The crude oil was extracted from rubber seeds collected from private and indus- trial plantations in Côte d’Ivoire. The seeds were dried, crushed, and pressed with a mechanical press. The composition of the brown oil obtained is shown in SM 1. The main chemicals used in the study (potassium hydroxide (KOH) pellets of 85 wt.% purity, sulphuric acid (H₂SO₄) of 96 wt.% purity, methanol (MeOH) of 99.7 wt.% purity, ethanol (EtOH) of 99 wt.% purity, and magnesium sulphate (MgSO₄) of 99 wt.% purity) were provided by Merck Ltd (Germany).

The transesterification was carried out in liquid phase under various conditions according to the experimental design. In alkaline conditions, the synthesis of biodiesel was carried out with a molar ratio MeOH/oil (or EtOH/oil) of 6:1 and 1% (w/w) of KOH relative to the oil, while in acidic conditions, a molar ratio MeOH/oil (or EtOH/oil) of 6:1 and 2.25% (mol/mol) of the mixture were used according to Mohamad et al. (2002) [36] . Two alcohols were used, MeOH and EtOH. The experimental set-up used was a 500 mL batch reactor magnetically stirred and equipped with a heater This reactor is surmounted by a coolant to prevent the alcohol from evaporating, especially when the reaction reaction takes place beyond the boiling temperature of the alcohol. At the end of the reaction, the mixture was collected and subjected to settling. The upper layer was then collected and washed with hot distilled water. The moisture in the washed biodiesel was subsequently removed using anhydrous MgSO₄.

SM 1. Fatty acid profile of crude rubber seed oil (RSO) (analysis by gaz chromatogrphy coupled with a Detector of Flame ionization (GC/DFI) Hewlett-Packard® 5890 II set provided with an automatic sample ferryman of Agilent 6890).

Among existing experimental designs [26] , the Plackett and Burman model [37] is the most suitable for screening. In this study, the transesterification was examined using a Hadamard matrix with five factors: temperature (U₁), stirring speed (U₂), reaction time (U₃), type of solvent (U₄), and type of catalyst (U₅). Specific gravity and kinematic viscosity were considered as the responses.

Analysis of the effects of the factors on the two responses was performed using Equation (2). In this equation P_i is the contribution of each factor on the response.

P i = 100 × ( b i 2 ∑ b i 2 ) ; i ≠ 0 (2)

where b_i is the estimate of the main effect of factor i.

A full factorial matrix (2^k, k being the number of factors) was used for quantitative optimization of the factors. Full factorial matrices examine two or more factors, each with discrete possible values or levels, across all possible combinations of levels and factors. A full factorial design (FFD) may also be called a fully crossed design. The effect of each individual factor, and the effects of interactions between factors, can be examined using this approach. In this study, the effects of temperature (U₁), stirring speed (U₂), and reaction time (U₃) were evaluated.

Response surface methodology (RSM) using a central composite design (CCD) with five levels and two factors (stirring speed and reaction time) was used for to model and optimize the relation between these factors and specific gravity and viscosity. The experimental runs were randomized to minimize the effects of unexpected variability in the observed responses. The methodology employed enables the formulation of a second-order polynomial that describes the process. To correlate the response variable to the independent variables, multiple regressions were used to fit the coefficient of the second-order polynomial model of the response [34] .

Table 1 summarizes the experimental range and levels of the independent process variables studied for each part of this work. For screening, the main fac- tors involved in biodiesel synthesis and their limits were chosen according to the literature [38] . The experimental domain of the full factorial design is defined from the results of the screening. Similarly, the experimental domain of central composite design is defined from the results of the full factorial design. The experimental design and responses observed during the screening are shown in Table 2.

The main interactions, correlation coefficients, variance analysis, residuals, and standard deviations were calculated using the NEMROD-W program (design NEMROD-W, version 9901 Française, LPRAI-Marseille Inc., France).

In order to find a global optimum, a single database was established bymerg- ing the observed responses of the full factorial and central composite design analyses. This database, described in Table 3, was used to model the process with an artificial neural network. The resulting models were then used to search for a global optimum with a genetic algorithm.

