From the understanding of the wild conditions of
With biological technologies: it used optimum media on mycelial growth of
With mathematical models: some researches focus on building mathematical models for the progress of producing
Artificial algorithms and models have been used in the bioprocess, particularly for the optimization of culture conditions. In [
In this work, we start from operating 45 experiments for producing
In this section, biological experiments are performed for finding optimal value of certain single factor.
In Table
Experiments with PH values ranging from 1 to 14 and initial volume ranges from 40 mL to 140 mL.

PH  Temp.  Initial volume  Rotation speed  Including inoculum  Seed age  Fermentation time 

45.929  1  28°C  100 mL  140  5%  8  8 
35.077  2  28°C  100 mL  140  5%  8  8 
45.654  3  28°C  100 mL  140  5%  8  8 
534.39  4  28°C  100 mL  140  5%  8  8 
702.81  5  28°C  100 mL  140  5%  8  8 
1467.7  6  28°C  100 mL  140  5%  8  8 
189.20  7  28°C  100 mL  140  5%  8  8 
91.049  8  28°C  100 mL  140  5%  8  8 
60.841  9  28°C  100 mL  140  5%  8  8 
57.255  10  28°C  100 mL  140  5%  8  8 
43.238  11  28°C  100 mL  140  5%  8  8 
36.288  12  28°C  100 mL  140  5%  8  8 
20.943  13  28°C  100 mL  140  5%  8  8 
22.306  14  28°C  100 mL  140  5%  8  8 


508.495  6  28°C  40 mL  140  10%  8  8 
900.662  6  28°C  60 mL  140  10%  8  8 
1273.594  6  28°C  80 mL  140  10%  8  8 
1153.937  6  28°C  100 mL  140  10%  8  8 
1123.330  6  28°C  120 mL  140  10%  8  8 
1088.064  6  28°C  140 mL  140  10%  8  8 
In Table
Experiments with including inoculum ranging from 2% to 16% and temperature ranging from 25

PH  Temp.  Initial volume  Rotation speed  Including inoculum  Seed age  Fermentation time 

546.609  6  28 
100 mL  140  2%  8  8 
606.345  6  28 
100 mL  140  4%  8  8 
1320.794  6  28 
100 mL  140  6%  8  8 
1447.519  6  28 
100 mL  140  8%  8  8 
1841.729  6  28 
100 mL  140  10%  8  8 
1631.990  6  28 
100 mL  140  12%  8  8 
481.1172  6  28 
100 mL  140  14%  8  8 
449.5187  6  28 
100 mL  140  16%  8  8 


1145.669  6  25 
40 mL  140  10%  8  8 
1506.055  6  30 
60 mL  140  10%  8  8 
1374.982  6  35 
80 mL  140  10%  8  8 
875.341  6  40 
100 mL  140  10%  8  8 
Experiments with fermentation time ranging from 1 to 12 hours.

PH  Temp.  Initial volume  Rotation speed  Including inoculum  Seed age  Fermentation time 

56.606  6  28°C  100 mL  150  2%  8  1 
83.435  6  28°C  100 mL  150  4%  8  2 
303.984  6  28°C  100 mL  150  6%  8  3 
449.919  6  28°C  100 mL  150  8%  8  4 
777.331  6  28°C  100 mL  150  10%  8  5 
1103.987  6  28°C  100 mL  150  12%  8  6 
1619.554  6  28°C  100 mL  150  14%  8  7 
1597.995  6  28°C  100 mL  150  16%  8  8 
1546.336  6  28°C  100 mL  150  10%  8  9 
1502.487  6  28°C  100 mL  150  10%  8  10 
1489.364  6  28°C  100 mL  150  10%  8  11 
1465.664  6  28°C  100 mL  150  10%  8  12 
We consider here using regression analysis and geneset based genetic algorithm to find the optimized culture conditions for maximizing the production of
In statistical modeling, regression analysis is a statistical process for estimating the relationships among variables [
Regression analysis is widely used in data mining, particularly for biological data analysis in recent years, with the purpose of finding a feasible statistical law by the large amount of data of experiments. The general process is given as follows.
Determine the variables.
Establish the prediction model.
Relate analysis.
Calculate the prediction error.
Determine the predicted value.
From the data collected in Section
Inoculum size 0.5%~1.2%.
PH 5~7.
Initial liquid volume 60~100 mL.
Temperature 25~30°C.
Seed age 4~9 days.
Fermentation time 6~12 days.
Rotation speed 140~200 r/m.
After data filtering, a statistical model is made to represent these data. It is known that there is a correlation between these data relationships, so we applied linear regression analysis to fit them. At this stage, a lot of models were tested one by one with IBM SPSS software and response surface methodology. The statistical model is
Although the relationship between the data may not be linear, we can put squared term for a type of data into these data. If this term is useful it will be retained after linear regression analysis; otherwise, the data will be deleted.
In the regression analysis, it needs to focus on the values of
Regression analysis results.
Sum of square  df  Mean square 



Standard error  

Regression  3796787.42  14  249770.53  5.234  0.93  0.88  218.48 
Residuals  47719.89  10  47719.54  
Sum  3973983.26  24 
It is obtained that significance = 0.006 < 0.05; that is, the regression results are obvious.
Genetic algorithm (GA) was first proposed by J. Holland in 1975 [
GA process.
In geneset based GA, a chromosome is treated as a set of genesets, instead of a set of genes as in classical GAs. It starts with genesets of the largest size equal to half the chromosome length. It is most appropriate to genetics model because each geneset represents a set of adjacent parameters of certain factor of the culture conditions.
It is noted that, in the selection, only the winning individuals from the population can be selected. Select operators are also known as reclaimed operator (reproduction operator), whose purpose is to optimize the selection of individuals (or solutions) to the next generation. Population can be updated by fitness ratio method and random sampling method to traverse, local selection. Cross operator refers to the part of the structure of the two parent individuals to generate new recombinant replacing individual operation. Variation is to make GA have local random search capability. When the GA crossover neighborhood is close to the optimal solution, the use of such a mutation operator of local random search capability can accelerate the convergence to the optimal solution.
The statistical model obtained by regression analysis is used as the fitness function here, and geneset based GA is used to optimize the culture condition for maximizing the production of
After 156 iterations the geneset based GA process returns the best individual and shuts down the process in Figure
GA best fitness.
After the regression analysis and GA process, an optimized culture condition is obtained, shown in Table
Optimized culture conditions.
Type  Experiment data  Computer data 

Inoculum size  10%  12% 
PH  6  5.8 
Initial liquid volume  100 mL  100 mL 
Temperature  28°C  28°C 
Age  8  9 
Fermentation time  8  9 
Rotation speed  150  150 
Flavonoid yield  2164.512  2150.128 
The results obtained by our method have accordance with experimental experience in literature of
In this work, 45 experiments are firstly operated for collecting data related to the production of
Neurallike computing models, such as artificial neural networks [
The authors declare that they have no competing interests.
The research is under the auspices of National Natural Science Foundation of China (nos. 41276135, 31172010, 61272093, 61320106005, 61402187, 61502535, 61572522, and 61572523), Program for New Century Excellent Talents in University (NCET131031), 863 Program (2015AA020925), Fundamental Research Funds for the Central Universities (R1607005A), and China Postdoctoral Science Foundation funded project (2016M592267).