a hybrid algorithm to

ORIGINAL ARTICLE

A hybrid algorithm to optimize cutting parameterfor machining GFRP composite using alumina cutting tools

M. Adam Khan & A. Senthil Kumar & A. Poomari

Received: 21 January 2011 /Accepted: 25 July 2011# Springer-Verlag London Limited 2011

Abstract In this paper, two different evolutionaryalgorithm-based neural network models were developed tooptimise the unit production cost. The hybrid neuralnetwork models are, namely, genetic algorithm-based neuralnetwork (GA-NN) model and particle swarm optimization-based neural network (PSO-NN) model. These hybridneural network models were used to find the optimalcutting conditions of Ti[C,N] mixed alumina-based ceramiccutting tool (CC650) and SiC whisker-reinforced alumina-based ceramic cutting tool (CC670) on machining glassfibre-reinforced plastic (GFRP) composite. The objectiveconsidered was the minimization of unit production costsubjected to various machine constraints. An orthogonaldesign and analysis of variance was employed to determinethe effective cutting parameters on the tool life. Neuralnetwork helps obtain a fairly accurate prediction, evenwhen enough and adequate information is not available.The GA-NN and PSO-NN models were compared for theirperformance. Optimal cutting conditions obtained with thePSO-NN model are the best possible compromise com-pared with the GA-NN model during machining GFRPcomposite using alumina cutting tool. This model alsoproved that neural networks are capable of reducinguncertainties related to the optimization and estimation ofunit production cost.

Keywords GFRP composite . Ceramic . Hybrid algorithm .

GA . PSO . Neural network

AbbreviationsGA-NN Genetic algorithm-based neural networkPSO-NN Particle swarm optimization-based neural

networkBP Back-propagationL/D Length-to-diameter ratioS/N Signal-to-noise ratioLB Lower is betterNB Nominal is bestHB Higher is betteryi Response of cutting performance resultsMLP Multilayer perceptronLM Levenberg–MarquardtTANSIG Tangent sigmoidMAE Mean absolute errore j Error signal at the output neuron jy j Output of neuronξ (n) Instantaneous error energyξav Average squared error energyCO Operating costCNO Non-operating costCR Tool replacement costCT Tool costUC Unit production costTs Setup timeTi Idle timeTc Tool change timeTm Machining timeTL Tool lifeKO Sum of overhead and labour costKT Cutting edge costXA Actual cutting parameterXU Cutting parameter—upper boundXL Cutting parameter—lower boundf(x) Fitness function

M. A. Khan (*) :A. S. Kumar :A. PoomariDepartment of Mechanical Engineering,Sethu Institute of Technology,Virudhunagar Dist.,Tamil Nadu, Indiae-mail: [email protected]

Int J Adv Manuf TechnolDOI 10.1007/s00170-011-3553-6

g(x) Minimum of cost value (objective function)Pm Mutation probabilityC1, C2 Learning factorsw Weightage factorVid Particle velocityPid Best location about the particlesPgd Globally best particleVmax Particle maximum velocityMRR Material removal rate

1 Introduction

In any machining operation, it is an important task to selectcutting parameters for achieving high-quality cutting perfor-mance [27]. Usually, the desired cutting parameters aredetermined based on the experience or by the use of standardhandbooks. Intelligent selection of cutting parameter achievessubstantial savings in terms of money and time if it integratesan efficient automated process planning. Optimum selectionof cutting conditions importantly contributes to the increaseof productivity and the reduction of costs [32].

In the olden days, analytical-direct space search procedureswere followed to optimise the machining parameters. Theywere dynamic programming, geometric programming, stochas-tic programming, etc. These techniques are not adequate tosearch the wide spectrum of the problem domain. Often, theyare also not robust because the numerous constraints consideredmake the search complex [3, 18]. Even though they werepreviously used for many complex problems, the search isvery complicated [15]. There are other suitable methods, suchas hill climbing, tabu search, simulated annealing and geneticalgorithm. The solutions found by these methods are oftenconsidered as near-optimal solutions [28].

