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Library design using genetic algorithms for catalyst discovery and optimization
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10.1063/1.1906086
/content/aip/journal/rsi/76/6/10.1063/1.1906086
http://aip.metastore.ingenta.com/content/aip/journal/rsi/76/6/10.1063/1.1906086

Figures

Image of FIG. 1.
FIG. 1.

General overview of a genetic algorithm.

Image of FIG. 2.
FIG. 2.

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.

Image of FIG. 3.
FIG. 3.

Crossover types in genetic algorithms: (a) 1-Single point crossover, (b) 2-multipoint crossover, and (c) uniform crossover with 0.5 gene-flip probability.

Image of FIG. 4.
FIG. 4.

The mutation in genetic algorithms: a gene is randomly modified.

Image of FIG. 5.
FIG. 5.

(Color online) Screenshot of a OptiCat software: a genetic algorithm is illustrated.

Image of FIG. 6.
FIG. 6.

(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.

Image of FIG. 7.
FIG. 7.

(Color online) Effects of the modalities on the criteria assessment for virtual benchmark.

Image of FIG. 8.
FIG. 8.

(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.

Image of FIG. 9.
FIG. 9.

Catalyst elemental composition search space in Selox.

Image of FIG. 10.
FIG. 10.

(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. .

Image of FIG. 11.
FIG. 11.

(Color online) Selox response surface for (a) conversion: and (b) Selectivity: .

Image of FIG. 12.
FIG. 12.

Desirability functions for (left) CO conversion in SELOX , (right) CO2 selectivities , and (c) temperature . if and if ; ; .

Image of FIG. 13.
FIG. 13.

(Color online) Selox benchmark landscape after applying the desirability functions .

Image of FIG. 14.
FIG. 14.

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.

Image of FIG. 15.
FIG. 15.

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.

Image of FIG. 16.
FIG. 16.

Overview of hybridization GA-KDGA.

Image of FIG. 17.
FIG. 17.

Hybrid GA-KDGA evolutionary behavior for Selox benchmark.

Image of FIG. 18.
FIG. 18.

Hybrid GA-KDGA evolutionary behavior for virtual benchmark.

Tables

Generic image for table
Table I.

Experimental planning for the screening of GA configurations (designed by the software Nemrodw) and corresponding coding values for the variance analysis for virtual benchmark.

Generic image for table
Table II.

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.

Generic image for table
Table III.

Catalyst solutions found during the GA runs for the Selox benchmark.

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/content/aip/journal/rsi/76/6/10.1063/1.1906086
2005-05-18
2014-04-24
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Library design using genetic algorithms for catalyst discovery and optimization
http://aip.metastore.ingenta.com/content/aip/journal/rsi/76/6/10.1063/1.1906086
10.1063/1.1906086
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