### Materials

Immobilized lipase from *Mucor miehei* (Lipozyme IM) was produced by Novo Nordisk (Denmark). Palm oil (MW = 3 × average of saponification equivalent of palm oil) was obtained from Southern Edible Oil Sdn. Bhd. (Malaysia). Fatty acid compositions of Malaysian palm oil are 0.1 – 0.3% of lauric acid, 0.9 – 1.5% of myristic acid, 39.2 – 45.2% of palmitic acid, 3.7 – 5.1% of stearic acid, 37.5 – 44.1% of oleic acid and 8.7 – 12.5% of linoleic acid [33]. Oleyl alcohol was obtained from Fluka Chemika (Switzerland). Ester standards, oleyl laurate, oleyl myristate, oleyl palmitate, oleyl stearate, oleyl oleate, oleyl linoleate and methyl linoleate were obtained from Sigma Aldrich (USA). Hexane was obtained from J.T. Baker (USA). All other chemicals were of analytical grade.

### Experimental design

A five-level-four-factor central composite rotary design (CCRD) was employed in this study, requiring 30 experiments [34]. The fractional factorial design consisted of 16 factorial points, 8 axial points and 6 center points. The variable and their levels selected for the wax esters synthesis were: time (2.5 – 10 h); temperature (30 – 70°C); amount of enzyme (0.1 – 0.2 g) and substrate molar ratio (1 mmol palm oil to 1 – 5 mmol oleyl alcohol, 1:1 – 1:5). All experiments were carried out at the water activity equal to one.

The experimental data [35 points include CCRD design (Table 1) and optimization data (Table 5)] was divided into three sets: training set, testing set and validating set.

### Synthesis and analysis

Different molar ratios of palm oil and oleyl alcohol were added to 10 ml *n*-hexane, followed by different amounts of enzyme. The mixture of palm oil, oleyl alcohol and Lipozyme IM were incubated in a horizontal water bath shaker (150 rpm) at different reaction temperatures and reaction times. The reactions were analyzed by a gas chromatograph (Hitachi model G-3000, Tokyo, Japan), using an Rtx-65TG capillary column (30 m × 0.25 mm). Helium was used as the carrier gas at a flow rate 30 ml min-1. The temperature was programmed at 2 min at 150°C, 20°C min-1 to 300°C and 10 min at 300°C. The product composition was quantitated by an internal standard method with methyl linoleate as the internal standard. The concentrations of esters were calculated by equation 2:

*C*_{
x
}**= (** *A*_{
x
}**/** *A*_{
IS
}**)(** *C*_{
IS
}*D*_{
Rf IS
}**/** *D*_{
Rf
x
}**)** (2)

where *C* is the amount of component *x* or internal standard, *A* is area for component *x* or internal standard and *D*_{Rf} is detector response factor for component *x* or internal standard (*D*_{Rfx} = *A*_{
x
}/*C*_{
x
}and *D*_{Rf IS} = *A*_{IS}/*C*_{IS}).

The percentage yield of produced ester was calculated by equation 3:

**Percentage yield (%) = [ester produced (mmol)/palm oil used (mmol)] × 100**

### Response surface methodology analysis

The CCRD design experimental data was used for model fitting in RSM to find the best polynomial equation. This data was analyzed using design expert version 6.06 and then interpreted. Three main analytical steps: analysis of variance (ANOVA), a regression analysis and the plotting of response surface were performed to establish an optimum condition for the alcoholysis. Then, the predicted values obtained from RSM model, were compared with actual values for testing the model. Finally the experimental values of predicted optimal conditions (Table 5) were used as validating set and were compared with predicted values.

### Artificial neural network analysis

A commercial ANN software, NeuralPower version 2.5 (CPC-X Software) was used throughout the study. Multilayer normal feedforward and multilayer full feedforward neural networks were used to predict the percentage yields of palm-based wax ester that were trained by different learning algorithms (incremental back propagation, IBP; batch back propagation, BBP; quickprob, QP; genetic algorithm, GA; and Levenberg-Marquardt algorithm, LM). The network architecture consisted of an input layer with four neurons, an output layer with one neuron, and a hidden layer. Molar ratio of palm oil and oleyl alcohol, amount of enzyme, reaction temperature and reaction time were used as networks inputs and the percentage yield of palm-based wax ester, as target output. To determine the optimal network topology, only one hidden layer was used and the number of neurons in this layer and the transfer functions of hidden and output layers (sigmoid, hyperbolic tangent function, Gaussian, linear, threshold linear and bipolar linear) were iteratively determined by developing several networks. Each network was trained until the network root of mean square error (RMSE), average correlation coefficient (R) and average determination coefficient (DC) were lower than 0.01, equal to 1 and 1, respectively. Other parameters for network were chosen as the default values of the used software. At the start of the training, weights were initialized with random values and adjusted through a training process in order to minimize network error.