Genetic algorithm (GA) exploits the idea of survival offitness and an interbreeding population and creates a noveland innovative strategy [7]. Goldberg [5] describes that GAis the search algorithm based on the mechanics of naturalselection and genetics. GAs are known as very efficientheuristic algorithms, surmounting problems of traditionaloptimization algorithms, and are applied to many engineer-ing problems. GA starts with an initial set of randomsolution made of chromosomes and produces more numberof solutions with the help of GA operators in a chromosomeevolving method [4, 18]. GA provides a near-optimalsolution for a complex problem having a large number ofvariables and constraints [26].

It contrast to traditional optimization algorithms, non-traditional methods such as particle swarm optimization(PSO), artificial bee colony, ant colony optimization andsimulated annealing were used to compare the convergencerate of the algorithm. One among these algorithms, PSO,

accomplishes the same goal as GA optimization in a newand faster way. PSO possesses the features of straightfor-ward logic, simple realization and underlying intelligence[30]. Particle swarm optimization has been successfullyapplied to some manufacturing processes such as pulsedlaser micromachining, electrochemical machining, frictionwelding, boring, milling, etc., by various researchers [16,19]. PSO and GA both work with a population of solutions;combining the searching abilities of both methods seems tobe a very good approach.

Researchers have attempted to compare the application andperformance of GA and PSO techniques [15]. Thesetechniques are inspired by nature and proved themselves tobe effective solutions to optimization problems. Moreover,PSO utilizes a single way of information flow without thecomplex genetic operators of the GA, such as crossover andmutation; more differently, PSO adopts the current optimalsolution as the mechanism for renewing the whole searchprocess, in contrast to the GA, such that the PSO has theability to quickly converge to a reasonably good solution [9].From the point of parameter evolution, PSO is better thanGA. The convergence rate of the PSO algorithm is very lessthan that of GA, and it requires only a small number ofiterations for convergence of optimal solution. However,both PSO and GA consider more expanded ranges ofsolution space than other existing algorithms [6].

Artificial neural networks (ANN) are currently beingused in a variety of applications with great success [1].Neural network models play a major role in the predictionof response for linear or nonlinear problems. Experimentaldata required to model neural network are very few whencompared with the other models [29]. Neural networkmodels are free from the expression and equation foroptimization [24]. Neural network learns the problem byexample like the human brain. There are several learningalgorithms in neural network. Back-propagation (BP) is oneof the best and uses the unique learning principle which iscalled the delta rule [2, 25]. BP algorithm is used tocalculate the error gradient of neural network with respectto modified weight. The main principle behind the BPalgorithm is the minimization of errors in neural networkoutput. Neural-based optimization algorithms can beemployed to predict results with higher precision [3, 31].These neural-based optimization algorithms ensure asimple, faster and efficient optimisation of all turningparameters. Neural network models are also capable ofrepresenting the performance of cutting parameters withproper training of data.

One of the most promising techniques is the adaptation ofnetwork training with evolutionary algorithms (EA). Themerging of EA and ANN will gain adaptability to dynamicenvironment and will lead to significantly better intelligentsystems than relying on ANN, PSO, or GA. Very reclusive

Int J Adv Manuf Technol

articles were published in a way adapting network modeltrained with EA on machining studies. The design of experi-ments, especially analysis of variance (ANOVA), is widelyused to identify the critical process parameters which can beadapted to the optimization techniques [13, 14].

In this paper, a GA-based neural network (GA-NN) modeland a PSO-based neural network (PSO-NN) model wereframed to optimise the unit production cost of the turningprocess. The optimization was carried out for Ti[C,N] mixedalumina cutting tool and SiC whisker-reinforced aluminacutting tool whilst machining glass fibre-reinforced plastic(GFRP) composite. This alumina-based ceramic cutting toolis one of the best attractive cutting tools for hard machiningprocess, and they produce good surface finish [11, 21, 22].Very few articles have been published to compare GA-NNand PSO-NN models and the utilization of the abovetechniques for the optimization of alumina cutting tools,whilst machining GFRP is rarely available in the literature.Hence, an attempt is made to optimise the alumina cuttingtools on machining GFRP, and the optimization techniquesGA-NN and PSO-NN are compared for their performance.

