Global optimization of thermal conductivity using stochastic algorithms

Figures & data

Figure 1. Pseudo-code for stochastic algorithms.

Figure 2. (a) Computational domain. (b) Diagram of the plate freezer with instrumentation.

Table 1. Best parameter settings used in experiments.

GAF		DE		SOMA
npop	10	npop	10	npop	10
Selection rate	0.9	fm	0.4	MinDiv	0
Mutation rate	0.2	CR	0.8	PathLength	2.1
Crossover rate	0.8	Generations	100	Migrations	10
Generations	100			Step size	0.21
				PRT	0.5

Figure 3. Convergence for the best fitness of GAF using (a) Equation (20) and (b) Equation (21).

Figure 4. Convergence for the best fitness of DE using (a) Equation (20) and (b) Equation (21).

Figure 5. Convergence for the best fitness of SOMA using (a) Equation (20) and (b) Equation (21).

Figure 6. Convergence for the mean fitness of GAF using (a) Equation (20) and (b) Equation (21).

Figure 7. Convergence for the mean fitness of DE using (a) Equation (20) and (b) Equation (21).

Figure 8. Convergence for the mean fitness of SOMA using (a) Equation (20) and (b) Equation (21).

Table 2. Parameters of Equation (20).

Algorithms	x1	x2	x3	x4	x5	R^2	f
GAF	2.4431	0.0226	−3.1645	0.0051	0.5004	0.6912	2.4520
DE	2.4589	0.0487	−3.2515	−0.0024	0.7106	0.9932	0.3639
SOMA	2.4172	0.4628	−0.4970	−0.0011	0.6610	0.9894	0.4556

Table 3. Parameters of Equation (21).

Algorithms	x1	x2	x3	R^2	f
GAF	0.0261	−0.0009	0.6545	0.9927	0.3753
DE	0.02605	−0.00089	0.6552	0.9928	0.3742
SOMA	0.02604	−0.00115	0.6633	0.9940	0.3635

Table 4. Performance of the optimization algorithms using Equation (20).

Algorithms	Maximum	Mean	Minimum	Standard deviation
GAF	39.9538	21.5216	2.4520	15.7346
DE	30.8646	10.0950	0.3639	11.5921
SOMA	30.8605	7.3836	0.4556	10.7460

Table 5. Performance of the optimization algorithms using Equation (21).

Algorithms	Maximum	Mean	Minimum	Standard deviation
GAF	4.9892	1.6874	0.3753	1.2225
DE	30.8605	3.9682	0.3742	9.4662
SOMA	1.2035	0.5435	0.3639	0.3441
Note on Tables 2–5: the best results of each optimization method are emphasized with bold font.

Figure 9. Thermal conductivity of the carrot purée.

Figure 10. Profiles of temperature in carrot purée for T_∞ = −38.5°C and h = 400 W m⁻²°C⁻¹.

Table 6. Computing time (s) required for the optimization algorithms selected in this study.

	Algorithms
Equations	GAF	DE	SOMA
(20)	3091.0	2386.1	2638.7
(21)	3069.7	2305.6	2315.4