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1 Results of ICrA---Model Parameter Identification Results

1 Results of ICrA---Model Parameter Identification Results

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InterCriteria Analysis of Genetic Algorithms Performance



247



Table 2 Observed μC,C , νC,C values of criteria pairs: sorted by μC,C values of average results

Obtained μC,C , νC,C values in case of

Average results

Worst results



Criteria pairs

C1

C2

C1

C3

C1

C3

C2

C2

C1

C4



↔ C2

↔ C4

↔ C4

↔ C4

↔ C3

↔ C5

↔ C3

↔ C5

↔ C5

↔ C5



0.91, 0.08

0.78, 0.21

0.74, 0.26

0.55, 0.44

0.41, 0.58

0.38, 0.60

0.36, 0.62

0.27, 0.71

0.26, 0.74

0.11, 0.89



0.79, 0.20

0.84, 0.15

0.88, 0.12

0.33, 0.66

0.34, 0.65

0.64, 0.35

0.18, 0.80

0.22, 0.77

0.14, 0.86

0.07, 0.93



Best results

0.74, 0.19

0.53, 0.44

0.63, 0.33

0.71, 0.26

0.49, 0.44

0.30, 0.68

0.35, 0.59

0.51, 0.46

0.36, 0.59

0.25, 0.75



Case of best results

When applying ICrA on (IMbest )T , the resulting two IMs—IMμ5 (μC,C ) and IMν6

(νC,C ), are as follows:



C1

C2

μ

IM5 =

C3

C4

C5



C1

1

0.74

0.49

0.63

0.36



C2

0.74

1

0.35

0.53

0.51



C3

0.49

0.35

1

0.71

0.30



C4

0.63

0.53

0.71

1

0.25



C5

C1 C2

0.36

C1 0 0.19

0.51

C 0.19 0

, IMν6 = 2

0.30

C3 0.44 0.59

0.25

C4 0.33 0.44

1

C5 0.59 0.46



C3

0.44

0.59

0

0.26

0.68



C4

0.33

0.44

0.26

0

0.75



C5

0.59

0.46

0.68

0.75

0



Criteria relation, sorted by μC,C values in the case of average results, are presented

in Table 2. The resulting ICrA relations are compared with the obtained values of

μC,C , νC,C in the cases of best and worst results. The results show that there are

some differences between ICrA evaluation for the degrees of “agreement” μC,C

and the degrees of “disagreement” νC,C in the three cases—average, best and worst

results. The same results are graphically presented in Figs. 1 and 2. In the figures the

observed differences in the obtained μC,C and νC,C values can be seen more clearly.

For example, Fig. 1 shows that for the criteria pairs C4 ↔ C5 , C1 ↔ C5 , C1 ↔ C3

and C3 ↔ C4 the obtained μC,C values are higher for the best results compared to the

average and worst ones. The largest values of μC,C for the pairs C2 ↔ C4 , C1 ↔ C4

and C3 ↔ C5 make an impression, too. Figure 2 is a mirror image of Fig. 1 with

the exceptions for the pairs where there is a degree of “uncertainty” πC,C (Eq. (4)).

The observed “uncertainty” is presented in Table 3. In this case, the obtained πC,C

values are very small and we can assume that the results are adequate and there is

no substantial uncertainty in them.



248



O. Roeva et al.

1,000



average estimates



0,900



worst esimates



best estimates



0,800

0,700

0,600

0,500

0,400

0,300

0,200

0,100

0,000

C1-C2 C2-C4 C1-C4 C3-C4 C1-C3 C3-C5 C2-C3 C2-C5 C1-C5 C4-C5



Fig. 1 Degrees of “agreement” (μC,C values) for all cases

1.000

0.900



average estimates



worst esimates



best estimates



0.800

0.700

0.600

0.500

0.400

0.300

0.200

0.100

0.000

C1-C2 C2-C4 C1-C4 C3-C4 C1-C3 C3-C5 C2-C3 C2-C5 C1-C5 C4-C5



Fig. 2 Degrees of “disagreement” (νC,C values) for all cases



Taking into account the stochastic nature of GAs, we will consider the ICrA results

in the case of average estimates as those with the highest significance. For the analysis

of the results, we use the scheme proposed in [7] for defining the consonance and

dissonance between each pair of criteria. Further discussion is made following the

scheme presented in Table 4.