2 Experimental work

2.1 GFRP composite

The GFRP composite rod with a diameter of 65 mm and alength of 400 mm, having a L/D ratio 6.15 [12], was preparedin our laboratory using filament winding process. Figure 1shows the SEM micrograph of the GFRP composite preparedusing the filament winding process. From the SEM picture, itcan be noted that the glass fibres are strongly bonded andhomogeneously impregnated with polyester matrix material.

2.2 Machining study

Machining studies were carried out to machine the GFRPcomposite material in precision lathe using Ti[C,N] mixed

alumina cutting tool (CC650) and SiC whisker-reinforcedalumina cutting tool (CC670). Machining studies wereperformed by varying the cutting speed, the feed rate andthe depth of cut. The flank wear and the surface finish ofthe machined GFRP composite were observed. Flank wearis measured using Metzer Toolmakers microscope, andsurface roughness was measured using TR200 surfaceprofile meter.

3 Solution methodology

3.1 Contribution of cutting parameters

The main objective of this paper was to minimise the unitproduction cost of the machining process. Selection of cuttingparameter plays a major role with different machine con-straints to optimise the unit production cost. There are manymachining parameters, such as cutting speed, feed rate, depthof cut, tool geometry, cutting tool temperature, lubricationsystem, cutting tool treatment, etc. In consideration of thesecutting parameters, the development of a mathematical modelor to fix an objective function to predict the response ofcutting operation will be very difficult and complex. To avoidsuch a situation, an ANOVA-based design of experimentmodel was developed to check the contribution of the cuttingparameters. According to the Taguchi quality design concept,an L9 orthogonal array was chosen as a set of experimentalwork to predict the contribution of cutting parameters andpresented in Table 1. The levels of cutting parameters aregiven in Table 2.

ANOVA was used to investigate the response of thecutting parameters; the responses of the cutting parameterare further transformed into a signal-to-noise (S/N) ratio.There are several S/N ratios available depending on thetype of characteristics, namely, lower is better (LB), NB orHB. Each performance characteristic may belong to adifferent category in the analysis of the S/N ratio [12, 17].

Fig. 1 SEM micrograph of the GFRP composite material

Table 1 Experimental layout using L9 orthogonal array

Exp no. Cutting velocity(m/min)

Feed rate(mm/rev)

DOC(mm)

1 1 1 1

2 1 2 2

3 1 3 3

4 2 1 3

5 2 2 1

6 2 3 2

7 3 1 2

8 3 2 3

9 3 3 1


The lower surface roughness and the lower tool wear givean apparently better cutting performance. Therefore, the LBwas selected in this study for both the tool wear and surfaceroughness. The response of cutting performance results yiof n repeated number is:

S=NLB ¼ �10 log1

n

Xni¼1

y2i

!

The S/N ratios of the tool wear and the surfaceroughness were calculated for each level of the cuttingparameters. These findings are consistent with the experi-mental results. From the ANOVA, the contributions ofcutting parameters are plotted in Figs. 2 and 3 for flankwear (in millimetres) and surface roughness (in micro-metres). From these figures, the contribution of the cuttingspeed and the feed rate is much higher than that of thedepth of cut. It shows that the cutting speed and the feedrate play major role on tool wear and surface roughness.The total contribution of cutting speed and feed rate is morethan 86% and 91% for flank wear and surface roughness,respectively.

3.2 Problem formulation of hybrid algorithm

For the optimization process, a multilayer perceptron(MLP) algorithm was adapted with the cutting speed andfeed rate in the input layer having two hidden layers of nineneurons in each and the production cost as a single real-

time output. LM algorithms have been proposed with thehyperbolic tangent sigmoid (TANSIG) layers transferfunction to train and to test the MLP algorithm. Thealgorithm is hierarchically connected and the networkdirected with varying numbers of the hidden layers withthe help of the back-propagation of fully connectedprocessing elements. The inputs from the continuousdomain are mapped to outputs normalized to a range of0–1.0. The basic goal in training any neural network is tominimise the overall MAE of the network. Training ofANN was made with the experimentally calculated cuttingdata. Expected training nodes in input layer and inputs inevery other node are the sum of the weighted outputs of theprevious layer. Each node is brought as an active casedepending on the input of one node, the activation functionand the threshold value of the node. The error signals at theoutput of neuron j at iteration n (i.e. presentation of the nthtraining examples) are defined by

ejðnÞ ¼ djðnÞ � yjðnÞwhere the neuron j is an output node and γj is the output ofneuron which is calculated by the function yj ¼ 1

1þexp �vjð Þ, withthe locally induced field vj (i.e. weighted sum of all synapticinput plus the bias) of neuron j. This is commonly used,called as sigmoidal nonlinearity defined logistic function.

