRID OF GA AND PSO FOR ARM

AR using either GA or PSO methodology often generates rules with

high PA! 1ut balancing between e%ploration and e%ploitation is often a

tailbac"! GA has good e%ploration capability, but at times it leads to e%ploiting

the search space! PSO has the capability to converge 2uic"ly thus avoiding

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e%ploitation but results in premature convergence! 3ybrid system combining

GA and PSO is a solution for the balancing phenomena!

Recently the hybridization between evolutionary algorithms &-As+ andother metaheuristics has shown very good performance in many "inds of multi0

ob4ective optimization problems, and thus has attracted considerable attention

from both academic and industrial communities!

An evolutionary circle detection method based on a novel haotic

3ybrid Algorithm combines the strength of PSO, GA and chaotic dynamics! /t

involves the standard velocity and position update rules of PSO, with the ideas

of selection, crossover and mutation from GA & hun03o at al!, 56(6+! A hybrid

multi0ob4ective evolutionary algorithm incorporating the concepts of personal

best and global best in PSO and multiple crossover operators to update the

population, maintains a nondominated archive of personal best &Tang and

7ang, 56(5+! A hybrid method combining GA and PSO creates individuals in a

new generation not only by crossover and mutation operations as found in GA,

but also by mechanisms of PSO! #urther the above approach solves the

problem of local minimum of the PSO, and has higher efficiency of searching

global space & 8ie Ru and 9ue :ianhua 566.+!

The hybridization methods of GA and PSO analyzed here are process

based, integrating the GA steps into PSO or vice versa! Population based

hybridization is attempted in this study, where the population is split based onfitness values and both methods are run individually on the respective

subpopulation! The ob4ective of this hybrid methodology is to sum up the

advantages of both GA and PSO in overcoming the drawbac"s!

6.3.1 GA-PSO Hybri A!"#ri$%& '#r ARM

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-ach evolutionary algorithm proposed in the literature has some

advantage over the other! PSO provides a faster convergence than GA! A hybrid

techni2ue utilizing the effectiveness and uni2ueness of these two algorithms

can be implemented to achieve high performance &;ong et al!, 56(5+! The proposed hybrid methodology that is the GPSO proposed combines the features

of GA and PSO to enhance the performance of AR ! The uni2ueness of GA

and PSO are

• The optimization process of GA is a steady state process converging at

global optima!• The global search space is maintained by GA avoiding premature

convergence!• PSO is faster a process with the ability to search the solution space

2uic"ly• PSO "eeps trac" of each particles< best position thereby effectively

fi%ing up the search space

The hybrid methodology employs these features for evolution of individualsover generations! The total population is split into two subpopulations based on

fitness values! The fitness function designed is for ma%imization and the

individuals with ma%imum fitness values are aimed to evolve towards the

global optima! So GA is applied on the subpopulation with higher fitness

values! PSO with the ability to converge 2uic"ly is applied on the lower ran"ed

subpopulation based on fitness values! The GA with optimization at global

optima enhances the e%ploration capability and PSO with easy convergence

avoids e%ploitation! Thus the hybrid methodology effectively balances between

e%ploration and e%ploitation thereby resulting in ARs with better PA! The upper

and lower ran"ed subpopulations after evolution through GA and PSO are

updated at the end of each iteration! This aims at consistency in performance,

avoiding the loss of the better individuals over generations!

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Genetic Algorithm

Particle Swarm Optimization

Evaluate Fitness

Upper

Lower

Initial Population Ranked Population Updated Population

127

Applying GA on the upper ran"ed subpopulation avoids premature

convergence! -volution through PSO on lower ran"ed subpopulation avoids

e%ploitation of GA of individuals, thereby increasing the speed of evolution

process! The proposed hybrid model is shown in #igure =!(!

Fi"(r) 6.1 Hybri GA* PSO +GPSO, M# )!