In the case of the average values of the examined criteria, we found the following

pair dependencies:

• There is no observed strong positive consonance or strong negative consonance

between any of the ten criteria pairs. Since the observed values depend on the

number of objects if we can expand their number, it is possible to obtain values in

these intervals.

• For the pair C4 ↔ C5 (i.e. T ↔ J ) a negative consonance is identified. Such

dependence is logical—for a large number of algorithm iterations (i.e. greater

computation time T ) it is more likely to find a more accurate solution, i.e. smaller

value of J .



InterCriteria Analysis of Genetic Algorithms Performance



249



Table 3 Observed πC,C values of criteria pairs

Criteria pairs

C1

C1

C1

C1

C2

C2

C2

C3

C3

C4



↔ C2

↔ C3

↔ C4

↔ C5

↔ C3

↔ C4

↔ C5

↔ C4

↔ C5

↔ C5



Obtained πC,C values in case of

Average results

Worst results



Best results



0.011

0.011

0

0

0.022

0.011

0.011

0.011

0.011

0



0.077

0.066

0.044

0.044

0.055

0.033

0.033

0.022

0.022

0



Table 4 Consonance and

dissonance scale



0.011

0.011

0

0

0.022

0.011

0.011

0.011

0.011

0



Interval of μC,C , %



Meaning



[0–5]

(5–15]

(15–25]

(25–33]

(33–43]

(43–57]

(57–67]

(67–75]

(75–85]

(85–95]

(95–100]



Strong negative consonance

Negative consonance

Weak negative consonance

Weak dissonance

Dissonance

Strong dissonance

Dissonance

Weak dissonance

Weak positive consonance

Positive consonance

Strong positive consonance



• The pairs C2 ↔ C5 (i.e. k S ↔ T ) show identical results—these criteria are in

weak dissonance. The third model parameter Y S/ X and T are in dissonance. The

conclusion is that the total computation time is not dependent solely on one of the

model parameters. Logically, the triple of these parameters should be in consonance with T .

• For the pairs C1 ↔ C3 (i.e. μmax ↔ Y S/ X ) and C2 ↔ C3 (i.e. k S ↔ Y S/ X ) a dissonance is observed. Considering the physical meaning of the model parameters [8],

it is clear that there is no dependence between these criteria. A strong correlation

is expected between criteria C1 ↔ C2 (i.e. μmax ↔ k S ) [8]. The results confirmed

these expectation—these criteria are in a positive consonance.

• The observed low value of μC3 ,C4 , i.e. strong dissonance between Y S/ X ↔ J show

the low sensitivity of this model parameter. According to [17], the parameter Y S/ X

has lower sensitivity compared to parameter μmax .



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O. Roeva et al.



• Due to the established strong correlation between criteria C1 ↔ C2 (i.e. μmax ↔

k S ), we observe that C1 ↔ C4 (i.e. μmax ↔ J ) and C2 ↔ C4 (i.e. k S ↔ J ) are

in respectively weak dissonance and weak positive consonance. Similarly to the

relations with T , the conclusion is that the accuracy of the criterion is not dependent

solely on one of the model parameters. Logically, the triple of these parameters

should be in consonance (or strong consonance) with the criterion value. Moreover,

taking into account the parameters sensitivity, it is clear that the more sensitive

parameter will be more linked to the value of J .

Due to the stochastic nature of GAs considered here, we observed some different

criteria dependences in the other two cases—of the worst and of the best results:

• In the case of the worst results, we found a weaker relation between C1 ↔

C2 , C3 ↔ C4 , C2 ↔ C3 , C1 ↔ C5 , C2 ↔ C5 and C4 ↔ C5 . For the pairs C1 ↔

C4 , C2 ↔ C4 and C3 ↔ C5 , we observed a higher value of μC,C . Compared to the

case of the average results, there are no large, strongly manifested discrepancies.

In case of discrepancy, the considered criteria pair appears in an adjacent scale

according to Table 4. For example, in the case of average results the pair C1 ↔ C2

is in positive consonance, while in the case of the worst results it is in weak positive

consonance.