Correspondingly, the instantaneous value ξ(n) of the totalerror energy is obtained by summing 1

2 e2j ðnÞ over all

neurons in the output layer; these are the only ‘visible’neurons for which error signals can be calculated directly.We may thus write it as

xðnÞ ¼ 1

2

Xj2c

e2j ðnÞ

where set C includes all the neurons in the output layer ofthe network. Let N denote the total number of patternscontained in the training set. The average squared errorenergy is obtained by summing ξ(n) over all n and then

51.1580.15

36.10

4.247.37 93.575.5

39.12

0

10

20

30

40

50

60

70

80

076CC+PRFG056CC+PRFGCutting Parameter

Con

trib

utio

n %

Cutting Speed (m/min) Feed rate (mm/rev) DOC (mm) Error (%)

Fig. 2 Contributions of cutting parameters for flank wear

Table 2 Level of cutting parameters for machining GFRP compositematerial

Cutting parameter Level I Level II Level III

Cutting velocity (m/min) 150 190 300

Feed (mm/rev) 0.06 0.08 0.12

DOC (mm) 0.1 0.2 0.3

46.54 44.7449.33 47.74

1.60 3.132.53 4.39

0

10

20

30

40

50

60

70

076CC+PRFG056CC+PRFGCutting Parameter

Con

trib

utio

n %

Cutting Speed (m/min) Feed rate (mm/rev) DOC (mm) Error (%)

Fig. 3 Contributions of the cutting parameters to surface roughness


normalizing with respect to the set size N, as shown by

xav ¼1

N

XNj�1

xðnÞ

The instantaneous energy error ξ(n), and therefore theaverage error energy ξav, is a function of all the freeparameters of the network. The arithmetic average of theseindividual weight changes over the training set is thereforean estimate of the true change that would result frommodifying the weights based on minimising the objectivefunction. The main objective function of the problem wasframed with the basic elements of cost with respect to themachining parameters; the mathematical model was pro-posed in a previous research work [20]. This cost functionis divided into four basic cost elements: operating cost(CO), non-operating cost (CNO), tool replacement cost (CR)and tool cost (CT). The cost function can be expressed as:

UC ¼ COþ CNOþ CRþ CT

UC ¼ Ko � Tm þ Ko � Ti þ Tsð Þ þ Ko � TC � Tm=TLð Þ þ Kt � Tm=TLð Þ

In continuation, details of the elements of cost and theparameter bounds are given in Tables 3 and 4.

In this approach, the solution space consists of all thedifferent combinations of hidden layers and hidden neu-rons, i.e. of all the architecture. In this research paper, theGA and PSO are employed for such a complex problem tosearch the solution space for the ‘best’ architecture, where‘best’ is defined according to predefined machining con-ditions. Practically, it means that the solution space isdivided into subsets that are evaluated in order to find thebest solution using the basic idea of the GA and PSOconcepts. The mathematical model of these algorithmsdictates the coding of solution in binary strings calledchromosomes, the use of the objective function to evaluatehow good the chromosomes (goodness of fit) are.

3.2.1 Genetic algorithm-based neural network

Goldberg [5] described that genetic algorithms are searchalgorithms based on the mechanics of natural selection

and natural genetics. The GA technique starts with aninitial set of random solution called ‘initial population’which is made of group of chromosomes. Each chromo-some in the population is real coded and contains theactual values of cutting conditions fed to the neuralnetwork model to obtain the accurate fitness value. Avery small and a very large size of population leads topremature and slow rates of convergence of GA. There-fore, a population size of 20 chromosomes is selected forthe present algorithm. The fitness value for each chromo-some in the initial population is estimated using the fitnessfunction f(x). The chromosomes with large fitness valuesin the population are selected by the reproduction operatorfor a second generation [23]. Parents are recombined toproduce offspring. All offspring are mutated with a certainprobability. The fitness of the offspring is then computed.The offspring are inserted into the population replacing theparents, producing a new generation. If the optimizationcriteria are not met, the creation of a new generation starts.Individuals are selected according to their fitness for theproduction of offspring. This cycle is performed until theoptimization criteria are reached. Detailed procedure forthe GA concept was explained in a previously publishedarticle [20].

