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A hybrid of back propagation neural network and genetic algorithm

for optimization of injection molding process parameters

Fei Yin a, Huajie Mao a,⇑, Lin Hua b

a School of Materials Science and Engineering, Wuhan University of Technology, Wuhan 430070, Chinab School of Automobile Engineering, Wuhan University of Technology and Hubei Key Laboratory of Advanced Technology of Automotive Parts. Wuhan 430070, China

a r t i c l e i n f o

 Article history:

Received 9 December 2010

Accepted 29 January 2011

Available online 24 February 2011

Keywords:

A. Polymers

C. Moulding

F. Defects

a b s t r a c t

This paper presents a hybrid optimization method for optimizing the process parameters during plastic

injection molding (PIM). This proposed method combines a back propagation (BP) neural network

method with an intelligence global optimization algorithm, i.e. genetic algorithm (GA). A multi-objective

optimization model is established to optimize the process parameters during PIM on the basis of the

finite element simulation software Moldflow, Orthogonal experiment method, BP neural network as well

as Genetic algorithm. Optimization goals and design variables (process parameters during PIM) are spec-

ified by the requirement of manufacture. A BP artificial neural network model is developed to obtain the

mathematical relationship between the optimization goals and process parameters. Genetic algorithm is

applied to optimize the process parameters that would result in optimal solution of the optimization

goals. A case study of a plastic article is presented. Warpage as well as clamp force during PIM are inves-

tigated as the optimization objectives. Mold temperature, melt temperature, packing pressure, packing

time and cooling time are considered to be the design variables. The case study demonstrates that the

proposed optimization method can adjust the process parameters accurately and effectively to satisfy

the demand of real manufacture.

Ó 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Process parameters during Plastic Injection Modeling (PIM)

were mostly relied on the technicians’ personal experience in the

past. Although a better combination of process parameters can

be found with the help of the computer numerical simulation

technology nowadays, it is still hard to find the optimum combina-

tion of the processing parameters accurately and quickly. As a mul-

ti-objective and nonlinear optimization problem, process

optimization of PIM has attracted more and more attentions

worldwide. Many researches have been carried out to optimize

the process parameters during PIM.

In 2008, Gao et al. proposed an effective optimization method to

minimize the warpage in injection molding by using the Kriging

model. The warpage of a cellular phone cover was investigated,

and the warpage of the cellular phone cover was effectively de-

creased by the proposed optimization method [1]. Subsequently

they proposed an adaptive optimization method based on

Kriging-surrogate model to minimize the warpage of injection

molded parts in 2009 [2]. Deng et al. applied Taguchi’s parameter

design method, regression analysis, and the Davidon–Fletcher–

Powell method to propose an approach for determining the

optimal process parameter settings of plastic injection molding un-

der single quality characteristic considerations [3]. Zhang et al.

applied a mode-pursuing sampling (MPS) method for warpage

optimization by integrating injection molding simulation with

MPS, and by proposing a reinforced convergence criterion for the

optimization process, in an attempt to search for the optimal

process parameters of injection molding for minimizing warpage

defect [4]. Deng et al. presented an optimization method for min-

imizing the warpage of injection molded plastic parts based on

mode-pursuing sampling method and genetic algorithm (GA).

Warpage of a food tray plastic part was minimized by using the

proposed method [5]. Altan minimized the shrinkage of rectangu-

lar-shaped specimens by Taguchi, experimental design and the

analysis of variance (ANOVA) method. Neural network was also

used to predict the shrinkage of the part [6]. Hasan Kurtaran

et al. proposed an efficient minimization method of warpage on

thin shell plastic parts by integrating finite element (FE) analysis,

statistical design of experiment method, response surface method-

ology (RSM), and genetic algorithm [7]. Shen et al. minimized the

shrinkage of a plastic part by using the artificial neural network

and genetic algorithm [8]. Kurtaran et al. considered mold temper-

ature, melt temperature, packing pressure, packing time and cool-

ing time as the key process parameters during PIM and got the

optimum values of process parameters in injection molding of a

0261-3069/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved.doi:10.1016/j.matdes.2011.01.058

⇑ Corresponding author. Tel.: +86 13807171614; fax: +86 027 87168391.