As can be seen in #igure =!(, GA and PSO both wor" with the same

initial population! The hybrid approach ta"es 8 individuals that are randomly

generated! These individuals may be regarded as chromosomes in the case of

GA, or as particles in the case of PSO! The 8 individuals are sorted by fitness,

and the upper half individuals are fed into the GA to create new individuals by

crossover and mutation operations! The lower half of the population sorted

through fitness values are fed into PSO for evolution! The velocity update and

position update are done based on the personal best and global best positions

determined on the lower half individuals! The output of GA and PSO are

combined for propagating into ne%t generation and the process repeated till an

end criterion is met!

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1y performing evolution based on GA on the upper half of the individuals

sorted through fitness value the global optimal solution space is retained! This

facilitates the steady progress towards the optimization through e%ploration!

PSO applied on the other half of the individuals where fitness value is low, theconvergence is achieved easily avoiding e%ploitation! Thus, the hybrid GPSO

model balances between e%ploration and e%ploitation by combining the

strengths of GA and PSO! The pseudo0code for GPSO is given below>

/nitialize all GA variables

/nitialize all PSO variables

Repeat

alculate fitness value of the population

Ran" the population based on fitness function

Split the population into two halves> higher ran"ed range, lower

ran"ed range

On higher ran"ed range partition perform GA

S)!) $i#/0 Select two parent chromosomes from the population

according to their fitness

Cr# # )r0 7ith a crossover probability cross over the parents to

form a new offspring

M($ $i#/0 7ith a mutation probability mutate new offspring at

each locus

U4 $i#/0 Place the resulting new offspring in a new population

On low ran"ed partition perform PSO

#or each particle

U4 $) velocity

U4 $) position

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U4 $) p1est and g1est

-nd for

?pdate new population combining PSO particles and GA chromosomes

?ntil &stopping condition+

The population size is fi%ed based on the size of the dataset for which

AR is applied! 1inary encoding is adopted for representation of data! The

fitness function as given in -2uation &@!5+ is adopted for calculating the fitness

values! The e%perimental setting and results of the GPSO methodology for

mining ARs are presented in ne%t section!

6.3.2 E54)ri&)/$ ! R) (!$ / Di ( i#/

To test the performance of the hybrid GPSO for mining ARs,

e%periments were carried out on the well0"nown benchmar" datasets from ? /

repository!

The parameters, which play a ma4or role during the rule discovery in the

hybrid GPSO methodology, are listed in Table =!(! The population size is the

size of the individuals ta"en up for e%perimentation! The crossover and

mutation rates are the GA operator specifications! c ( and c 5 are the acceleration

coefficients used in velocity updation of PSO as in -2uation & !5+!

-volutionary algorithms are relatively simple to implement, robust and

perform very well on a wide spectrum of problems! This study proposes a

hybrid methodology of evolutionary algorithms> GA and PSO for AR ! The

scope of this study on mining ARs using GPSO is to>

• Study the performance of GA over generations• Analyze the performance of PSO over generations• /dentify the limitations of GA and PSO while mining ARs in terms of

PA and e%ecution speed!• ompare the performance of GPSO with GA and PSO

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T b!) 6.1 GPSO P r &)$)r '#r ARM

P r &)$)r !()Population Size $enses > 56

ar -valuation > B663aberman 66Post0operative Patient are > .6Coo > (66

rossover Rate $enses > 6!=ar -valuation > 6!B

3aberman 6!BD

Post0operative Patient are > 6!.Coo > 6!.utation Rate $enses > 6!D

ar -valuation > 6!@3aberman 6!5DPost0operative Patient are > 6!5Coo > 6!5

Selection Operation Roulette wheel selectionc( 5c5 5

8o! of Generations D6

E #!($i#/ # )r G)/)r $i#/ A/ !y i

GA is "nown for maintaining the global optima throughout evolution

and steady progress in performance over generations, whereas, PSO converges

2uic"ly with chances of converging at local optima! So to analyze the

performance of GPSO over generations, the ma%imum PA of the ARs mined byGPSO is recorded at intervals over evolution for all the five datasets! This data

is plotted against the results obtained with GA and PSO as shown in #igure =!5!