3.2.2 PSO-based neural network

The particle swarm optimization algorithm is a relativelynew computational intelligence technique to simulate a sortof social behaviour [8, 30]. In PSO, a point in the problemspace is called a particle, which is initialized with a randomposition and search velocity. The particles, which arepotential solutions in the PSO algorithm, fly around in themultidimensional search space and the positions of indi-

Details Notation Unit Value

Setup time Ts min 0.6

Idle time Ti min 0.2

Tool change time Tc min 0.5

Volume of material removal (GFRP) V mm3 65111

Sum of overhead and labour cost KO US $/min 0.08

Cutting edge cost for CC650 KT(CC650) US $/cutting edge 8

Cutting edge cost for CC670 KT(CC670) US $/cutting edge 12

Table 3 Details of costs, timeand volume of material removal

Table 4 Parameter bounds for optimization algorithm

Parameters Unit Lower bound Upper bound

Cutting velocity m/min 150 500

Feed rate mm/rev 0.06 0.12

Depth of cut mm – 0.2


vidual particles are adjusted according to its previous bestposition, and the neighbourhood best or the global best.Since all particles in PSO are kept as members of thepopulation throughout the course of the searching process,PSO is the only evolutionary algorithm that does notimplement survival of the fittest. PSO has been successfullyshown to optimise a wide range of continuous optimizationproblems. Similar to the GA-NN algorithm, individualparticle positions from the PSO are fed to the neuralnetwork model to obtain the accurate best solution,continued to the number of iterations. The global best orlocal best solution in PSO is only reported for the otherparticles in a swarm. Therefore, evolution only looks for thebest solution and the swarm tends to converge to the bestsolution quickly and efficiently, thus increasing the proba-bility of global convergence. After a certain number ofgenerations, the algorithm terminates.

3.3 Steps in hybrid model developed for optimization

A flowchart of a hybrid GA-based neural network (GA-NN algorithm) and PSO-based neural network (PSO-NNalgorithm) developed to optimise the cutting parametersis shown in Fig. 4a, b; the steps involved in the processare as follows.

1. Start: Random initial population is generated contain-ing cutting information such as speed and feed rate asbinary digits. The length of string assigned for eachparameter is 10 bits.

2. Decoding and actual cutting parameters are calculatedwith respect to the fixed parameter bound.

XA ¼ XL þ Xu � XL

2n � 1

� �� Decode value

3. Testing data: Decoded cutting parameters generatedusing the GA and PSO algorithms are normalized.Normalization of data means that all the data must havetheir values between 0 and 1.

4. Training data: From the experimental work done, thecost function and the fitness value were calculated inthe data matrix. Data of the cutting speed, feed rate andcost value obtained from the experimental work arealso normalized between 0 and 1, which are to be usedas the training data for the neural network model.

5. Use of ANN: The neural network utilized in this workis based on a multilayer perceptron model whichconsists of input, hidden and output layers, and back-propagation algorithm scale conjugate gradient for data

Training DataTesting Data

Neural Network Model

(MATLab)

START

Randomly Generated Population (Binary String)

Parameter Decoding & Data Normalization


Calculation of Cost Value

Technological Data Base V, f, TL, MRR, etc...

Fitness EvaluationPopulation Selection

Crossover & Mutation

Optimum condition

gen = max gen gen = gen+1

STOP

Training DataTesting Data

Neural Network Model

(MATLab)

START

Initialize the random location & initial particle velocity



Calculation of Cost Value

Technological Data Base V, f, TL, MRR, etc...

Best location (Pbest)

Update Particle velocity

Update Particle location

Globally best location (Gbest)

gen = max gengen = gen+1

STOP

a b

Fig. 4 a Flowchart of GA—neural network algorithm for optimum cutting condition. b Flowchart of PSO—neural network algorithm for optimumcutting condition


learning [10]. With the above neural network basicconcepts, the cost value for the initially generatedcutting parameters was calculated.