E-mail address: maohj@whut.edu.cn (H. Mao).

Materials and Design 32 (2011) 3457–3464

Contents lists available at ScienceDirect

Materials and Design

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / m a t d e s

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bus ceiling lamp base to achieve minimum warpage by using neu-

ral network model and genetic algorithm [9].

All the researches cited beforehand accomplished their pur-

poses of optimizing process parameters during PIM and improved

the quality of plastic parts greatly. However, a clear mathematical

model and a systematical optimization method that can be gener-

ally used in process optimization during PIM are still required. In

addition, previous researches solved the optimization problem just

as a single-objective programming. Warpage or shrinkage of the

parts were investigated and decreased greatly. However, in real

manufacture, quality of products is only one of the most important

factors to be considered. Energy consumption as well as the pro-

duction cycle and other factors during PIM should also be taken

into consideration. Based on finite element analysis software

Moldflow, Orthogonal experiment method, Back Propagation (BP)

neural network as well as genetic algorithm, a multi-objective

mathematical optimization model as well as a hybrid of BP/GA

optimization method of injection molding process parameters are

presented systematically in this paper. In addition, a plastic part

is utilized to demonstrate the efficiency and validity of the pro-

posed optimization method. Warpage of plastic as well as the

clamp force during PIM are investigated in a multi-objective func-

tion. A series of solutions are achieved by changing the weights of 

the optimization objectives in the multi-objective optimization

function.

2. BP/GA hybrid method for optimization of injection molding 

process parameters

 2.1. The mathematical model

As a multi-objective and nonlinear optimization problem, pro-

cess optimization of PIM can be stated as follows:

Find X  ð1Þ

Minimize F ð X Þ ¼Xn

i¼1kiobji ¼

Xn

i¼1ki f ið x1; x2; . . . ; xmÞ

Subject to X min 6 X 6  X max

Xn

i¼1

ki ¼ 1

where F ( X ) denotes the multi-objective optimization function of the

process optimization; obji stands for the ith optimization goal,

i = 1, 2, . . . , n; f i represents the functional relationship between obji

and the key process parameters; ki denotes the weight of the obji;

 X = [ x1, x2, . . . , xm] stands for the matrix consists of injection model-

ing process parameters, mP 1; X max, X min stand for the upper and

lower bounds of the process parameters, respectively.

In addition, in order to eliminate the dimension of each objec-

tive, function (2) is used to preprocess each objective by normaliz-ing the inputs so that they fall in the interval [À1, 1]. The algorithm

can be expressed as follows:

 pn ¼ 2ð p À minð pÞÞ=ðmaxð pÞ À minð pÞÞ À 1 ð2Þ

where p denotes matrix of input (column) vectors; pn represents

matrix of normalized input vectors.

During the injection process, a number of defects may occur to

the moldings, such as warpage, shrinkage, sink marks as well as

weld lines and so on. These defects greatly influence the quality

of the plastic and should be controlled seriously. In the proposed

optimization model, these defects can be selected to be the optimi-

zation objectives. Meanwhile, the energy consumption of the pro-

duction and some other requirements such as the production cycle,

and production cost can also be selected to be the optimizationobjectives of the optimization model. And the process parameters

during PIM such as the mold temperature, melt temperature, pack-

ing pressure, packing time and cooling time which contribute

greatly to the cause of these considerations can be specified as de-

sign variables.

 2.2. Establishment of the objective functions based on BP neural

network

Establishment of objective functions is the key step of the opti-

mization model. However, it is very hard to express the relation-

ship between injection process parameters and optimization

objectives by explicit mathematical functions. Hence, a so-called

black-box function established by BP neural network is used in

the mathematical model.