The genetic algorithm (GA) was used to determine a global optimum mini- mizing equations (x) and (y) under constraint. GAs are stochastic search tech- niques whose theoretical bases were defined by J. H. Holland [39] . They are based on a natural biological process: the evolution of living species. They evolve through two mechanisms: natural selection and reproduction. Selection ensures that only the fittest individuals survive, while reproduction recombines parental characteristics to create descendants with new possibilities. The combination of these two phenomena (selection and reproduction) leads, generation after generation, to populations that are better and better adapted to the environment in which they live.

Artificial neural network (ANN) is a powerful modeling tool, used in various fields. In this study, specific gravity and kinematic viscosity variation were predicted using the Multilayer Perceptron (MP) [40] [41] . The ANN architecture included an input layer with three neurons (representing temperature, stirring speed and reaction time) and an output layer with two neurons (representing specific gravity and kinematic viscosity). The optimal network topology was determined using MATLAB programm (Matlab R2015a).

The main objective was to simultaneously minimize the specific gravity and kinematic viscosity. Such an optimization was performed via aggregation of the multiple objectives into a single objective function [40] [41] , as expressed by Equation (3).

Min   Y ; with   Y = Y 1 + Y 2 70 ≤ X 1 ≤ 90 ˚ C , 100 ≤ X 2 ≤ 400   rpm , 105 ≤ X 3 ≤ 165   min . (3)

The computational parameters of the GA were the following: 1) population size = 200; 2) Elite count = 2; 3) Number of Generation = 1500; 4) Fitness scaling function = @fitscalingrank; 5) Selection function = Selection function; 6) Crossover function = @crossoverscattered; 7) Mutation function = @mutationuni- form; 8) Mutation probability = 0.05.

An ABBE WYA-IS refractometer was used to determine the refraction index. Kinematic viscosity was measured using a capillary tube viscometer (HVU 482). Specific gravity was determined with a DMA 4500 M densimeter. A digital scale (OHAUS) with a precision of 0.001 g was used to measure weight. Physico- chemical characteristics such as acid, ester, peroxide, iodine, and saponification index, water and volatile matter content, specific gravity, viscosity, cetane index, refractive index, and heating value were determined according to the AFNOR [42] [43] and ASTM norms or by calculation [33] [44] [45] . The fatty acid pro- file of crude rubber seed oil is determined by gaz chromatogrphy coupled with a Detector of Flame ionization (GC/DFI) Hewlett-Packard® 5890 II set provided with an automatic sample ferryman of Agilent 6890.

The physicochemical properties determined and compared to those of the gasoil are presented in SM 2.

SM 2. Some physicochemical characteristics of rubber seed oil compared to diesel.

From the foregoing, it should be noticed that the density, viscosity, and the acidity of the rubber seeds oil are limiting factors for the direct use in a diesel engine. This conclusion is consistent with many authors [2] [4] [15] [33] [38] [46] - [51] when they argue that among the physicochemical characteristics of oils, these parameters cause practical problems. As part of this study, their value far removed from the specifications show that it is not opportune to use such oil in a diesel engine. Therefore, a transformation is needed to be carried out, as it is undertaken using the transesterification method according to Hadamard Matrix.

The standard deviations of specific gravity and viscosity, estimated by NEMROD-W sofware, were 0.003 and 2.5 cSt respectively. These values validate the chosen experimental field. It therefore appears that specific gravity and viscosity were sensitive to changes in the factors examined. Statistical analysis of the coefficients, illustrated in SM 3, showed that two coefficients had sufficient significance to be taken into account.

These coefficients were b₄ and b₅, respectively reflecting the effects of solvent and catalyst. Other factors, such as temperature, stirring speed, and reaction time, were low significance. Calculations using equation (2) indicate that the catalyst and the solvent were responsible for 66.50% and 32.47%, respectively, of specific gravity variation, for a combined percentage of 98.97%. Similarly, the catalyst and the solvent were responsible for 51.99% and 35.52%, respectively, of viscosity variation, for a combined percentage of 87.51%.

