Optimization of medium composition for two-step fermentation of vitamin C based on artificial neural network–genetic algorithm techniques

Figures & data

Table 1. Design matrix and results obtained in the central composite design (CCD).

						2-KGA production (g·L^−1)
Standard order	χ1 L-sorbose (g·L^−1)	χ2 Urea (g·L^−1)	χ3 Corn steep liquor (g·L^−1)	χ4 CaCO3 (g·L^−1)	χ5 MgSO4 (g·L^−1)	Observed	RSM	ANN
1	70(–1)	10(–1)	14(–1)	3(–1)	0.3(1)	55.76	56.42	55.77
2	90(1)	10(–1)	14(–1)	3(–1)	0.1(–1)	63.46	64.94	63.42
3	70(–1)	14(1)	14(–1)	3(–1)	0.1(–1)	56.53	58.04	56.56
4	90(1)	14(1)	14(–1)	3(–1)	0.3(1)	63.84	62.33	63.85
5	70(–1)	10(–1)	16(1)	3(–1)	0.1(–1)	60.22	59.17	60.49
6	90(1)	10(–1)	16(1)	3(–1)	0.3(1)	66.12	65.73	66.17
7	70(–1)	14(1)	16(1)	3(–1)	0.3(1)	65.42	65.06	65.49
8	90(1)	14(1)	16(1)	3(–1)	0.1(–1)	64.22	64.68	64.27
9	70(–1)	10(–1)	14(–1)	5(1)	0.1(–1)	56.92	57.79	56.96
10	90(1)	10(–1)	14(–1)	5(1)	0.3(1)	56.18	56.75	56.19
11	70(–1)	14(1)	14(–1)	5(1)	0.3(1)	57.12	58.68	57.19
12	90(1)	14(1)	14(–1)	5(1)	0.1(–1)	57.14	59.52	57.19
13	70(–1)	10(–1)	16(1)	5(1)	0.3(1)	66.15	65.16	66.18
14	90(1)	10(1)	16(1)	5(1)	0.1(–1)	63.84	63.66	63.94
15	70(–1)	14(1)	16(1)	5(1)	0.1(–1)	60.38	60.23	60.39
16	90(1)	14(1)	16(1)	5(1)	0.3(1)	65.76	66.27	65.78
17	60(–2)	12(0)	14(0)	4(0)	0.2(0)	61.23	61.45	61.53
18	100(2)	12(0)	14(0)	4(0)	0.2(0)	71.15	68.43	71.12
19	80(0)	8(–2)	14(0)	4(0)	0.2(0)	61.07	61.36	60.92
20	80(0)	16(2)	14(0)	4(0)	0.2(0)	66.12	65.73	66.13
21	80(0)	12(0)	10(–2)	4(0)	0.2(0)	62.12	57.29	62.21
22	80(0)	12(0)	18(2)	4(0)	0.2(0)	62.69	65.01	62.72
23	80(0)	12(0)	14(0)	2(–2)	0.2(0)	66.07	61.36	66.14
24	80(0)	12(0)	14(0)	6(2)	0.2(0)	63.84	66	63.81
25	80(0)	12(0)	14(0)	4(0)	0(–2)	63.26	61.85	63.32
26	80(0)	12(0)	14(0)	4(0)	0.4(2)	66.19	65.1	66.14
27	80(0)	12(0)	14(0)	4(0)	0.2(0)	67.3	68.36	68.06
28	80(0)	12(0)	14(0)	4(0)	0.2(0)	66.92	68.36	68.06
29	80(0)	12(0)	14(0)	4(0)	0.2(0)	67.69	68.36	68.06
30	80(0)	12(0)	14(0)	4(0)	0.2(0)	68.46	68.36	68.06
31	80(0)	12(0)	14(0)	4(0)	0.2(0)	68.07	68.36	68.06
32	80(0)	12(0)	14(0)	4(0)	0.2(0)	69.22	68.36	68.06

Table 2. Comparison of 2-KGA-producing ability of K. vulgare with different companion strains.

Mixed strains	K. vulgare + B. megaterium 2980	K. vulgare + B. subtilis A9
2-KGA production (g·L^−1)	55.38	68.94

Table 3. ANOVA of the fitted quadratic model.

Source	Sum of squares	Degrees of freedom	F value	Prob > F
Model	466.82	20	3.27	0.0237
χ1	73.15	1	10.25	0.0084
χ2	5.86	1	0.82	0.3842
χ3	89.32	1	12.52	0.0046
χ4	11.40	1	1.60	0.2323
χ5	15.84	1	2.22	0.1643
χ1χ2	4.854E-02	1	8.07E-03	0.9300
χ1χ3	2.66	1	0.37	0.5541
χ1χ4	18.84	1	2.64	0.1325
χ1χ5	3.20	1	0.45	0.5166
χ2χ3	0.51	1	0.072	0.7939
χ2χ4	3.19	1	0.45	0.5177
χ2χ5	12.43	1	1.74	0.2137
χ3χ4	9.58	1	1.34	0.2711
χ3χ5	15.88	1	2.23	0.1638
χ4χ5	3.03E-03	1	4.24E-04	0.9839
${\chi }_1^2$	21.43	1	3.00	0.1109
${\chi }_2^2$	66.31	1	9.30	0.0111
${\chi }_3^2$	95.15	1	13.34	0.0038
${\chi }_4^2$	39.71	1	5.57	0.0379
${\chi }_5^2$	43.73	1	6.14	0.0308
Residual	78.47	11
Lack of fit	75.03	6	18.19	0.0030

Figure 1. Training course of BP neural network.

Figure 2. Comparison of experimental production and predicted production by RSM and ANN.

Figure 3. Evolution of the best and mean fitness in the GA.