Artificial neural network (ANN) is developed based on the

working principle of the nervous system of organism. As a kind

of information processing system, the network consists of a num-

ber of artificial neural cells. Each artificial neural cell is connected

by the connection weight just as the synapse of the nervous sys-

tem. A designed artificial neural network has the ability to obtain

the internal law of input information by learning and training pro-

cess. BP neural network is one of the most widely used and

acknowledged artificial neural networks nowadays [10–12]. Its

powerful ability of nonlinear interpolation is utilized in this paper

to obtain the relationship between process parameters and optimi-

zation goals. In this study, a multilayer BP neural network model is

designed by using the Matlab neural network toolbox. The struc-

ture of the BP neural network can be seen in Fig. 1.

Fig. 1 illustrates the structure of the BP neural network designed

in this study. It can be generally applied to the optimization of 

injection molding process parameters. The network consists of 

one input layer with m neurons standing for the process parame-

ters x1, x2, . . . , xm, respectively; z  hidden layers with several neu-

rons each and one output layer having n neurons representing

optimization goals obj1, obj2, . . . , objn, respectively.

The input of each neuron comes from the output of the neurons

contained in the preceding layer by the transition function shownas follows:

net i ¼XN  j¼0

xij x j ð3Þ

where net i is the total input of the ith neuron in the computing

layer; N  denotes the number of the neuron in the forward layer;

xij stands for the connection weight of the jth neuron in the for-

ward layer and ith neuron in the computing layer; x j represents

the output of the jth neuron in the forward layer. Output of the

ith neuron in the computing layer (out i) is generated by processing

Fig. 1. Structure of the designed BP neural network.

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the input (net i) through a transfer function f s. The function can be

described as follows:

out i ¼ f sðnet iÞ ¼1 À eÀnet i

1 þ eÀnet ið4Þ

Mathematical relationship between process parameters and

objectives can be gained by training the experimental data got

from FE simulations on the commercial software Modelflow plat-form. During training process, the connection weights are calcu-

lated to minimize the error between the predictive data and

experimental data. The objective function contained in the trained

BP neural network can be expressed approximatively as follows:

obji ¼ f ið X Þ ¼ f lX

w z þ1 f s Á Á Á f s

Xw2 f 

sX

w1 X 

ð5Þ

where obji stands for the ith optimization objective; X = [ x1,

 x2, . . . , xm] denotes the matrix consists of the values of process

parameters; f l is the liner transfer function between hidden layer

 z  and output layer; f s is the transfer function between input layer

and hidden layer 1, as well as hidden layer i and hidden layer

i + 1, i = 1, 2, . . . , z À 1; w1, w2, . . . , w z +1 represent the connection

weights between input layer and hidden layer 1, hidden layer 1

and hidden layer 2. . .

, hidden layer z and output layer, respectively.

 2.3. Solution of the mathematic model

An intelligence global optimization algorithm, i.e. genetic algo-

rithm, is employed to solve the mathematical model established in

this paper. Genetic algorithm simulates biological evaluation pro-

cess: Darwin’s ‘‘survival of the fittest’’ and has been widely used

in engineer application [13,14]. At the beginning of the solution,

a set of potential solutions are randomly selected as the initial

chromosomes. The entire set of these chromosomes constitutes a

population. Then on the basis of the ‘‘survival of the fittest’’ theory,

new generations are generated through copy, crossover or muta-

tion method. The new chromosomes are then evaluated via a cer-

tain fitness criteria and the best ones are kept while the others are

discarded. After several generations, the fitness of the chromo-

somes will be increased. And the chromosome having the best

fitness is taken as the best solution of the problem. Fig. 2 illustrates

the solution procedure of the GA.

The entire technical line of the hybrid BP/GA process optimiza-

tion method for PIM can be seen in Fig. 3.

3. Case study 

In this paper, a plastic part is utilized to demonstrate the

efficiency and validity of the proposed optimization method. As

one of the most common and prominent defects of plastic, warpage

affects both the usage and the appearance of the part and is consid-

ered to be one of the most critical considerations for the produc-

tion of a quality plastic part. Hence, warpage minimization is

specified to be one of the optimization objectives in this paper.

Besides, capacity of the equipment and energy consumption are

considered in this paper.