• In the case of the best results we identify the same results—in case of discrepancy, the considered criteria pairs appear in an adjacent scale. However, in this

case we observed some larger discrepancies. Taking into account the nature of

the GA, we consider that the results in case of average criteria values have the

highest significance. Therefore, the best and the worst results are of a lower rank

or importance.



4.2 Results of ICrA—Genetic Algorithms Performance

Based on the presented above results of ICrA, we can analyze only the relations of the

considered criteria (C1 , C2 , . . . , C5 ), i.e. the relation between the model parameters

(μmax , k S and Y S/ X ) and GA outcomes (J and T ). We cannot find any connections

and dependencies between the 14 differently tuned GAs. Such a relation will be very

useful information about the choice of an optimal tuned GA for the considered model

parameter identification problem.

Here, we propose a schema for ICrA of GAs performance. Based on available data

(model parameters estimates, and objective function value and computation time for

30 runs of all 14 GAs), the ICrA of GAs performance is performed following the

schema:

Step 1.

Step 2.



Perform ICrA based on the IMs IMG A5 , IMG A10 , IMG A20 , . . . , IMG A100 ,

IMG A110 , IMG A150 , IMG A200 .

Perform ICrA of ICrA results from Step 1.



InterCriteria Analysis of Genetic Algorithms Performance



251



In Step 1 we obtain 14 IMs for μC,C and 14 IMs for νC,C of the criteria pairs.

Therefore, for every criteria pair C, C we have 14 different μC,C estimates depending on the applied GA. Using these results, we construct new IM with the following

objects: the 10 criteria pairs (C1 ↔ C2 , C1 ↔ C3 , C1 ↔ C4 , C1 ↔ C5 , C2 ↔ C3 ,

C2 ↔ C4 , C2 ↔ C5 , C3 ↔ C4 , C3 ↔ C5 , C4 ↔ C5 ) and with the following criteria: the 14 differently tuned GAs (G A5 , G A10 , G A20 , . . . , G A100 , G A110 , G A150 ,

G A200 ). The resulting IM contains the μC,C values obtained in Step 1. In Step 2, we

perform ICrA of the ICrA results from Step 1. Now we can analyze the correlations

between all the considered GAs applied for the model parameter identification of E.

coli fed-batch process (Eqs. (5)–(8)).

ICrA of ICrA: Step 1

The ICrA is performed for the following 14 IMs:

IMG A5 , IMG A10 , IMG A20 , . . . , IMG A100 , IMG A110 , IMG A150 , IMG A200 .

The resulting IMs that determine the degrees of “agreement” (μC,C ) and degrees

of “disagreement” (νC,C ) between criteria are as follows:



μ

IMG A5



IMμG A10



μ



IMG A20



C1

C2

=

C3

C4

C5



C1

1

0.88

0.40

0.84

0.33



C2

0.88

1

0.31

0.78

0.31



C3

0.40

0.31

1

0.47

0.58



C4

0.84

0.78

0.47

1

0.40



C5

C1 C2

0.33

C1 0 0.12

0.31

C2 0.12 0

ν

, IMG A5 =

0.58

C3 0.60 0.68

0.40

C4 0.16 0.22

1

C5 0.65 0.67



C3

0.60

0.68

0

0.53

0.40



C4

0.16

0.22

0.53

0

0.58



C5

0.65

0.67

0.40

0.58

0



C1

C2

=

C3

C4

C5



C1

1

0.94

0.26

0.91

0.30



C2

0.94

1

0.24

0.90

0.29



C3

0.26

0.24

1

0.27

0.61



C4

0.91

0.90

0.27

1

0.28



C5

C1 C2

0.30

C1 0 0.05

0.29

C 0.05 0

, IMνG A10 = 2

0.61

C3 0.73 0.75

0.28

C4 0.09 0.10

1

C5 0.67 0.68



C3

0.73

0.75

0

0.72

0.36



C4

0.09

0.10

0.72

0

0.70



C5

0.67

0.68

0.36

0.70

0



C1

C2

=

C3

C4

C5



C1

1

0.97

0.23

0.90

0.22



C2

0.97

1

0.24

0.91

0.22



C3

0.23

0.24

1

0.32

0.70



C4

0.90

0.91

0.32

1

0.28



C5

C1 C2

0.22

C1 0 0.03

0.22

C 0.03 0

, IMνG A20 = 2

0.70

C3 0.74 0.73

0.28

C4 0.10 0.08

1

C5 0.76 0.75



C3

0.74

0.73

0

0.66

0.25



C4

0.10

0.08

0.66

0

0.70



C5

0.76

0.75

0.25

0.70

0



252



μ



IMG A30



μ



IMG A40



μ



IMG A50



IMμG A60



μ



IMG A70



O. Roeva et al.



C1

C2

=

C3

C4

C5



C1

1

0.94

0.37

0.80

0.33



C2

0.94

1

0.34

0.80

0.30



C3

0.37

0.34

1

0.48

0.53



C4

0.80

0.80

0.48

1

0.29



C5

C1 C2

0.33

C1 0 0.04

0.30

C 0.04 0

, IMνG A30 = 2

0.53

C3 0.61 0.62

0.29

C4 0.20 0.18

C5 0.64 0.66

1



C3

0.61

0.62

0

0.49

0.42



C4

0.20

0.18

0.49

0

0.67



C5

0.64

0.66

0.42

0.67

0



C1

C2

=

C3

C4

C5



C1

1

0.94

0.30

0.82

0.23



C2

0.94

1

0.27

0.80

0.24



C3

0.30

0.27

1

0.38

0.62



C4

0.82

0.80

0.38

1

0.21



C5

C1 C2

C1 0 0.04

0.23

C 0.04 0

0.24

, IMνG A40 = 2

C3 0.67 0.69

0.62

C4 0.17 0.18

0.21

C5 0.73 0.72

1



C3

0.67

0.69

0

0.60

0.32



C4

0.17

0.18

0.60

0

0.75



C5

0.73

0.72

0.32

0.75

0



C1

C2

=

C3

C4

C5



C1

1

0.93

0.48

0.80

0.35



C2

0.93

1

0.45

0.80

0.32



C3

0.48

0.45

1

0.57

0.54



C4

0.80

0.80

0.57

1

0.35



C5

C1 C2

0.35

C1 0 0.05

0.32

C 0.05 0

, IMνG A50 = 2

0.54

C3 0.50 0.51

0.35

C4 0.19 0.18

1

C5 0.62 0.64



C3

0.50

0.51

0

0.42

0.42



C4

0.19

0.18

0.42

0

0.63



C5

0.62

0.64

0.42

0.63

0



C1

C2

=

C3

C4

C5



C1

1

0.93

0.48

0.77

0.26



C2

0.93

1

0.42

0.75

0.26



C3

0.48

0.42

1

0.57

0.52



C4

0.77

0.75

0.57

1

0.32



C1 C2

C5

0.26

C1 0 0.05

0.26

C2 0.05 0

ν

, IMG A60 =

0.52

C3 0.50 0.54

0.32

C4 0.23 0.23

1

C5 0.73 0.71



C3

0.50

0.54

0

0.41

0.45



C4

0.23

0.23

0.41

0

0.66



C5

0.73

0.71

0.45

0.66

0



C1

C2

=

C3

C4

C5



C1

1

0.95

0.43

0.75

0.28



C2

0.95

1

0.40

0.72

0.26



C3

0.43

0.40

1

0.54

0.54



C4

0.75

0.72

0.54

1

