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A Robust Intelligent Framework for Multiple Response Statistical Optimization Problems Based on Artificial Neural Network and Taguchi Method

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Hindawi Publishing CorporationInternational Journal of Quality, Statistics, and Reliability Volume 2012, Article ID 494818, 11 pagesdoi:10.1155/2012/494818
Research Article
ARobustIntelligentFrameworkforMultipleResponseStatisticalOptimizationProblemsBasedonArtiﬁcialNeuralNetworkandTaguchiMethod
AliSalmasnia,
1
MahdiBastan,
2
andAsgharMoeini
3
1
Department of Industrial Engineering, Faculty of Engineering, Tarbiat Modares University, Tehran, Iran
2
Department of Industrial Engineering, Eyvanekey University, Semnan, Iran
3
Department of Industrial Engineering, Faculty of Engineering, Shahed University, Tehran, Iran
Correspondence should be addressed to Ali Salmasnia, ali.salmasnia@modares.ac.irReceived 12 February 2012; Revised 16 May 2012; Accepted 3 June 2012Academic Editor: Tadashi DohiCopyright © 2012 Ali Salmasnia et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the srcinal work is properly cited.An important problem encountered in product or process design is the setting of process variables to meet a required speciﬁcationof quality characteristics (response variables), called a multiple response optimization (MRO) problem. Common optimizationapproaches often begin with estimating the relationship between the response variable with the process variables. Among thesemethods, response surface methodology (RSM), due to simplicity, has attracted most attention in recent years. However, in many manufacturing cases, on one hand, the relationship between the response variables with respect to the process variables is far toocomplextobee
ﬃ
cientlyestimated;ontheotherhand,solvingsuchanoptimizationproblemwithaccuratetechniquesisassociatedwith problem. Alternative approach presented in this paper is to use artiﬁcial neural network to estimate response functions andmeet heuristic algorithms in process optimization. In addition, the proposed approach uses the Taguchi robust parameter designto overcome the common limitation of the existing multiple response approaches, which typically ignore the dispersion e
ﬀ
ect of the responses. The paper presents a case study to illustrate the e
ﬀ
ectiveness of the proposed intelligent framework for tacklingmultiple response optimization problems.
1.Introduction
Controllable input variables set to an industrial process toachieve proper operating conditions are one of the commonproblems in quality control. Taguchi method [1–3] is a
widely accepted technique among industrial engineers andquality control practitioners for producing high quality products at low cost. In this regard, Ko et al. [4] employedTaguchi method and artiﬁcial neural network to performdesign in multistage metal forming processes consideringwork ability limited by ductile fracture. Su et al. [5] proposeda new circuit design optimization method where geneticalgorithm (GA) is combined with Taguchi method. Lo andTsao [6] modiﬁed an analytical linkage-spring model basedon neural network analysis and the Taguchi method todetermine the design rules for reducing the loop heightand the sagging altitude of gold wire-bonding process of the integrated circuit (IC) package. In Taguchi’s designmethod, the control variables (factors can be controlled by analyst) and noise variables (factors cannot be controlledby analyst) are considered inﬂuential on product quality.Therefore, the Taguchi method is to choose the levels of control variables and to reduce the e
ﬀ
ects of noise variables.That is, control variables setting should be determinedwith the intention that the quality characteristic (responsevariable) has minimum variation while its mean is closeto the desired target. Nevertheless, so far, the Taguchimethod can only be used for a single response problem; itcannot be used to optimize a multiple response optimizationproblem. But, in most industrial problems, we have dealtwith more than one response variable and improving themsimultaneously is very important. Common problem in thesimultaneous optimization of response variables is to bedi
ﬀ
erent and sometimes contradictory to their optimality
2 International Journal of Quality, Statistics, and Reliability direction. Thus, optimizing the manufacturing process thanone response variable led to nonoptimal amounts of otherresponses. So when dealing with multiresponse problemshad better separately to optimize the response variables(Taguchi method) and ﬁnally, according to process engineer,is determined the optimum combination of design vari-ables. Therefore, it is very important to design a methodto optimize simultaneously responses. Another importantpoint in the optimization process of the responses is toestimate the relationship between the response and controlvariables. In many cases, regression relationships do nothave the ability to estimate properly the relationship betweenresponse and control variables and large amounts of meansquare error (MSE) regression models can be seen that show the poor quality of these relationship descriptions [7]. Inmost cases, this problem occurs for two reasons: (i) reversalof the independence assumptions of input variables; (ii)being a complex relationship between response and controlvariables. In these cases, intelligent approaches (approachbased on neural network and approach based on fuzzy)are an appropriate alternative to achieve a good estimation.In this regard, [8] proposed an approach based on neuralnetworks to solve the quality optimization problem inTaguchi’s dynamic experiment. However, this method isapplicable only when there is a response variable.Reference [9] proposed the neural network method andthe data envelopment analysis (DEA) [10] to e