Ozcelik et al. stated that packing pressure is the most influential

parameter on the warpage of PC/ABS material [15]. In addition,

Huang et al. also pointed out that the packing pressure has the

greatest influence on the warpage, and with the increase of the

packing pressure; the warpage of plastic can be decreased [16].Namely, warpage of plastic can be greatly decreased by increasing

packing pressure during PIM. However, considering the capacity of 

the equipment and cost of production, packing pressure can not be

increased without limit. Hence, the maximum clamp force greatly

determined by packing pressure is specified to be the other optimi-

zation objective. Mold temperature, melt temperature, packing

pressure, packing time as well as the cooling time are considered

to be design variables.

Fig. 2. Solution of the GA. Fig. 3. Technical line of hybrid BP/GA process optimization method for PIM.

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The commercial injection molding Computer-Aided Engineering

(CAE) software Moldflow is employed to simulate the injection

molding process. Warpage defects as well as the maximum clamp

force can be retrieved from the simulation results.

 3.1. Problem description

Geometry of the plastic part utilized in this study is shown in

Fig. 4a. Its width, length and maximum part thickness are

200 mm, 200 mm and 2 mm, respectively. The material of the part

is PP. And the material mode of PP with the trade name of BP

Amoco 1046 and manufactured by BP Chemicals which is from

the library of the moldflow software database was employed as

the material of the part during simulations. The detailed material

properties can be seen in Table 1. Fig. 4b shows the CAE analysis

model of the plastic established under Moldflow environment.

The part is meshed in fusion mesh method and the meshed part

includes 7696 elements. Mesh condition as well as the filling sys-

tem and cooling system can also be seen in Fig. 4b.

Five key process parameters are selected as the design variables

in the mathematical model. These are mold temperature (T mold),

melt temperature (T melt ), packing pressure (P  p), packing time (t  p)

as well as the cooling time (t c ). The upper and lower bounds of 

the process parameters are set based on the recommended values

provided by Moldflow software, and the ranges of the process

parameters can be seen in Table 2.The mathematical model of the multi-objective optimization

problem can be formulated as follows:

Find X ¼ ½T melt ; T mold;P  p; t  p; t c � ð6Þ

Minimize k1 f nðW Þ þ k2 f 

nðF C Þ

Subject to : 30 6 T mold 6 60 220 6 T melt 6 260 50

6 P  p 6 120 5 6 t  p 6 15 5 6 t c 6 20

Fig. 4. (a) Geometry and (b) FE model of the plastic cover.

 Table 1

Material properties of PP.

Material properties Performance

Melt density (g/m3) 0.7751

Solid density (g/m3) 0.92889

Eject temperature (°C) 93

Maximum shear stress (MPa) 0.26Maximum shear rate (sÀ1) 24000

Thermal conductivity (W/m°C) 0.15

Elastic module (MPa) 1340

Poisson ratio 0.392

 Table 2

Ranges of the process parameters.

Process parameters Ranges

Mold temperature (°C) 30–60

Melt temperature (°C) 220–260

Packing pressure (% injection pressure) 50–120

Packing time (s) 5–15

Cooling time (s) 5–20

Fig. 5. The structure of the BP neural network used in this case.

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where W  denotes the warpage of the part; F C  represents the maxi-

mum clamp force during the injection molding process; f n repre-

sents the normalized function as shown in function (2); k1, k2

represent the weight of warpage and clamp force, respectively.

 3.2. Implementation of the proposed BP/GA optimization procedure

 3.2.1. Objective functions founded by BP neural network

A 5-9-9-2 BP network is used to gain the mathematical relation-

ship between optimization objectives and process parameters. The

structure of the designed network can be seen in Fig. 5.

The function of the designed neural network is to predict the

warpage of the part as well as the clamp force during PIM under

a specified combination of the process parameters. In order to

make the designed network acquiring the ability of prediction, it

should be trained by a number of samples first. To save the com-

puting resource and improve the coverage of the samples, orthog-

onal experiment method is employed to conduct the FE

simulations under Moldflow environment. Sixteen samples de-

signed by the orthogonal experiment method as well as other 44

samples randomly generated by computer, 60 samples in sum,

are used to train the designed network. The distribution of the

samples can be seen in Fig. 6.