0.27



C5

C1 C2

0.28

C1 0 0.02

0.26

C 0.02 0

, IMνG A70 = 2

0.54

C3 0.54 0.54

0.27

C4 0.25 0.25

1

C5 0.70 0.70



C3

0.54

0.54

0

0.43

0.41



C4

0.25

0.25

0.43

0

0.71



C5

0.70

0.70

0.41

0.71

0



InterCriteria Analysis of Genetic Algorithms Performance



μ



IMG A80



μ



IMG A90



C1

C2

=

C3

C4

C5



C1

1

0.91

0.43

0.81

0.28



C2

0.91

1

0.40

0.81

0.26



C3

0.43

0.40

1

0.53

0.50



C4

0.81

0.81

0.53

1

0.32



C5

C1 C2

0.28

C1 0 0.07

0.26

C 0.07 0

, IMνG A80 = 2

0.50

C3 0.54 0.57

0.32

C4 0.19 0.17

C5 0.71 0.71

1



C3

0.54

0.57

0

0.45

0.47



C4

0.19

0.17

0.45

0

0.66



C5

0.71

0.71

0.47

0.66

0



C1

C2

=

C3

C4

C5



C1

1

0.90

0.51

0.81

0.32



C2

0.90

1

0.45

0.77

0.29



C3

0.51

0.45

1

0.62

0.43



C4

0.81

0.77

0.62

1

0.33



C5

C1 C2

0.32

C1 0 0.08

0.29

C 0.08 0

, IMνG A90 = 2

0.43

C3 0.46 0.51

0.33

C4 0.18 0.20

1

C5 0.66 0.67



C3

0.46

0.51

0

0.35

0.52



C4

0.18

0.20

0.35

0

0.65



C5

0.66

0.67

0.52

0.65

0



100



C1

C2

=

C3

C4

C5



C1

1

0.90

0.54

0.59

0.33



C2

0.90

1

0.47

0.57

0.30



C3

0.54

0.47

1

0.66

0.46



C4

0.59

0.57

0.66

1

0.39



C5

C1

0.33

C1 0

0.30

C 0.07

, IMνG A100 = 2

0.46

C3 0.44

0.39

C4 0.41

1

C5 0.65



C2

0.07

0

0.49

0.39

0.66



C3

0.44

0.49

0

0.33

0.51



C4

0.41

0.39

0.33

0

0.60



C5

0.65

0.66

0.51

0.60

0



110



C1

C2

=

C3

C4

C5



C1

1

0.91

0.47

0.73

0.33



C2

0.91

1

0.40

0.72

0.30



C3

0.47

0.40

1

0.57

0.49



C4

0.73

0.72

0.57

1

0.35



C5

C1

0.33

C1 0

0.30

C 0.06

, IMνG A110 = 2

0.49

C3 0.51

0.35

C4 0.27

1

C5 0.66



C2

0.06

0

0.56

0.26

0.67



C3

0.51

0.56

0

0.41

0.49



C4

0.27

0.26

0.41

0

0.64



C5

0.66

0.67

0.49

0.64

0



150



C1

C2

=

C3

C4

C5



C1

1

0.91

0.47

0.75

0.36



C2

0.91

1

0.42

0.72

0.32



C3

0.47

0.42

1

0.58

0.60



C4

0.75

0.72

0.58

1

0.37



C5

C1 C2

0.36

C1 0 0.05

0.32

C 0.05 0

, IMνG A150 = 2

0.60

C3 0.51 0.54

0.37

C4 0.24 0.25

1

C5 0.61 0.63



C3

0.51

0.54

0

0.40

0.36



C4

0.24

0.25

0.40

0

0.60



C5

0.61

0.63

0.36

0.60

0



μ



IMG A



μ



IMG A



μ



IMG A



253



254



O. Roeva et al.



μ



IMG A



200



C1

C2

=

C3

C4

C5



C1

1

0.89

0.40

0.53

0.23



C2

0.89

1

0.37

0.53

0.25



C3

0.40

0.37

1

0.71

0.49



C4

0.53

0.53

0.71

1

0.39



C5

C1

0.23

C1 0

0.25

C 0.07

, IMνG A200 = 2

0.49

C3 0.57

0.39

C4 0.46

1

C5 0.76



C2

0.07

0

0.57

0.44

0.71



C3

0.57

0.57

0

0.28

0.49



C4

0.46

0.44

0.28

0

0.61



C5

0.76

0.71

0.49

0.61

0



According to the proposed schema, the obtained 14 different results for the degrees

μ

of “agreement” μC,C (IMG Ai ) of the considered 10 criteria pairs are used to construct

the following IM IMG A (Eq. (27)):