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&a+

GA0

10

20

30

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6070

80

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100

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ethodolog!

Predictive Accurac! "#$

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GA0

10

20

30

40

50

6070

80

90

100

10

20

30

40

50

ethodolog!

Predictive Accurca! "#$

0

10

20

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10 20 30 40 5 0

ethodolog!

Predictive Accurac! "#$

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0

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20

30

40

50

6070

80

90

100

10 20 30 40 50

ethodolog!

Predictive Accurac! "#$

ar -valuation ;ataset

&b+ 3aberman

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&e+ Coo ;atasetFi"(r) 6.2 Pr) i $i ) (r y . N#. #' G)/)r $i#/

'#r ARM 7i$% GPSO

#rom #igure =!5 it is observed that mining ARs using GA results in

lesser PA than PSO and GPSO! The increase in PA is achieved steadily over

generations! The PSO methodology for mining ARs generates AR with better

PA at earlier stages of evolution! /n further generations, the particles move

away from global optima bringing down the accuracy, thus e%ploiting the

search space! #or all the five datasets, GPSO methodology generates ARs with

better PA and maintains the same over generations, thereby balancing between

e%ploitation and e%ploration! Thus the stability in performance is obtained

while mining ARs with GPSO!

#rom the #igure =!5 a to e it is observed that• The performance of GA in terms of PA increases over generations

indicating its effectiveness in terms of global search capability*• PSO generates ma%imum accuracy at initial generations thereby

converging 2uic"ly*• The deviation from global optima and convergence at local optima is

attained in later generation for PSO! This e%ploitation of search space

results in reduction of PA*• GPSO produces consistent PA with minimal difference over generations

and• The PA of GPSO is better than GA and PSO!

Pr) i $i ) A (r y A/ !y i

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The ob4ective of the study is to enhance the PA of ARs mined by

utilizing the uni2ueness of both GA and PSO! The PA of the ARs mined by

GPSO is plotted for the five datasets as shown in #igure =! ! The results

obtained using simple GA and PSO are also shown in same figure for comparison!

50

60

70

80

90

100

GA PSO GPSO

%ataset

Predictive Accurac!"#$

Fi"(r) 6.3 C#&4 ri #/ #' Pr) i $i ) A (r y #' GPSO 7i$% GA / PSO

The PA of rules mined with PSO is better than GA! The PA obtained by

GPSO is enhanced when compared to GA or PSO! The PA for the $enses and

Coo datasets are e2uivalent to that of PSO, but better than GA! /ncrease in PA

upto DE is achieved over PSO by GPSO! An increase of 6E is obtained by

GPSO over GA for 3aberman

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A/ !y i #' E5) ($i#/ Ti&)

AR with GPSO performs both GA and PSO operations on their respective subpopulation! The effect of GPSO on e%ecution time while mining

ARs is shown in #igure =!@! The e%ecution time of GPSO is better than genetic

algorithm and ta"es more time than that of PSO! The evolution of the lower

ran"ed population by PSO ma"es the convergence 2uic"er, thereby reducing

the e%ecution time achieved compared to GA! The GA operations ta"e more

time and are comple%, when compared to PSO! Thus there is an increase in

e%ecution time of GPSO over PSO! The increase in prediction accuracy over

PSO compensates the time trade0off!

As standalone both GA and PSO produce results inconsistently for all

the five datasets! The drawbac" of GA is its lac" of memory, which limits, its

search and convergence ability! The mutation operation also leads to

e%ploitation and hence the inconsistency in accuracy for all the five datasets!

PSO tends to converge at local optima resulting in premature convergence,thereby generating inconsistent results! 1y combining the advantages of both

GA and PSO the GPSO method mine ARs with consistent performance! The

GPSO method of mining AR outperforms both GA and PSO methodology in

terms of prediction accuracy, consistence and e%ecution time!