During training process, the learn rate of the network is set as

0.03 and the mean square error of the training data is set as

0.0001. The training process takes about half an hour on HP per-

sonal workstation. Fig. 7 shows the training process of the network,

it can be seen from Fig. 7 that with the updating of the connection

weights, the mean square error between the network prediction

data and training data declines gradually and converges to

0.0001 interminably within 900,000 epochs.

Six groupsof processparametersnot used in the training process

are used to test theaccuracy and reliabilityof thepredictivesystem.

It can be seen from Fig. 8 that the predictive values are in good

agreement with the experimental values. The predictive error is

less than 5% on average. Hence, the trained network can be used

as the surrogate of the objective functionin the optimization model.

 3.2.2. Solution of GA

In the GA optimization process, the operation parameters

needed to be specified in GA are adapted. The population size,

the crossover rate, the mutation rate and the generation size are

set as 100, 0.5, 0.1 and 60, respectively. Four groups of weights dur-

ing optimization are given to the objective function:

Case 1: k1 ¼ 1 k2 ¼ 0.

Case 2: k1 ¼ 0:8 k2 ¼ 0:2.

Fig. 6. (a) Warpage and (b) Clamp force distribution of the samples.

Fig. 7. Training process of the 5-9-9-2 BP neural network.

Fig. 8. Testing results of the BP neural network.

 Table 3

Process parameters optimized by the proposed BP/GA method under different

weights of optimization objectives.

Process parameters Case 1 Case 2 Case 3 Case 4

Mold temperature (°C) 50.911 36.419 54.971 34.149

Melt temperature (°C) 226.656 232.13 241.53 252.58

Packing pressure (% injection

pressure)

116.116 100.36 71.281 53.558

Packing time (s) 12.361 10.402 11.835 10.457

Cooling time (s) 8.065 5 16.471 16.059

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Case 3: k1 ¼ 0:5 k2 ¼ 0:5.

Case 4: k1 ¼ 0:2 k2 ¼ 0:8.

It takes about half an hour of each solution on HP workstation

platform. Process parameters optimized by the proposed optimiza-tion method can be seen in Table 3.

4. Results and discussion

Process parameters are set as recorded in Table 3 on the

Moldflow platform, warpage results and clamp force results of 

the optimized process parameters can be seen in Fig. 9. In addition,to validate and compare the optimization results, we also obtain

Fig. 9. Warpage and clamp force analysis results of case 1–4.

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the warpage result as well as the clamp force result of the part by

employing the Moldflow recommended values for the process

parameters in the FE simulation. The recommended process

parameters are set as follows:

T mold ¼ 60; T melt  ¼ 240; P  p ¼ 100; t  p ¼ 8; t c  ¼ 15

The warpage and clamp force analysis results are 3.307 mm,

63.63 ton, respectively. And they can be seen in Fig. 10.In this study, to illustrate the efficiency and flexibility of the

proposed BP/GA optimization method, different weights of optimi-

zation objectives are specified to the multi-objective optimization

function. Fig. 9a–d shows the optimized results of case 1, 2, 3 and

4, respectively. And the comparison between the optimized results

and the recommended analysis results can be seen in Table 4

clearly.

Different optimized results are obtained by setting different

weights to the optimization objectives. In case 1, warpage is con-

sidered to be the only optimization objective. It can be seen from

Fig. 9a-1 and Table 4 that the optimized warpage value is

1.092 mm, which has been reduced by 66.9% comparing with the

warpage result, 3.307 mm, obtained by using Moldflow recom-

mended process parameters. Meanwhile, because the clamp forceis not taken into consideration during optimization, packing pres-

sure is just limited by the upper bound of packing pressure speci-

fied in the mathematical model. Hence, it can be increased without

limit to decrease the warpage of the part. Results show that the

optimized packing pressure of case 1 recorded in Table 3 is

116.116 MPa, which is very close to the upper bound of packing

pressure 120 MPa. The clamp force shown in Fig. 9a-2 is 79.01

ton, which has been increased by 24.1% comparing with the recom-

mended analysis result 63.63 ton.