6. Fitness: Based on the maximum fitness concept f(x)=1/[1+g(x)] (i.e. minimum of cost value g(x)) for eachindividual, fitness was evaluated and optimal solutionwas stored for each set of chromosomes.

7. Genetic concept: Initially generated cutting parameters(string) were selected for reproduction of a new set ofcutting parameters using rank selection method. Theseselected cutting parameters are made to swap at a singlecut point for the crossover process. The mutation processstarts immediately with the swapped parameters inrandom with the mutation probability of Pm=0.03.

PSO concept: Initially generated particles are updated bycalculating the particle velocity and particle position usingthe following equation.

VNewid ¼ w� VOld

id þ C1 � rand � pid � xoldid

� �þ C2 � rand� pgd � xoldid

� �

xNewid ¼ xoldid þ VNewid

where C1=C2=2 and w=(0.5+rand/2.0) [8]. Each particle isupdated according to the equation (Vid), and the best locationabout the particles (Pid) and the globally best particle (Pgd)location are identified within the neighbourhood. A particlevelocity in each dimension is clamped to a maximum velocity,Vmax, and the maximum velocity, Vmax, is set to a certainfraction of the range of the search space in each dimension.

8. Process is continued with steps 3 and 5 until it reachesthe number of iteration required.

9. At each and every generation (iteration), the bestsolution was stored in a database and the globally bestsolution was identified.

10. Stop: Finally, all the global best solutions are plottedin a graph and the optimal solution was identified foreach alumina cutting tool with the correspondingspeed and feed rate along with tool life.

4 Results and discussion

4.1 Validation of the neural network model

To predict an optimistic cutting parameter, a neural networkmodel was developed with two inputs and two hidden

layers having nine neurons each for interpolation. Themodel developed using MATLAB 7.0 is shown in Fig. 5. Aset of input and output parameters is repeated with theneural network model as training to reduce the averageerror whilst predicting the unit production cost. Figure 6shows the average error obtained whilst training the data forprediction of unit production cost with respect to 5,000epochs (number of iterations). At the beginning, the errorrating was observed in the rate of 10−1 when the iterativelearning process reaches 5,000 epoch iterations; it wasfound to be at the rate of 10−6 and stabilized with minimumerror. This is one of the main testimonies for error reductionin the prediction of production cost for a given set ofcutting parameters. Overall, the neural network modelexhibited good performance after training, and the outputresults indicate that the model is able to represent both thehybrid algorithms.

The hybrid algorithm models, a GA- and PSO-basedneural network, are used to obtain optimal cutting param-eters having minimum unit production cost. The fitnessvalue (for minimum unit production cost) obtained foralumina cutting tools using a GA-based neural networkmodel (GA-NN) and a PSO-based neural network model(PSO-NN) result has been presented in Fig. 7a, b withrespect to 50 generations.

Fig. 5 Model neural network problem using MATLAB software

Fig. 6 Variation of error in prediction of cost with respect to thenumber of iterations


4.2 Comparison of GA-NN and PSO-NN models

The optimal results obtained using the GA-NN andPSO-NN models for Ti[C,N] mixed alumina cutting tool

(CC650) and SiC whisker-reinforced alumina cuttingtool (CC670) are tabulated for performance comparison(Table 5). The computational results (fitness value)obtained with respect to the number of generations showsthat the GA-NN and PSO-NN models overlap each otherwith a micro-level variation (Fig. 7). PSO uses simplemathematical operators whereas the GA uses crossoverand mutation mechanisms for population reproduction. Itis well known that a simple mathematical operation runsmuch faster than other position changing operations andmechanisms for reproduction of a next generation. Therate of convergence in a PSO-based neural network modelis better than the GA-based neural network model. It isevident that the convergence rate on predicting the optimalcutting condition with the PSO-NN model is much fastercompared with the GA-NN model. Comparing the optimalcutting condition of alumina cutting tools duringmachining ofthe GFRP composite, the cutting speed is around 240–255 m/min for both the alumina cutting tool with a feedrate of 0.11 mm/rev using both hybrid models.