The coefficient analysis shown in SM 3 demonstrates that use of sulfuric acid, ethanol, a temperature of 80˚C, a stirring speed of 1100 rpm, and a reaction time of 145 min leads to a significant decrease in kinematic viscosity and specific gravity and consequently a better transesterification. These results are in agree- ment with those of several other authors [38] [46] - [51] , which suggested that with high-acidity oils (free fatty acid levels ≥ 4%), it is preferable to use ethanol and perform acid catalysis transesterification at moderate temperatures and high reaction times.

The results of this screening study indicate that the factors that have the

SM 3. Screening estimated coefficients related to specific gravity.

greatest influence on both the density and the kinematic viscosity of the main product of the transesterification (biodiesel) are type of catalyst and type of alcohol; molar ratios oil/alcohol being fixed to 6:1, and the concentrations of the catalysts to 1% w/w and 2.25% mol/mol respectively for the KOH and H₂SO₄, according to the works of Mohamad et al. (2002) [36] . Both are qualitative factors, so they shall be fixed at the lowest levels (H₂SO₄ and EtOH) that significantly reduce specific gravity and kinematic viscosity.

Statistical treatment of the full factorial data revealed that the standard devia- tions of the responses were 0.0008 and 0.8 cSt respectively for specific gravity and kinematic viscosity. For specific gravity, the correlation coefficient R² = 0.99 ≥ 0.95, indicating a good fit for the model illustrated by Equation (4). The evolution of the specific gravity values was consistent with a first-order model. This was not the case with the viscosity, for which the coefficient R² = 0.81 ≤ 0.95. Consequently, a linear model is not sufficient to explain the variation in viscosity, justifying the use of a second-order model.

Y 1 ( X 1 , X 2 , X 3 ) ⋅ 10 3 = 893.7 − 4.9 X 1 − 1.4 X 2 + 1.6 X 3 − 2.4 X 1 X 2 − 0.9 X 1 X 3 − 0.9 X 2 X 3 (4)

In the eexperimental field chosen (Table 1), solving this equation leads to the following optimal conditions: U₁ = 90˚C, U₂ = 300 rpm, and U₃ = 125 min, leading to a specific gravity of 0.882.

These results are consistent with those of Ghanei et al. (2011) [35] , who showed that specific gravity follows a linear law during the transesterification reaction.

As Equation (4) indicates, specific gravity variation is strongly influenced by temperature (b₁ = −0.0049), which has a positive effect on reduction of the spe- cific gravity of biodiesel. These results are in agreement with those of Betiku et al. (2015) [34] . Indeed, they show that among the independent variables for biodiesel synthesis, temperature had the greatest influence on the reaction yield. As shown in SM 4, specific gravity decreased by 0.0098 (2*−0.0049) when 90˚C was used instead of 70˚C.

The effects of these factors and their interactions on the variation (reduction) in specific gravity of biodiesel during the transesterification reaction have been put into evidence using Equation (2) [28] . The contribution of each factor to the response was calculated using this formula.

The interaction between temperature and stirring speed produced the most important effect, with a coefficient value b₁₂ equal to 0.0024. This interaction can be explained by considering the data shown in SM 5.

Above the boiling temperature of ethanol (78˚C), strong agitation would be superfluous. On this figure (SM 5), each vertex represents the average value of the responses obtained under the same experimental conditions. When the stirring speed was set at either a high level (300 rpm) or a low level (100 rpm),

SM 4. Factorial estimated coefficients related to specific gravity.

SM 5. Interaction b₁₂ between temperature and the stirring speed.

temperature had a significant effect on specific gravity variation. In both cases, specific gravity declined from about 0.90 to about 0.89, i.e., a reduction of about 0.01. Consequently, the effect of temperature was dependent on stirring speed. Its negative sign indicates that higher temperatures did not require higher stirring speeds.