ﬃ
ciently optimize the multiple response problem in the Taguchimethod. With the neural network, the signal-to-noise (SN)ratios of responses are estimated by the known experimentaldata for each control variables combination, which alsonamed decision making unit (DMU). Then, DEA is usedto ﬁnd each DMU’s relative e
ﬃ
ciency so that the optimalcontrol variables combination can be found by relativee
ﬃ
ciency value 100%. A three-step approach presentedby [11] consists in (1) using neural networks to estimatemean square deviation (MSD) of responses for all possiblecombinations of control variable levels, (2) using DEA tocompute the relative e
ﬃ
ciency of all of those combinations,selecting those that are e
ﬃ
cient, and (3) using DEA againto select among the e
ﬃ
cient combinations the one whichleads to a most robust quality loss penalization. A four stepprocedure to resolve the parameter design problem involvingmultiple responses is proposed by [12]. In this method,multiple signal-to-noise ratios are mapped into a singleperformance index called multiple response statistics (MRS)throughneurofuzzybasedmodeltoidentifytheoptimallevelsettings for each control variable. Analysis of variance isﬁnally performed to identify control variables signiﬁcant tothe process. The above methods discuss only control variablevalues used in experimental trials; therefore, it cannot ﬁndthe global optimal control variable settings considering allcontinual control variable values within the correspondingbounds.Reference [13] presented the approach for solving prob-lems with multiresponse surface using neural networks.In this approach, two neural networks are used, one fordiscovering optimal control factors vector and the other forestimating responses. Although parameter optimization canbe obtained, the e
ﬀ
ect of control variables on responses stillcannotbeachieved.Asimilarmethodbasedonartiﬁcialneu-ral network (ANN) is presented by [14]. In this method, nomatter whether the control variables are due to the level formor the real value, it can be employed. At the same time, thee
ﬀ
ect of the control variables multiple responses can be alsoobtained. Reference [15] proposed to use an artiﬁcial neuralnetwork to estimate the quantitative and qualitative responsefunctions. In the optimization phase, a genetic algorithm(GA) in conjunction with a desirability function (DF) is usedto determine the optimal control variable settings. Reference[16] presented a data mining approach to dynamic multipleresponse problem consisting of four stages which apply themethodologies of ANN, exponential desirability function(EDF), and simulated annealing (SA). First, an ANN isemployed to construct the response model of a dynamicmultiple response system by applying the experimental datato train the network. The response model is then employedto predict the corresponding quality responses by inputtingspeciﬁc control variable combinations. Second, each of the responses is evaluated by using EDF. Third, EDFs areintegrated into an overall performance index (OPI) for eval-uating a speciﬁc control variable combination. Finally, a SAis performed to obtain optimal control variable combinationwithinexperimentalregion. Anotherdynamic multiresponseapproach is presented in [17]. In this method, similar toChang’s work [16], optimal phase is performed by GA,whereas optimal phase is performed by SA. Reference [18]focused on an optimization problem that involves multiplequalitative and quantitative responses in the thin quad ﬂatpack (TQFP) modeling process. A fuzzy quality loss functionis ﬁrst employed to the qualitative responses. Neural network is then applied to estimate a nonlinear relationship betweencontrol and response variables. A GA together with EDFis applied to determine the optimal setting. Reference [19]presented the use of fuzzy-rule base reasoning and SN ratiofor the optimization of multiple responses. The idea is tocombine multiple SN ratios into a single performance index called multiple performance statistic (MPS) output, fromwhich the optimum level settings of control variables can beobtained by maximizing MPS. A similar approach to [19] foroptimizing the electrical discharge machining process withmultiple performance characteristics has been reported by [20]. In this approach, several fuzzy rules are derived basedon the performance requirement of the process. Next, theinference engine performs a fuzzy reasoning on fuzzy rulesto generate a fuzzy value. Finally, the defuzziﬁer convertsthe fuzzy value into a single performance index and theoptimal combination of the machining parameter levels canbe determined based on maximizing performance index.Reference [21] formulated MRO problem as a multiobjectivedecision making problem and followed the basic idea of Zimmermann’s [22] method. This approach ﬁrst models theresponses through multiple adaptive neurofuzzy inferencesystem (MANFIS), then according to maximin approach,overall satisfaction is obtained by comprising via the use of membership functions among all the responses. Finally, aGA is applied to search the optimal solution on the responsesurfaces modeled by MANFIS.