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&'&&&

(&&&

)&&&

*&&&

+&&&&

GA

PSO

GPSO

%atasets

E,ecution -ime "ms$

Fi"(r) 6.8 C#&4 ri #/ #' E5) ($i#/ Ti&) #' GPSO 7i$% GA / PSO

6.8 PSO 9ITH LOCAL SEARCH

Some important situations that often occur in PSO is overshooting ,

which is a "ey issue to premature convergence and essential to the performance

of PSO! #rom the velocity update mechanism of PSO, it is observed that the

p1 est and g1 best ma"e the particles oscillate! The overshooting problem

occurs due to the velocity update mechanism, leading the particles to the wrong

or opposite directions against the direction to the global optimum! As a

conse2uence, the pace of convergence of the whole swarm to the global

optimum slows down! One possible way to prevent the overshooting problem

from happening is to appropriately ad4ust the algorithmic parameters of PSO!

3owever, it is a difficult tas", as the parameter ad4ustment depends a lot on

domain "nowledge and the optimization problem!

/n conse2uence of overshooting, the particle will move to the opposite

direction against the direction to the global optimum! Two ma4or approaches

that can be used to tac"le the overshooting problem are described below!

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• A/ !y i #' 4r#b!)& > 1y analyzing the structure of problems or

identifying the fitness landscape of problems, a lethal movement could

be prevented! /t poses great challenge on automated problem structure

analysis &1ucci and Pollac", 566@+

• G)/)r $) / $) $ $r $)"i) > There are many methods to generate a

new solution for testing, such as> heuristics of the specific problem,

statistic sampling, and local search techni2ues! 3owever, the

computation costs in generating and testing new solutions may be

generally high!

/n order to develop a general0purpose algorithm and overcome the

overshooting problem, an efficient local search strategy F Shuffle #rog $eaping

Algorithm &S#$A+, is adopted and combined with the standard PSO for AR !

6.: PSO 9ITH SFLA FOR MINING ASSOCIATION RULES

Population0based heuristics inherently improve the implementation of a

local search algorithm, since the heuristic approach of a population of solutionsresults in rather poor local search properties! /ncorporating local search

algorithm into the population based heuristic is called a emetic Algorithm!

/n published literature many $S schemes have been employed with PSO

for optimization! Petalas et al! &566B+ employed a stochastic iterative $S

techni2ue in their A, called R7;-, where a se2uence of appro%imations of

the optimizer are generated by assuming a random vector as a search velocity!

/t was noticed by ictoire and :eya"umar &566@+ that early on in the PSO

search, particles were almost close to the pro%imity of the global optimum, then

move away from these areas! #or this reason the local search method was

chosen for implementation! /nspired from literature a memetic PSO with S#$A

for local search is proposed for mining ARs!

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The S#$A is a memetic metaheuristics that is designed to see" a global

optimal solution by performing a heuristic search! /t is based on the evolution

of memes carried by individuals and a global e%change of information among

the population &-usuff and $ansey 566 +! The S#$A involves a population of possible solutions defined by a set of frogs &i!e! solutions+ that is partitioned

into subsets referred as memeple%es! The different memeple%es are considered

as different cultures of frogs, each performing a local search! 7ithin each

memeple%, the individual frogs hold ideas that can be influenced by the ideas

of other frogs, and evolve through a process of memetic evolution! After a

number of memetic evolution steps, ideas are passed among memeple%es in a

shuffling process &$iong and Ati2uzzaman 566@+! The local search and the

shuffling processes continue until convergence criteria are satisfied &-usuff and

$ansey 566 +!

6.:.1 M)$%# #!#"y

/nitially the particles are distributed in the search space and fitness of the

particles is calculated! The velocity and position updation of the particles are

carried out using PSO

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G)/)r $i#/ #' i/i$i !4#4(! $i#/+P, / ) !( $i/" $%)

'i$/) #' ) % 4 r$i !)

)!# i$y / 4# i$i#/ (4 $i#/#' 4 r$i !)