The CCRD design experimental data was divided into training and testing sets. For training, 26 points were used (Tables 1 and 4). One strategy for finding the best model is to summarize the data, it is well established [32] that in ANN modeling, the replicates at center point do not improve the prediction capability of the network because of the similar inputs. That is why we improved our model by using mean of center points instead of 6 center points (Tables 1 and 4, italic numbers). For testing the network, 4 remaining points were used (Tables 1 and 4, bold numbers). On the other hand, experimental values of predicted optimal conditions (Table 5) were used as validating set.

### Verification of estimated data

The estimation capabilities of the techniques, RSM and ANNs were tested. For this purpose, the estimated responses obtained from RSM and ANNs were compared with the observed responses. The coefficient of determination (R^{2}) and absolute average deviation (AAD) were determined and these values were used together to compare ANNs to each other for finding the best ANN model, and the best ANN model with RSM. The AAD and R^{2} are calculated by equations 4 and 5, respectively.

\text{AAD}=\{[{\displaystyle \sum _{\text{i}=1}^{\text{p}}(|{\text{y}}_{\text{i},\mathrm{exp}}-{\text{y}}_{\text{i},\text{cal}}|/{\text{y}}_{\text{i},\mathrm{exp}})]/\text{p}\}\times 100}

(4)

where *y*_{i,exp}and *y*_{i,cal}are the experimental and calculated responses, respectively, and *p* is the number of the experimental run.

{\text{R}}^{2}=1-\frac{\frac{\Sigma}{\text{i}=1-\text{n}}{({\text{modelprediction}}_{\text{i}}-{\text{experimentalvalue}}_{\text{i}})}^{2}}{\frac{\Sigma}{\text{i}=1-\text{n}}{(\text{averageexperimentalvalue}-{\text{experimentalvalue}}_{\text{i}})}^{2}}

(5)

where *n* is the number of experimental data.

R^{2} is a measure of the amount of the reduction in the variability of response obtained by using the repressor variables in the model. Because R^{2} alone is not a measure of the model's accuracy, it is necessary to use absolute average deviation (AAD) analysis, which is a direct method for describing the deviations. Evaluation of R^{2} and AAD values together would be better to check the accuracy of the model. R^{2} must be close to 1.0 and the AAD between the predicted and observed data must be as small as possible. The acceptable values of R^{2} and AAD values mean that the model equation defines the true behavior of the system and it can be used for interpolation in the experimental domain [32].

#### Optimization of reaction

The predicted optimal conditions could be easily calculated using model equation. The stationary point (minimum or maximum point) of a second order equation is the point where the first derivative of the function equals to zero:

\begin{array}{l}\begin{array}{ccc}Let& y=f({x}_{1},{x}_{2})& and\end{array}\hfill \\ ={\beta}_{0}+{\beta}_{1}{x}_{1}+{\beta}_{2}{x}_{2}+{\beta}_{11}{x}_{1}^{2}+{\beta}_{22}{x}_{2}^{2}+{\beta}_{12}{x}_{1}{x}_{2}\hfill \end{array}

(6)

The stationary point is found by computing *∂y*/*∂x*_{1} and *∂y*/∂*x*_{2} and setting zero:

\begin{array}{l}\partial y/\partial {x}_{1}={\beta}_{1}+2{\beta}_{11}{x}_{1}+{\beta}_{12}{x}_{2}=0\hfill \\ \partial y/\partial {x}_{2}={\beta}_{2}+2{\beta}_{22}{x}_{2}+{\beta}_{12}{x}_{1}=0\hfill \end{array}

(7)

The system of equations is solved to find the values of *x*_{1} and *x*_{2}. To determine whether the stationary phase is minimum or maximum, the second derivative of the equation is used. If it is a negative value, the optimum point is a maximum but if it is a positive value, the optimum point is a minimum [32].