International Journal of Quality, Statistics, and Reliability 3With respect to the aforementioned approaches, it canbe concluded that the major focus of these methods is onthe location e
ﬀ
ect only, ignoring the dispersion e
ﬀ
ect of theresponses. In other words, they assume that the variance forthe responses is constant over the experimental space.Reference [23] presented an integrated technique forexperimental design of processes with multiple correlatedresponses, composed of three stages which (1) use expert sys-tem, designed for choosing an orthogonal array, to design anactual experiment, (2) use the Taguchi quality loss functionto present relative signiﬁcance of responses, principal com-ponent analysis (PCA) to uncorrelate responses, and gray relational analysis (GRA) to synthesize components into asingle performance measure, (3) use neural networks to con-struct the response function model and genetic algorithmsto optimize control variable design. An artiﬁcial intelligencetechnique that combines PCA, GRA, and GA with ANN anduses data collected from full factorial experimental design foroptimization of Nd:YAG laser drilling of Ni-based superalloy sheets was proposed by [24]. We note that since principalcomponents are linear combinations of srcinal responsevariables, when PCA is conducted on quality loss values,their optimization directions might be lost. Regardless of thisissue, aforementioned methods maximize the componentvalues. In other words, they do not correctly consider thelocation e
ﬀ
ect of the responses. To overcome this problem,Salmasnia et al. [25] suggested a systematic procedure viaPCA and desirability function that imposes speciﬁcationlimits on the responses to be achieved. Also, an AI tool,namely, ANFIS, is used to estimate the complicated relationbetween input (design variables) and outputs (responses),but this approach does not consider relative importance of responses in process optimization.The purpose of this study is to develop a new intelligentapproach that accommodates all of location and dispersione
ﬀ
ects besides relative importance of responses in a singleframework. It also does not depend on the type of relation-ship between response and control variables, hence makingits application in cases where these relations are unknown.Another advantage of the proposed method which is in con-trast to many other approaches considering discrete regionsto search for optimal solution searches the experimentalregion continuously. We compare the characteristics of thedi
ﬀ
erent intelligent multiresponse approaches presented inliterature to the proposed method in Table 1.(i) Type of solution problem (TSP).(ii) Aggregation approach (AA).(iii) Location e
ﬀ
ect (LE).(iv) Dispersion e
ﬀ
ect (DE).(v) Relative importance of responses (RI).(vi) Type of estimation (TE).(vii) Type of search in the experimental region (TS).The rest of the paper is organized in the following order.Section 2describestheproposedgeneralintelligentapproachfor the design of a multiple response process that uses theTaguchi signal-to-noise ratio function, ANN and GA. InSection 3, the application of the proposed model on a casestudy from literature is illustrated. Finally, conclusions arereported in Section 4.
2.TheProposedMethod
This study proposes a robust intelligent optimization pro-cedure for multiple response problems with complex rela-tionship between response and process variables based onsignal-to-noise ratio and artiﬁcial neural network. There arevarious methods to optimize multiple responses but most of them employ regression models to estimate relation functionbetween response and process variables. Furthermore, they neglect dispersion e
ﬀ
ect of responses and assume thatresponse variances are constant over the experimental space.This research proposes a new methodology which considersdispersion e
ﬀ
ect as well as location e
ﬀ
ect. In addition,the approach used to model building phase is artiﬁcialneural network (ANN), to resolve shortcomings of above-mentioned regression models, to capture nonlinearity inrelationship.To develop the methodology, we ﬁrst deﬁne the parame-ters and the variables used in the proposed approach. Then,the new methodology is described in detail.
