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Share This Paper. Figures and Tables from this paper. Figures and Tables. Citations Publications citing this paper. Modeling and optimization of extracellular polysaccharides production by Enterobacter A47 Rodolfo Marques. Naval , Luis G. Sison , Eduardo R. Determination of inhibition in the enzymatic hydrolysis of cellobiose using hybrid neural modeling Fernanda de Castilhos Corazza , Luiza P. Hybrid modelling of bioprocesses.

Benjamin J Hodgson. Parameter estimation for stiff equations of biosystems using radial basis function networks Yoshiya Matsubara , Shinichi Kikuchi , Masahiro Sugimoto , Masaru Tomita. Decoupling dynamical systems for pathway identification from metabolic profiles Eberhard O.

Voit , Jonas S. Clemente , Manuel J. Priming nonlinear searches for pathway identification Siren R. Veflingstad , Jonas S. Almeida , Eberhard O. References Publications referenced by this paper. Structural identi"cation of nonlinear mathematical models for bioprocesses. Bernard , G. In this way, making a strong link between the MLP model and NSGAII in our first priority in order to achieve the highest efficiency and the optimum concentrations of sterilants as well as immersion times during in vitro sterilization process.

Generally, the objective of this study was to model and optimize the proper concentrations of sterilants and immersion times for sterilization of leaf explant of chrysanthemum, as a case study. The leaf explants were washed with tap water for 30 min and washed again after cleaning with a liquid soap solution. Additional surface sterilization was applied in a laminar airflow chamber.

Afterward, 25 mm 2 leaf segments abaxial side were incubated on ml glass flasks containing 40 ml basal medium. MS Murashige and Skoog medium as a basal medium used in this experiment having 0. The experiments were conducted based on completely randomized design CRD with a factorial arrangement with 15 replicates per treatment following with three sub-sets.

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The effect of sterilants and immersion times on in vitro sterilization of chrysanthemum were evaluated based on the six following treatments;. Table 1. Effect of different concentrations of NaOCl at various immersion times on in vitro sterilization of chrysanthemum. Table 2.

Effect of different concentrations of Ca ClO 2 at various immersion times on in vitro sterilization of chrysanthemum. Table 3. Effect of different concentrations of HgCl 2 at various immersion times on in vitro sterilization of chrysanthemum.

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Table 4. Effect of different concentrations of H 2 O 2 at various immersion times on in vitro sterilization of chrysanthemum. Table 5. Effect of different concentrations of AgNO 3 at various immersion times on in vitro sterilization of chrysanthemum. Table 6. Effect of different concentrations of Nano-Silver at various immersion times on in vitro sterilization of chrysanthemum.

After 21 days of culture, the efficiency of different concentrations and types of sterilants, as well as immersion times on contamination frequency CF and explant viability EV were determined.

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Moreover, the dataset was checked for confirming the range of train set contains the test data. To improve the performance of considered models and determine the best construct of each model, various values for significant model's parameters were tested based on a trial and error analysis. Finally, for each model, the best-resulted output with the minimum estimation error was determined based on Root Mean Square Error RMSE as well as the coefficient of determination R 2 as follows:.

MLP uses a supervised training procedure that consists of provided inputs and outputs to the network; the training process should be in such a way that the following function would be minimized:. Determining MLP architecture plays an important role in its efficiency Khorsandi et al. Therefore, in the architecture of an MLP, the number of hidden layers and the number of neurons in each layer should be determined.

Hornik et al. Thus, the number of neurons in the hidden layer would be important in determining the architecture of an MLP. Some scholars have been suggested the appropriate number of neurons m based on a number of input n or the number of data K. As an example, Tang and Fishwick , Wong , and Wanas et al. Finally, by using trial and error method, the optimal number of neurons in the hidden layer should be determined while the reported offers can be used as a starting point.

The low number of neurons makes the simplicity of the network and the large number of them makes the complexity of the network, therefore a simple network results in under-fitting, and vice versa. In this study, feed forward back-propagation 3-layer back-propagation network , as the bases of the common network structure, was used for running an MLP model. For hidden and output layers transfer functions of hyperbolic tangent sigmoid tansig and linear purelin were applied, respectively.

Also, for the training of the network, a Levenberg-Marquardt algorithm was applied for determining the optimal weights and bias. In order to select the best non-dominated solutions via a step-by-step procedure, NSGA-II should mainly depend on binary tournament selection, elitist non-dominated sorting, and crowding distance.

Mutation operations, selection, and cross-over are three main components for simulation process that can be useful for evaluating objective functions and decision variables. Afterward, the solutions, which are not dominated by the others and categorized as different non-dominated fronts of the population, are derived based on the non-dominated sorting concept. Each non-dominated front can be sorted as a rank or level data, and the population is ranked again except for the first Pareto front. Therefore, the non-dominated front, considered as the first rank, is the last generation of the optimal Pareto.

The latest procedure is to remove the member that possess the highest rank lower priority and the select others to generate parent population of the next generation. Afterward, each objective function should be estimated by crowding distance of a specific solution. Crowding distance is based on the average of two related neighboring solutions. Considering the lowest density of solutions that have less priority, the solutions of each level are categorized by crowding distance in descending order. The next step after sorting solution is a selection step.

The binary tournament selection operator is commonly used in the selection step. Thus, children population is generated based on repeating the selection operator with applying the mutation operators and cross-over, same as the exact size of the parent population.

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Finally, the non-dominated sorting is utilized for the combination of children and parent populations after performing a simulation process for estimating the objective functions. In this study, CF and EV were considered as two objective functions to determine the optimum values of inputs. The ideal point of pareto was chosen such that CF and EV became the minimum and maximum, respectively. In other words, a point in the pareto front was considered as the solution such that. Figure 2. The sensitivity CF and EV against the investigating growth elements was evaluated by using the following criterion;.

The variable sensitivity error VSE value stands for the overall performance of the developed MLP model in the case that the particular independent variable is not available. The higher the VSR, the more important variable will be.

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Therefore, all input variables can be ranked based on their importance. The mathematical code was written conveniently for Matlab version 9. Our results indicated that there was no contamination observed at 1. The highest EV There was no contamination observed in 9.

No contamination was record for 0. Also, the highest EV The lowest CF Based on these results, it would be clear that the type and concentration of sterilants along with explant exposure times to sterilant play a vital role in in vitro sterilization that each sterilant needs to be adjusted based on their optimum concentration and immersion time.

Assessment of predicted and observed data describes the efficiency of the MLP model. The graphs Figure 3 may apply to comprehend the perfect sterilization response and to measure the combined effects of sterilants and immersion times. Generally, performance criteria Table 7 illustrated that the MLP models were able to efficiently fit published data on the performances of in vitro sterilization to different types and concentrations of sterilants at different immersion times. Table 7. Figure 3. Scatter plot of model predicted vs. Fitted simple regression line on scatter points was indicated by a solid line.

The ultimate purpose of this study was to analyze the MLP model to provide an accurate answer of what levels of sterilants and immersion times may be applied to obtain the maximum CF and EV. Thus, we have linked the model to NSGAII for finding the maximum efficiency and the optimum sterilants levels and immersion time which are essential for significant in vitro sterilization.

Figure 4 and Table 8 showed the results of the optimization process. The lower bound and upper bound of input variables Tables 1 — 6 were considered as constraints during the optimization process, and the point with the lowest CF and the highest EV was considered as the ideal point.

As can be seen in Table 8 , 1. Figure 4. The red point indicates the ideal point. Table 8. The comparative rank of input data was calculated through the entire data lines training and testing to determine the general VSR. Table 9.