After completion of the experimental tests, the Nemrod-W software was used to analyze the statistical data (shown in SM 5). The experimental response can be described by a nonlinear polynomial model (Equation (5)), as follows:

Y 2 ( X 2 , X 3 ) ⋅ 10 3 = 7082 − 69 X 2 − 130 X 3 + 71 X 2 2 + 66 X 3 2 (5)

The corresponding correlation coefficient was R² = 0.98 ≥ 0.95, which validates the model, and shows the nonlinearity of the evolution of kinematic viscosity during the transesterification reaction. This model is assumed to be good if the sum of squares due to residuals (i.e., due to fit error) is ≤ 33.33% of the sum of squares due to the regression [22] . As shown in Table 4, analysis of

variance (ANOVA) indicates that the sum of squares due to error was very low (0.25%), confirming that the model was well fitted [52] . The model can be rep- resented by the response surface and contour plot illustrated in Figure 1. In this figure, X₁ and X₂ represent the stirring speed and the reaction time, respectively.

Figure 1 shows that kinematic viscosity is lowest in the region where the stirring speed is between 300 rpm and 400 rpm and where the time is between 125 min and 146 min. The best compromise zone leading to minimizing the kinematic viscosity is indicated by the arrow. To determine the extremum (the minimum in the case of this study) of this function, in the chosen experimental domain, the resolution of the system of the relation (6) is necessary.

{ Min   Y 2 ( X 2 , X 3 ) − 1.414 ≤ X 2 ≤ 1.414 − 1.414 ≤ X 3 ≤ 1.414 (6)

On the eexperimental field chosen (Table 1), the optimal conditions obtained by solving this equation (6) are U₂ = 400 rpm and U₃ = 145 min, leading to a kinematic viscosity of 6.80 cSt.

The difference between the measured responses (Yexp.) and the predicted responses (Ycalc.) from the fitted model did not exceed 5% [28] . As it can be seen in SM 6, all of the relative deviation values are lower than 5%. Thus, the second- order polynomial model described by Equation (5) was satisfactory.

This is consistent with the results of Ghanei et al. (2011) [35] , who showed that the viscosity of sunflower oil decreases nonlinearly with an increase of methyl ester wt.%. Similarly, when the ethyl ester wt.% in rubber seed oil increases, the kinematic viscosity of the resulting biodiesel decreases nonlinearly.

In short, it should be noted that the specific gravity and the kinematic viscosity of the main product of the transesterification reaction (biodiesel) follow two different models. Thus, a global modeling and optimization process is necessary to find the optimal compromise between these two responses.

Table 3 shows the experimental database, which can be divided into two parts. Runs 1 to 11 represent an extract from the full factorial matrix study, while runs

SM 6. Comparison of measured responses (Yexp.) and predicted responses (Ycalc.).

12 to 24 are results obtained from a study based on the central composite matrix.

Determination of the most powerful architecture, based on mean square error (MSE) and correlation coefficient (R), is a key step [40] [41] . Table 5 shows the performance studies for various topologies.

The correlation coefficients (R) varied from 0.9213 to 0.9987 and from 0.9124 to 0.9369 for the training subsets for specific gravity and kinematic viscosity, re- spectively. For the test subsets, the correlation coefficient varied from 0.8225 to 0.9774 and from −0.2227 to 0.9357 for specific gravity and kinematic viscosity, respectively. When the number of nodes in the hidden layer increased, the correlation coefficients also increased, peaking at the maximum values (0.9987; 0.9369) for the training subset, which is consistent with the results of Assidjo et al. (2008) [41] . For the test subset, the correlation coefficients and the number of neurons in the hidden layer did not evolve in the same direction. The correlation coefficient for specific gravity (Y₁) was higher for an architecture with 8 nodes (R = 0.9774), whereas the correlation coefficient for kinematic viscosity (Y₂) was higher for an architecture with 14 nodes (R = 0.9357) in the hidden layer. Thus, it is difficult to find a compromise between the correlation coefficients of the two output variables (Y₁, Y₂). Consequently, the MSE values must be considered to find the best network. As it can be seen in Table 5, the lowest MSE value was associated with an architecture with 7 nodes in the hidden layer.

According to Assidjo et al. (2008) [41] , the best network is a compromise between the results obtained during training and those with the generalization (test): the network that best characterizes the data of the phenomena is the

network with the least error. In this study, the best compromise (providing both a low value of MSE and a high value of R for the training and test sets) was obtained with the 3-7-2 structure ANN model depicted in Figure 2.