2.1. The Parameters and Variables.
The parameters and thevariables used throughout this paper are deﬁned as follows:
X
:thedesignvector(a
p
×
1vectorwhere
p
representsthe number of controllable variables),
y
ijk
: the observed value of the
j
th response under the
i
th experimental run in the
k
th replication,
y
ij
: the sample mean of the
j
th response under the
i
th experimental run,
S
ij
: the sample standard deviation of the
j
th responseunder the
i
th experimental run,SN
ij
:thesignaltonoise(SN)ratioofthe
j
thresponseunder the
i
th experimental run,NSN
ij
: the normalized SN ration of the
j
th responseunder the
i
th experimental run,SN
min
j
: the minimum SN ratio for the
j
th response,SN
max
j
: the maximum SN ratio for the
j
th response,
w
j
: the weight of the
j
th response,
Ω
: the experimental region.
2.2. Model Development.
The proposed method consists of three phases: (i) data gathering, (ii) response estimation, and(iii) optimization. In the ﬁrst phase, by employing a properexperimental design, the signiﬁcant factors are identiﬁed andthen the required data are gathered. Next, in order to reducethe response variation and bring the response means closeto the target values, signal-to-noise ratio and normalizedvalues of them are calculated in each experimental run. The
4 International Journal of Quality, Statistics, and Reliability
Table
1: A characteristic comparison of the existing methods with the proposed approach.Method TSP TS LE DE RI TE AASu and Hsieh [8] Single response Continuous
Neural network —Ko et al. [4] Single response Continuous
Neural network —Lo and Tsao [6] Single response Discrete
Neural network —Hsieh and Tong [13] Multiple response Continuous
Neural network —Hsieh [14] Multiple response Continuous
Neural network —Liao [9] Multiple response Discrete
Neural network DEAChiang and Su [18] Multiple response Continuous
Neural network EDFAntony et al. [12] Multiple response Discrete
Neuro fuzzy MRSCheng et al. [21] Multiple response Continuous
MANFIS —Lin et al. [20] Multiple response Discrete
Fuzzy rule base MPSTarng et al. [26] Multiple response Discrete
Fuzzy rule base MPSLu and Antony [19] Multiple response Discrete
Fuzzy rule base MPSNoorossana et al. [15] Multiple response Continuous
Neural network DFChang and Chen [17] Multiple response Continuous
Neural network EDFGuti´errez and Lozano [11] Multiple response Discrete
Neural network DEAChatsirirungruang [27] Multiple response Continuous
Linear regression LFSibalija and Majstorovic [23] Multiple response Continuous
Neural network GRASalmasnia et al. [25] Multiple response Continuous
ANFIS DFThe proposed method Multiple response Continuous
Neural network WSN
response estimation phase, an estimate of responses withrespect to design variables, is calculated. To do this, artiﬁcialneural network is used as an estimator. Finally, the thirdphase consists of optimization of process using GA andﬁnding the best solution. Figure 1 illustrates the conceptualframework of the proposed method.
Phase 1
(data gathering). This phase aims to gather therequired data for training neural networks. This phaseincludes four steps that are described in the following.
Step1
(identifyingthesigniﬁcantcontrolvariables). Theﬁrststep is to identify the process control variables that may inﬂuence the response(s) of interest which can be done by experts who are familiar to the area of system considered.
Step 2
(selecting a proper design of experiment). An exper-iment can be deﬁned as a test or a set of tests in whichpurposeful changes are made on the control variables toidentify the pattern of changes that may be observed in theresponse variables.
Step 3
(calculating the SN ratio for responses in eachexperimental run). Recently [1] introduced a family of performance measures called signal-to-noise (SN) ratios.The major aim of these criteria is to simultaneously reducethe response variation and bring the response means close tothe target values. According to the Taguchi method, there arethree types of responses. The responses with a ﬁxed targetare called the nominal of the best case (NTB). In addition,the cases in which the responses have a smaller-the-bettertarget or larger-the-better target are called STB and LTB,respectively. For these cases, the SN ratios are deﬁned asfollows:(i) nominal-the-bestSN
ij
=
10log
y
2
ij
S
2
ij
, (1)(ii) larger-the-betterSN
ij
=−
10log
1
m
m
k
=
1
1
y
2
ijk
, (2)(iii) smaller-the-betterSN
ij
=−
10log
1
m
m
k
=
1
y
2
ijk
.
(3)
Step 4
(normalizing the SN ratio for responses in eachexperimental run). The normalized SN ratio values can becomputed using (4):NSN
ij
=
SN
ij
−
SN
min
j
SN
max
j
−
SN
min
j
.