Di $rib($i#/ #' 'r#" i/$# M&)&)4!)5)

I$)r $i ) U4 $i/" #' 7#r $ 'r#"i/ ) % &)&)4!)5)

C#&bi/i/" !! 'r#" $# '#r& /)7 4#4(! $i#/

T)r&i/ $i#/ ri$)ri

$i 'i) ;

D)$)r&i/) $%) b) $ #!($i#/

S#r$i/" $%) 4#4(! $i#/ i/) )/ i/" #r )r i/ $)r& #'

'i$/) !()

SFLA

140

Fi"(r) 6.: F!#7 % r$ '#r PSO 7i$% SFLA '#r ARM

/n S#$A, the population consists of a set of frogs &solutions+ that is

partitioned into subsets and it is named as memeple%es! The different

memeple%es are considered as different cultures of frogs, each performing a

local search! 7ithin each memeple%, the individual frogs have different ideas,that can be influenced by the ideas of other frogs, and evolve through a process

of memetic evolution! After a defined number of memetic evolution steps,

ideas are passed among memeple%es in a shuffling process! The local search

and the shuffling processes continue until defined convergence criteria are

satisfied!

The S#$A starts with an initial population of P frogs created randomly!

Then, the frogs are sorted in a descending order of fitness! Then, the entire

N

Y

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Frog 6

Memeplex

1Memeplex

2Memeplex

3

Frog 1

Frog 2

Frog 3

Frog 7

Frog 5

Frog 4

Frog 8

141

population is divided into m memeple%es, each containing 8 frogs! /n this

process, the first frog goes to the first memeple%, the second frog goes to the

Second memeple%, frog goes to the th memeple%, and frog H( goes bac"

to the first memeple%, etc! The process is as shown in #igure =!=! 7ithin eachmemeple%, the frogs with the best and the worst fitness are identified as I b and

I w, respectively! Also, the frog with the global best fitness is identified as I g!

Then, a process similar to PSO is applied to improve only the frog with the

worst fitness &not all frogs+ in each cycle!

Fi"(r) 6.6 F#r& $i#/ #' M)&)4!)5)

Accordingly, the position of the frog with the worst fitness is ad4usted based on

-2uations &=!(+ and &=!5+!

Change ∈frog position ( Di)= rand ()∗ X b− X w &=!(+

New Position ( X w )= Current Position ( X w )+ ( D i ) &=!5+

7here rand & + is a random number between 6 and (* X

b is the

position of best frog in the group* X

w

is the position of worst frog in the

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group! /f this process produces a better solution, it replaces the worst frog!

Otherwise, the calculations in -2uations are repeated, but with respect to the

global best frog &i!e! I g replaces I b+!

The fitness function defined in e2uation &@!5+ is used for evaluating the

fitness of the individuals! 1oth PSO and APSO methods are combined with

S#$A resulting in two proposals, namely, PSOHS#$A and APSOHS#$A for

AR !

6.:.2 E54)ri&)/$ ! R) (!$ / Di ( i#/

The PSO and APSO methodologies are both combined with S#$A for local search to mine ARs as described in previous section! The five datasets

used for all the other methodologies is adopted for generating ARs!

ARs are mined from the datasets using the two proposals and the PA of

the generated rules are plotted as shown in #igure =!B!

PSOHS#$A methodology of mining ARs performs better than simple

PSO in terms of PA for all the five datasets ta"en up for analysis! TheAPSOHS#$A methodology for mining ARs outperforms the other three

methods!

*&

*'

*(

*)

**

.&

.'

.(

.)

.*

+&&

PSO APSO PSO+SFLA APSO+SFLA

%atasets

Predictive Accurac!

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Fi"(r) 6.< Pr) i $i ) A (r y C#&4 ri #/ '#r ARM The fitness function ob4ective is ma%imization! /n order to enhance the

results the fitness values generated should be optimal! The fitness values for the proposed methodologies are plotted in #igure .!. for all the five datasets!