In case 2, warpage is specified to be the main optimization

objective. Meanwhile, the clamp force during PIM is taken into

consideration. It can be seen in Fig. 9b-1 that the optimized war-

page value is 1.286 mm, which has been reduced by 61.1%, fewer

than 66.9% of case 1, comparing with the warpage result obtainedby using Moldflow recommended process parameters. At the same

time, the clamp force shown in Fig. 9b-2 is only increased slightly

comparing to the recommended analysis result.

In case 3, warpage and clamp force are specified the same

weight during optimization. Analysis results shown in Fig. 9c-1, 2

illustrate that warpage of the part as well as the clamp force during

PIM are both reduced and comparing with the analysis results ob-

tained by using Moldflow recommended process parameters, theyare decreased by 54.2% and 33.6%, respectively.

In case 4, the clamp force during PIM is specified to be the main

optimization objective. Results show that the clamp force during

PIM is decreased greatly, that is 55.6% comparing to the recom-

mended analysis result. At the same time, the warpage of the part

is also decreased.

In addition, it can be seen from Table 4 that all the cases have

decreased the warpage of the part. And with the decrease of the

weight of warpage in the multi-objective optimization function

from case 1 to case 4, the decrement of warpage is declined grad-

ually. Meanwhile, clamp force is increased in case 1 and case 2, be-

cause higher packing pressure is needed to decrease the warpage

of the part, which shows a good agreement with the conclusions

of the cited literatures [15,16]. However, with the increase of the

weight of clamp force, clamp force plays a more and more impor-

tant role in the multi-objective function and is limited more and

more seriously. That is why increment of clamp force in case 2,

6.1%, is fewer than that in case 1, 24.1%. In case 3 and case 4, the

weight of clamp force is large enough to impact or dominate the

optimization. Hence, the clamp force in case 3 and 4 are decreased

instead of increased. Warpage is decreased just by adjusting other

process parameters, such as packing time and cooling time, result-

ing in a longer production cycle.

Comparing with the researches of the cited literatures [1–6], the

proposed BP/GA optimization method in this investigation takes

both the warpage of the plastic part and energy consumption dur-

ing PIM into consideration. In addition, the proposed optimization

method has the advantage of flexibility. The optimization objec-

tives can be optimized in different degrees by specifying differentcombination of the weights. And each solution has its advantages

and disadvantages. Case 1 extremely decreased the warpage of 

the part, while its clamp force is the largest, which means process

of case 1 will consume more energy than other cases; cases 2, 3

and 4 take both warpage and clamp force into consideration, while

the ratio of the weights is different. Hence, the warpage and the en-

ergy consumption during PIM are optimized in different degree.

And a fittest solution can be selected by the demands and objective

factors of real manufacture.

5. Conclusions

In this study, a hybrid of BP/GA optimization method of injec-tion molding process parameters is presented systematically on

Fig. 10. (a) Warpage and (b) clamp force results by using Moldflow recommended process parameters.

 Table 4

Comparison between the optimized analysis results and the recommended analysis

results.

Analysis results Rate of change (%)

Warpage

(mm)

Clamp force

(Ton)

Warpage Clamp

force

Recommended 3.307 63.63 – –Case 1 1.092 79.01 À66.9 +24.1

Case 2 1.286 67.51 À61.1 +6.1

Case 3 1.513 42.28 À54.2 À33.6

Case 4 1.765 28.26 À46.6 À55.6

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the basis of finite element analysis software Moldflow, Orthogonal

experiment method, BP neural network and genetic algorithm. The

mathematical model and technique line for optimization of process

parameters during PIM are established clearly in this paper.

As an application, a plastic part is employed in this paper.

