General overview of a genetic algorithm.
Example of selection types procedure in genetic algorithms: (a) Observed fitness for a hypothetical seven catalyst population. (b) 40% threshold selection only individuals above the threshold can be selected. (c) Wheel selection probability; area parts (probability of being selected) are proportional to the fitness value. (d) Ranking selection probability; area parts are proportional to the rank of the individual.
Crossover types in genetic algorithms: (a) 1-Single point crossover, (b) 2-multipoint crossover, and (c) uniform crossover with 0.5 gene-flip probability.
The mutation in genetic algorithms: a gene is randomly modified.
(Color online) Screenshot of a OptiCat software: a genetic algorithm is illustrated.
(Color online) Average of the mean and of the best catalysts over 40 runs as a function of the generation number for three representative GA configurations 9, 16, and 11. The performance evaluation were performed on the smooth (S), noisy (N), and very noisy virtual benchmark (vN). Vertical lines represent the 95% confidence interval.
(Color online) Effects of the modalities on the criteria assessment for virtual benchmark.
(Color online) Effects of the modalities on the robustness (a) and convergence speed (b) for virtual benchmark on three different noise levels: without noise, with smooth noise, and very noisy.
Catalyst elemental composition search space in Selox.
(Left) Experimental design for a NM, TM and support for Selox real benchmark. The support amount is fixed. The dots represent the experimental points. (right) Example of the ternary Pt-V-Ti at subresponse surface. .
(Color online) Selox response surface for (a) conversion: and (b) Selectivity: .
Desirability functions for (left) CO conversion in SELOX , (right) CO2 selectivities , and (c) temperature . if and if ; ; .
(Color online) Selox benchmark landscape after applying the desirability functions .
GA configuration optimization for Selox benchmark: Parameters: 15% elitism (yes, no); population size (8, 16, 24, 48); crossover: 1 multi-point (MP-1), 3-multi-point (MP-3), 20% exchanges uniform (U-20) and 50% exchanges uniform (U-50); and selection type: wheel (Whe), threshold (Thr), tournament (Tour), and ranking (Rank). A crossover probability of 70% and mutation probability of 0.1 were used. Three individuals in tournament, 40% in the threshold, and a selective pressure of 1 for wheel and ranking selection types were used.
Optimization profile for the selected configuration in Selox benchmark: 15% elitism, tournament selection (three individuals per pool) and 1-point crossover, according to different population sizes. A crossover probability of 70% and mutation probability of 0.1 were considered. (a) Evolutionary behavior considering the total amount of catalysts and (b) with respect to the number of generations.
Overview of hybridization GA-KDGA.
Hybrid GA-KDGA evolutionary behavior for Selox benchmark.
Hybrid GA-KDGA evolutionary behavior for virtual benchmark.
Experimental planning for the screening of GA configurations (designed by the software Nemrodw) and corresponding coding values for the variance analysis for virtual benchmark.
Experimental planning for the screening of GA configurations (designed by the software Nemrodw) and corresponding coding values for the variance analysis for real Selox benchmark.
Catalyst solutions found during the GA runs for the Selox benchmark.
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