&

&/0

+

+/0

'

'/0

1

1/0

(

(/0

2enses %ataset

PSO APSO PSO+SFLA APSO+SFLA

Iteration 3um4er

Fitness 5alue

&

&/0

+

+/0

'

'/0

1

1/0

(

6a4erman7s Survival %ataset

PSO APSO PSO8SF2A APSO8SF2A

Iteration 3um4er

Fitness 5alue

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&&/0

++/0

''/0

11/0

((/0

0

9ar Evaluation %ataset

PSO APSO PSO8SF2A APSO8SF2A

Iteration 3um4er

Fitness 5alue

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Postoperative Patient %ataset

PSO APSO PSO8SF2A APSO8SF2A

Iteration 3um4er

Fitness 5alue

&

&/0

+

+/0

'

'/0

1

1/0

(

:oo %ataset

PSO APSO PSO8SF2A APSO8SF2A

Iteration 3um4er

Fitness 5alue

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Fi"(r) 6.= Fi$/) !() '#r PSO 7i$% SFLA '#r ARM

The fitness values of both proposed methodologies* PSO HS#$A and

APSOHS#$A are more than the respective individual PSO and APSO values!

Thus, both methods perform better by generating ARs with enhanced PA, than

PSO and APSO methods!

The performances of the proposed two methods are compared with GA

and PSO methods discussed so far in terms of the PA of the ARs mined and the

results for the five datasets are shown in Table =!5!

The APSOHS#$A methodology outperforms the other methods for all

the five datasets by generating ARs with better PA! The APSO methodology

too generates ARs with optimal accuracy compared to other methods! The data

independent adaptation methodologies &SAPSO(, SAPSO5 and SA PSO+ ran"

ne%t in terms of performance for all the five datasets! 3owever the performance

of other methods varies among datasets considered in this study!

The number of rules generated by each methodology for the datasets

ta"en up for analysis is given in Table =! ! The SA PSO( methodology performs better among the data independent adaptation methodologies,

considered for analysis here as SAPSO!

The APSOHS#$A methodology of mining ARs generates more rules

than the other methods discussed! The SAPSO &SAPSO(+ performs better by

generating optimal number of ARs!

Thus the proposed APSOHS#$A methodology performs better whencompared to the other methods, in terms of PA and number of rules generated!

The S#$A performs effective local search thereby balancing between

e%ploration and e%ploitation and hence better performance!

T b!) 6.2 C#&4 ri #/ #' $%) Pr) i $i ) A (r y '#r ARM

GA AGAE!i$i $

GA PSO9PS

OCPSO NPSO SAPSO APSO GPS>

PSS

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.D )(!= )(!= . !DB )B!)( .B!D ) !( )B!)( ).!( .B!D )ation .B )@ )B )B!=( ))!) ))!.= )B!( ))!)5 ))!.5 )D!(5 ))

n

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6.6 SUMMARY

A hybrid method combining both genetic algorithm and Particle Swarm

Optimization called GPSO has been proposed! This method brings a balance between e%ploration and e%ploitation, resulting in higher prediction accuracy of

the ARs mined and consistency in performance! Two methodologies using PSO

with S#$A for local search &PSOHS#$A and APSOHS#$A+ has been proposed!

Among them, APSOHS#$A methodology generate ARs with better PA, than all

other methodologies discussed so far!

CHAPTER <CONCLUSIONS AND FUTURE 9OR@

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The salient conclusions of this research wor" and the scope for future wor" are

presented in this chapter!

!

&i+ Genetic Algorithm when used for mining ARs performs better than

other e%isting traditional methods!

&ii+ Particle swarm optimization when applied for mining ARs produce

results better than GA, but with minimum e%ecution time! The

increase in PA of PSO over GA is> B!.E for $enses dataset, B!@E for

3aberman

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&v+ GPSO methodology produces consistent results in comparison with

GA and PSO! The PA achieved is almost same throughout the

generations for each dataset, by utilizing GA to maintain diversity on

high ran"ed population and applying PSO

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e%tended to comple% and real life problems belonging to une%plored

application0domains, and the e%ecution time analysis of these methods

can be carried out! ethods to reduce the e%ecution time could be

e%plored!