(4)The idea behind the normalization of SN ration values isto convert them into dimensionless numbers. This is simply because each response has di
ﬀ
erent units of measurements.The NSN varies from a minimum of zero to a maximum of one (i.e., 0
≤
NSN
ij
≤
1).
Phase 2
(response estimation). We suggest using BP neuralnetworks to estimate the values of NSN of the di
ﬀ
erent char-acteristics for all control variable combinations. To simplify training, we recommend using a separate BP neural network
International Journal of Quality, Statistics, and Reliability 5
Phase 3: optimizationPhase 2: response estimationPhase 1: data gatheringCollect experimental data and ﬁnd
SN
ratio values
SN
ratio valuesOptimization of process using GAand ﬁnding the best solutionBest solutionConstruct the articulation of neuralnetwork and response estimationusing itResponse functionapproximation
Figure
1: Conceptual framework of the proposed method.
foreachqualitycharacteristics.Eachoftheseneuralnetworksis trained with the data of the actual experiments. Each inputpattern corresponds to a control variable combination, whilethe output is its associated SN ratio. The two main reasonsfor using neural networks for this task instead of other clas-sical estimation (e.g., regression) are their non-parametriccharacter and their generalization capability. Thus, on onehand,neuralnetworkscanapproximate,withoutmakingany a prior assumption, any existing linear or nonlinear mappingbetween the control variables and SN ratios. On the otherhand, well-trained neural networks are able to estimate, withacceptable error levels, the output values for any controlvariable combination, not just the ones experimentally tested. This phase consists of three steps as follow.
Step 1
(selection of the training and the testing data sets). Itis usually that about one-ﬁfth of the total data as the test datais randomly selected and the remaining data as the trainingdata are considered [30].
Step 2
(determine the topology of neural network). Amongthe several conventional supervised learning neural net-works are the perceptron, back propagation neural network (BPNN), learning vector quantization (LVQ), and counterpropagation network (CPN). The BPNN model is employeddue to its ability to achieve e
ﬀ
ective solutions for variousindustrial applications and neural networks power in model-ing of a nonlinear and complex relationship between systemsinput and output in this study, to modeling the relationshipbetween response and control variables.At this step, a neural network would be trained for eachresponse to estimate its relation with control variables. Thus,the number of input neurons equals the number of controlvariables; the output layer has one neuron correspondingto an NSN. The transfer function for all neurons in thehidden layer(s) is hyperbolic tangent activation function.According to deﬁnition of NSN, it can vary from zero to one;hence, the transfer function for the output neuron is tangentsigmoid function. The topology of the BP neural network with a single hidden layer-based process model used in theproposed approach is illustrated in Figure 2.
Step3
(designingthemostappropriatenetwork’sarticulationto estimate each quality characteristic). As they are selected,the number of neurons of layers of input and output
......Hidden layerOutput layerInput layer
C o n t r o l v a r i a b l e s
x
1
x
2
x
p
NSN
j
Figure
2: The topology of the BPNN with a hidden layer-basedprocess model.
based on dimensions of the input and output vectors andappropriate number of hidden layer neurons often is setby using trial and error and based on indicators such asmean square error (MSE) or root mean square error (RMSE)laboratory, di
ﬀ
erent back propagation networks will evaluatefor discovering the appropriate network. Then, for eachnetwork is compared the network output for test data andtraining data with observations from experiments. Finally, anetwork with the lowest MSE is selected as optimal network.
Phase 3
(optimization). Once the BPNN has been properly trained and validated, they can be used to estimate the SNratiosforallpossiblecontrolvariablecombinations.Thenextstep is then to optimize process via GA. A GA is selectedto perform the optimization for two important reasons. (1)Gradient-basedoptimizationmethods,likeGRG,tocalculategradient and direction of improvement require responsesurfacewhileinthismethodisusedtoestimatevaluesinsteadof calculating the response surfaces from the neural network.(2) GA is known as a powerful heuristic search approachfor optimization of complex and highly nonlinear functions.In the rest of this phase, ﬁrst a robust parameter settingapproach is suggested. Then, a brief introduction of GA andthe implementation steps of it for ﬁnding optimal solution,shown in Figure 3, are given.
2.2.1. The Suggested Parameter Tuning Approach.
Meta-heuristics have a major drawback; they need some parametertuning that is not easy to perform in a thorough manner.Those parameters are not only numerical values but may alsoinvolve the use of search components. Usually, metaheuristicdesigners tune one parameter at a time, and its optimal

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