Solution of an inverse adsorption problem with an epidemic genetic algorithm and the generalized extremal optimization algorithm

Figures & data

Figure 1. The canonical GEO algorithm.

Table 1. Process and physico-chemical parameters for Chase's experiment with lisozyme 26.

Parameter	Value
H–column height (cm)	10.4
Ac–column cross-section (cm^2)	0.785
Q–volumetric flow rate (mL min^−1)	1.0
C0–adsorbate concentration at the column inlet (mg mL^−1)	0.1
qm–maximum adsorption capacity (mg mL^−1)	14
kd–dissociation rate constant (mg mL^−1)	0.025
k1–adsorption rate constant (mL mg · min^−1)	0.20

Table 2. Estimates for k_d and q_m for lisozyme using GEO with τ = 1.25 and Chase's experimental data 26. d = 0.11514 (Equation (13)).

Run	kd (mg mL^−1)	qm (mg mL^−1)	S Equation (12) (mg mL^−1)^2
1	0.0272	11.2862	0.0251
2	0.0335	11.8862	0.0243
3	0.0350	14.3182	0.0233
4	0.0287	14.0856	0.0327
5	0.0258	13.2334	0.0278
6	0.0325	12.0309	0.0231
7	0.0321	12.7347	0.0254
8	0.0215	12.7701	0.0236
9	0.0325	13.9952	0.0234
10	0.0316	11.0701	0.0235
Average μ	0.0300	12.7411
Standard deviation σ	0.0042	1.1669
	13.82	9.16

Table 3. Estimates for k_d and q_m for lisozyme using EGA with an initial population of 100 individuals, Chase's experimental data 26 and n_e = 3 and f_e = 0.1. d = 0.047396 (Equation (13)).

Run	kd (mg mL^−1)	qm (mg mL^−1)	S Equation (12) (mg mL^−1)^2
1	0.0372	14.0389	0.0240
2	0.0455	14.1111	0.0369
3	0.0475	14.2639	0.0270
4	0.0448	14.1780	0.0210
5	0.0446	14.1892	0.0205
6	0.0444	14.1681	0.0205
7	0.0406	14.0509	0.0208
8	0.0397	14.0909	0.0221
9	0.0374	13.9978	0.0241
10	0.0395	14.0770	0.0215
Average μ	0.0421	14.1166
Standard deviation σ	0.0037	0.0817
	8.74	0.58

Figure 2. Dispersion of the results obtained with GEO.

Figure 3. Dispersion of the results obtained with EGA.

Figure 4. Chase's experimental data 26 and calculated breakthrough curves using the average of the estimated values for q_m and k_d with GEO and EGA (Tables 2 and 3).

Table 4. Estimated values for k_d, being q_m fixed at 14 mg mL⁻¹, after 10 runs of GEO and EGA.

	GEO	EGA
(mg mL^−1)	0.0261	0.0381
σkd (mg mL^−1)	0.0009	4.438×10^−5
	3.34	0.12

Figure 5. Chase's experimental data 26 and calculated breakthrough curves using the average estimated values for k_d with GEO and EGA being q_m fixed at 14 mg mL⁻¹ (Table 4).

Table 5. Estimated values for q_m, being k_d fixed, after 10 runs of GEO.

kd (mg mL^−1)	(mg mL^−1)	σqm (mg mL^−1)
0.015	14.92	0.148	0.99
0.020	14.52	0.137	0.94
0.025	14.10	0.184	1.31
0.030	14.01	0.153	1.09
0.035	13.99	0.139	1.00

Table 6. Estimated values for q_m, being k_d fixed, after 10 runs of EGA.

kd (mg mL^−1)	(mg mL^−1)	σqm (mg mL^−1)
0.015	15.0	0	0
0.020	14.507	0.0035	0.02
0.025	14.201	0.0014	0.01
0.030	14.046	0.0006	0.005
0.035	14.007	0.0004	0.003

Figure 6. Chase's experimental data 26 and calculated breakthrough curves using the fixed value of k_d and the average estimated values for q_m with GEO (Table 5).

Figure 7. Chase's experimental data 26 and calculated breakthrough curves using the fixed value of k_d and the average estimated values for q_m with EGA (Table 6).

Chase, HA, 1984. Prediction of the performance of preparative affinity chromatography, J. Chromat. 297 (1984), pp. 179–202.

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