As Koffi et al. (2006) explained [53] , by convention, the relationship is perfect if R = 1; very strong if R > 0.8; strong if R is between 0.5 and 0.8; medium inten- sity if R is between 0.2 and 0.5; low if R is between 0 and 0.2; and zero if R = 0. In this study, the values of R were 0.94 for specific gravity and 0.91 for viscosity, i.e., very strong in both cases. The comparison between observed and calculated values depicted in Figure 3 also shows the strength of these relationships, confirming that the 3-7-2 ANN architecture best models the relationship between the input variables (temperature, stirring speed, reaction time) and the output variables (specific gravity and kinematic viscosity). However, Ghanei et al. (2011) [35] have shown that these parameters were affected by methyl ester wt.%. So, there are the relationship between the input variables and the reaction yield.

Thus, the 3-7-2 ANN model was found to be highly suitable for modeling the phenomena. Using this model, the multiobjective function described in equation (3) was optimized with the help of a genetic algorithm (GA). The optimal zone, obtained after 1500 iterations, is depicted in Figure 4.

This figure highlights the solution points that minimize both Y₁ and Y₂. Note the two parts of the optimal zone represented by curve portions O₁O and O₂O₃. The details of the optimal operating conditions and the corresponding responses are presented in SM 7.

As in Yao et al.’s (2007) study [40] , analysis of the effect of each independent variable on the reduction of specific gravity and kinematic viscosity of RSOB shows that the different independent input variables have different effects on the responses of Y₁ and Y₂. The results of simultaneous minimization are depicted

SM 7. Lower and upper limits obtained after compilation of the GA*.

*GA. Genetic Algorithm.

by the pareto front shown in Figure 4.

The first part of the optimal zone [O₁O] is interesting when the goal is to minimize specific gravity, whereas the second part [OO₂] is interesting when the goal is to minimize kinematic viscosity. To minimize both, a compromise is necessary, and the following recommended operating conditions were proposed: 87.14˚C ≤ X₁ ≤ 90˚C; 305˚C ≤ X₂ ≤ 331 rpm; 141˚C ≤ X₃ ≤ 155.89 min.

The optimal point was the couple O (0.883; 6.76), corresponding to a temperature of 90˚C, a stirring speed of 305 rpm, and a reaction time of 141 min, as shown by the front of the pareto curve in Figure 4. These results were consistent with those recorded by Betiku et al. (2015) [34] .

Experimental design permitted to make an optimization multiobjective with solver of Excel driving respectively to the minimal values of 0.884 and 6.82 cSt of the specific gravity and the kinematic viscosity in the following conditions: U₁ = 90˚C, U₂ = 400 rpm and U₃ = 145 min.

As using the ANN coupled to the genetic algoritm, a set of optimal conditions of which most interesting result are the following: U₁ = 90˚C, U₂ = 305 rpm, and U₃ = 141 min. These conditions permitted to have a minimal specific gravity of 0.883 and a kinematic viscosity of 6.76 cSt.

Both methods drive to the results of the same order. However, the ANN coupled with the AG permit to have an energizing gain and in time with weaker minimas.

Doing three experiences in the optimal conditions, corresponding to a temperature of 90˚C, a stirring speed of 305 rpm, and a duration of 141 min while using the ethanol as solvent and the sulphuric acid as catalyst, permitted to have the results presented in SM 8.

The averages of the specific gravity and the viscosity kinematics are respec- tivements (0.884 ± 0001) and (6.5 ± 0.1) cSt. While comparing these values to the predicted values, one gets some residues between 0.000 and 0.001 for the density and 0.15 and 0.37 cSt for the viscosity. An agreement almost perfected between the experimental values and the predicted values according to the previous works exists [54] [55] [56] . In our chosen experimental domain, optimization with of the artificial neural networks coupled to the genetic algorithm has been achieved well (the coefficients of variation being lower to 5%).

SM 8. Experimental verification for the biodiesel production.