The unit production cost of SiC whisker-reinforcedalumina cutting tool (CC670) is US $16.69 for the GA-NN model and US $16.70 for the PSO-NN model.However, the unit production cost of Ti[C,N] mixedalumina cutting tool (CC650) is US $15.25 for the GA-NN model and US $15.36 for the PSO-NN model. The unitproduction cost on machining the GFRP composite using Ti[C,N] mixed alumina cutting tool (CC650) is lower thanthat of machining with SiC whisker-reinforced aluminacutting tool (CC670). However, the tool life of SiCwhisker-reinforced alumina cutting tool is better than thatof the Ti[C,N] mixed alumina cutting tool. As the tool costplays a dominant role on machining the GFRP compositematerial, the cheaper CC650 is able to contribute areduction in the unit production cost, although theperformance is lower than that of the CC670 tool. However,the PSO model gave better results compared with the GAmodel in terms of accuracy as well as in convergence to theoptimal solution.

Fitness Vs Generation for CC670 tool

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0 10 20 30 40 50No. of generation

Fit

nes

s V

alu

e

GA based NN

PSO based NN

Fitness Vs Generation for CC650 tool

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0 10 20 30 40 50No. of generation

Fit

nes

s V

alu

e

GA based NN

PSO based NN

a

b

Fig. 7 a Fitness vs. number of generations for alumina-based ceramiccutting tool (CC650) in machining the GFRP composite materials. bFitness vs. number of generations for alumina-based ceramic cuttingtool (CC670) in machining the GFRP composite materials

Parameters Units GFRP+CC650 GFRP+CC670

GA+NN PSO+NN GA+NN PSO+NN

Speed m/min 240 238 254 255

Feed mm/rev 0.108 0.108 0.108 0.111

Tool life min 7.11 7.196 8.946 8.828

Surface roughness μm 7.892 7.810 6.109 6.212

MRR mm3/min 5184 5141 5486 5661

Cost US $ 15.27 15.23 16.98 16.67

Fitness – 0.0615 0.0616 0.565 0.0566

Table 5 Details of optimisedcutting parameters


4.3 Application of GA-NN and PSO-NN models

The proposed GA-NN and PSO-NN models have beensuccessfully applied to various applications. The evolu-tionary techniques (EA)-based neural network modelsare highly recommended for complex and nonlinearoptimization problems for their accurate results. Todemonstrate the effectiveness and efficiency of theproposed models, machining studies were carried outto optimise the cutting condition of alumina cuttingtool. Obviously, the PSO-NN model has been shown tooutperform the GA–NN model in computational effi-ciency, rate of convergence, optimality and robustness.The PSO-NN model can be effectively used for largeand complex problems like the optimization of flexiblemanufacturing machine cells and automatic-guidedvehicles as it is faster and converges quickly.

5 Conclusion

Two hybrid network models were developed to optimise theunit production cost of alumina cutting tools whilstmachining the GFRP composite. These hybrid models areinvestigated in terms of convergence rate and accuracy ofsolution for optimum cutting conditions in selectedmachining strategies; the following conclusions havebeen drawn from study:

1. The hybrid algorithms GA-NN and PSO-NN modelsperformed efficiently, and the optimal cutting condi-tions predicted by the above models are almost equal.However, the PSO-NN model produces the bestoptimal cutting condition in terms of convergence rateand accuracy compared with the GA-NN model.

2. The incorporation of a neural network into GA andPSO produces accurate optimal conditions due to theefficient training by neural network.

3. Unit production cost of Ti[C,N] mixed alumina cuttingtool is lower (approx. US $15) than the SiC whisker-reinforced alumina cutting tool (approx. US $16) whilstmachining the GFRP composite.

4. The important parameter that affects the flank wear andsurface roughness, which in turn affects the unitproduction cost, was identified using design of experi-ments, and the cutting velocity and the feed rate are thedominant parameters in machining the GFRP compos-ite material using alumina cutting tools.

In conclusion, the PSO-NN model exhibits betterperformance when compared to the GA-NN model. ThePSO-NN model produces efficient and faster results thanthe GA-NN model. The unit production cost of Ti[C,N]

mixed alumina cutting tool is lower than that of the SiCwhisker-reinforced alumina cutting tool in machining theGFRP composite material.

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