Warpage as well as the clamp force during PIM are chosen to be

the optimization objectives. Mold temperature, melt temperature,

packing pressure, packing time as well as the cooling time are con-

sidered to be design variables. A series of combination of weights

of optimization objectives are specified to the multi-objective opti-

mization model. After implementing the proposed BP/GA method,

warpage as well as the clamp force of the part is optimized in dif-

ferent degrees comparing with the warpage result obtained by

using Moldflow recommended process parameters. The fittest

combination of process parameters can be selected by the require-

ments of the real manufacture.

For its efficiency and flexibility, the proposed BP/GA optimiza-

tion method can be used generally to optimize defects of plastic

as well as other considerations such as production cycle, cost

and so on during PIM. In addition, the crystallization tempera-

ture of the injected materials plays an important role in shrink-

age and warpage of the plastic part during PIM, hence, it can be

taken into consideration during the optimization for PIM in the

future.

 Acknowledgment

The work was supported by a grant from National Science Fund

for Distinguished Young Scholars (No. 50725217). The supports are

gratefully acknowledged.

References

[1] Gao YH, Wang XC. An effective warpage optimization method in injection

molding based on the Kriging model. Int J Adv Manuf Technol 2008;37:

953–60.

[2] Gao YH, Wang XC. Surrogate-based process optimization for reducing warpage

in injection molding. J Mater Process Technol 2009;209:1302–9.

[3] Deng WJ, Chen CT, Sun CH, Chen WC, Chen CP. An effective approach for

process parameter optimization in injection molding of plastic housing

components. Polym-Plast Technol Eng 2008;47:910–9.

[4] Zhang Y, Deng YM, Sun BS. Injection molding warpage optimization based on a

mode-pursuing sampling method. Polym-Plast Technol Eng 2009;48:767–74.

[5] Deng YM, Zhang Y, Lam YC. A hybrid of mode-pursuing sampling method and

genetic algorithm for minimization of injection molding warpage. Mater Des

2010;31:2118–23.

[6] Altan M. Reducing shrinkage in injection moldings viathe Taguchi, ANOVAandneural network methods. Mater Des 2010;31:599–604.

[7] Kurtaran H, Erzurumlu T. Efficient warpage optimization of thin shell plastic

parts using response surface methodology and genetic algorithm. Int J Adv

Manuf Technol 2006;27:468–72.

[8] Shen CY, Wang LX, Li Q. Optimization of injection molding process parameters

using combination of artificial neural network and genetic algorithmmethod. J

Mater Process Technol 2007;183:412–8.

[9] Kurtaran H, Ozcelik B, Erzurumlu T. Warpage optimization of a bus ceiling

lamp base using neural network model and genetic algorithm. J Mater Process

Technol 2005;169:314–9.

[10] Baseri H, Rabiee SM, Moztarzadeh F, Solati-Hashjin M. Mechanical strength

and setting times estimation of hydroxyapatite cement by using neural

network. Mater Des 2010;31:2585–91.

[11] Dehghani K, Nekahi A. Artificial neural network to predict the effect of 

thermomechanical treatments on bake hardenability of low carbon steels.

Mater Des 2010;31:2224–9.

[12] YuWX,Li MQ, Luo J, Su SS, LiCQ. Predictionof the mechanicalproperties of the

post-forged Ti–6Al–4V alloy using fuzzy neural network. Mater Des

2010;31:3282–8.

[13] Fu ZM, Mo JH, Chen L, Chen W. Using genetic algorithm-back propagation

neural network prediction and finite-element model simulation to optimize

the process of multiple-step incremental air-bending forming of sheet metal.

Mater Des 2010;31:267–77.

[14] Yang Z, Gu XS, Liang XY, Ling LC. Genetic algorithm-least squares support

vector regression based predicting and optimizing model on carbon fiber

composite integrated conductivity. Mater Des 2010;31:1042–9.

[15] Ozcelik B, Sonat I. Warpage and structural analysis of thin shell plastic in the

plastic injection molding. Mater Des 2009;30:367–75.

[16] Huang MC, Tai CC. The effective factors in thewarpage problem of an injection

molded part with a thin shell feature. J Mater Process Technol 2001;110:1–9.

3464 F. Yin et al. / Materials and Design 32 (2011) 3457–3464