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Table 4 Statistics on the most successful runs of each main optimizer

From: Modeling metabolic networks in C. glutamicum: a comparison of rate laws in combination with various parameter optimization strategies

Model

reversible

irreversible

Algorithm

Population

 

Min

Avg

Std. Dev.

Min

Avg

Std. Dev.

  

GMAK

20.326

20.742

0.501

25.745

34.472

15.285

PSO linear 3, Ï•1 = Ï•2 = 2.05

25

 

20.403

21.787

1.297

25.183

31.694

13.255

DE, f = 0.8, λ = 0.5, CR = 0.3

100

 

21.975

23.812

1.604

24.741

49.045

21.285

binGA, adaptive MUT, no CROSS

250

 

24.321

27.598

2.091

30.704

35.670

3.125

cmaES

(5+25)

GMM

20.280

22.818

2.186

24.857

27.978

9.146

DE, f = 0.8, λ = 0.5, CR = 0.5

100

 

20.312

21.272

0.461

24.553

58.957

17.253

PSO star, Ï•1 = Ï•2 = 2.05

25

 

21.649

24.628

1.801

24.616

40.896

25.881

binGA, adaptive MUT, one-point CROSS

250

 

23.890

26.624

1.851

26.414

31.136

9.052

cmaES

(5+25)

CKMM

20.100

21.434

0.563

21.511

26.077

7.729

PSO grid3, Ï•1 = Ï•2 = 2.05

25

 

20.862

22.499

1.119

21.763

23.603

1.268

DE, f = λ = 0.8, CR = 0.3

100

 

21.431

23.222

1.066

25.632

28.055

2.697

cmaES

(10, 50)

 

22.092

23.353

0.666

25.040

25.346

0.176

binGA, adaptive MUT, no CROS

100

  1. For each model the minimal fitness and the corresponding standard algorithm are listed. The algorithm that achives the best average fitness and the corresponding average fitness are written in the last two columns together with the standard deviation. On the Langevin model, PSO with star topology, Ï•1 = Ï•2 = 2.05 and a population size of 100 is the most successfull algorithm with a fitness of 20.716.