IMG A =



G A5

G A10

G A20

G A30

G A40

G A50

G A60

G A70

G A80

G A90

G A100

G A110

G A150

G A200



C1 ↔ C2 C1 ↔ C3 C1 ↔ C4 C1 ↔ C5 C2 ↔ C3 C2 ↔ C4 C2 ↔ C5 C3 ↔ C4 C3 ↔ C5 C4 ↔ C5

0.88

0.40

0.84

0.33

0.31

0.78

0.31

0.47

0.58

0.40

0.94

0.26

0.91

0.30

0.24

0.90

0.29

0.27

0.61

0.28

0.97

0.23

0.90

0.22

0.24

0.91

0.22

0.32

0.70

0.28

0.94

0.37

0.80

0.33

0.34

0.80

0.30

0.48

0.53

0.29

0.94

0.30

0.82

0.23

0.27

0.80

0.24

0.38

0.62

0.21

0.93

0.48

0.80

0.35

0.45

0.80

0.32

0.57

0.54

0.35

0.93

0.48

0.77

0.26

0.42

0.75

0.26

0.57

0.52

0.32

0.95

0.43

0.75

0.28

0.40

0.72

0.26

0.54

0.54

0.27

0.91

0.43

0.81

0.28

0.40

0.81

0.26

0.53

0.50

0.32

0.90

0.51

0.81

0.32

0.45

0.77

0.29

0.62

0.43

0.33

0.90

0.54

0.59

0.33

0.47

0.57

0.30

0.66

0.46

0.39

0.91

0.47

0.73

0.33

0.40

0.72

0.30

0.57

0.49

0.35

0.91

0.47

0.75

0.36

0.42

0.72

0.32

0.58

0.60

0.37

0.89

0.40

0.53

0.23

0.37

0.53

0.25

0.71

0.49

0.39



(27)

It will be interesting to compare the obtained μC,C values for each criteria pair

with those obtained in the first case—ICrA of the model parameter identification

results. In the next figures we give the comparison for some of the criteria pairs. We

compare the 14 μC,C values with the μC,C values for the average, the worst and the

best results from the model parameters identification procedures.

In Fig. 3, μC,C values for the criteria pair C1 ↔ C2 is compared. As can be seen,

the μC,C values are similar in all the cases. The average μC,C value of 14 GAs results

is very close to the μC,C value for the average identification results. In the case of

comparison of the μC,C values criteria pair C1 ↔ C3 , there are some fluctuations,

but the average μC,C value of 14 GAs results is equal to the μC,C value for the

average identification results—μC,C = 0.41 (see Fig. 4). Almost the same are the

results about the criteria pair C2 ↔ C3 presented in Fig. 5—average μC,C = 0.36.

As the criteria pairs C1 ↔ C2 and C1 ↔ C3 represent the relations of the three model

parameters (μmax , k S and Y S/ X ), it is logical to obtain closer results in all cases.

On the other hand, the largest differences in the μC,C values are observed for

the pair C4 ↔ C5 (Fig. 6). Due to the stochastic nature of the GAs, it is obvious

that the relations between objective value and computation time are unpredictable.

The GA could solve the problem with a high accuracy for a very short time if the

algorithm initial solutions are close to the real ones. Conversely, the GA could reach



InterCriteria Analysis of Genetic Algorithms Performance

1.00

0.80

0.60

0.40

0.20

0.00



Fig. 3 μC1 ,C2 -values for all cases

1.00

0.80

0.60

0.40

0.20

0.00



Fig. 4 μC1 ,C3 -values for all cases

1.00

0.80

0.60

0.40

0.20

0.00



Fig. 5 μC2 ,C3 -values for all cases



255



256



O. Roeva et al.

1.00

0.80

0.60

0.40

0.20

0.00



Fig. 6 μC4 ,C5 -values for all cases



a solution with a high accuracy for a longer time if the algorithm initial solutions are

far from the real ones or if it does not reach a good solution even after a long time of

computations.

ICrA of ICrA: Step 2

To analyse the correlations between the 14 differently tuned GAs, the IMG A

(Eq. (27)) is used to perform ICrA. In this case, the 10 criteria pairs (C1 ↔ C2 ,

C1 ↔ C3 , etc.) become objects (O1 , O2 , . . . , O10 ) and the applied GAs (G A5 , G A10 ,

G A20 , . . . , G A100 , G A110 , G A150 , G A200 ) become criteria (C1 , C2 , . . . , C14 ). Thus,

the ICrA results will give relations and dependencies between the considered criteria,

i.e. the 14 GAs performances.

The obtained results for μC,C , νC,C , sorted by μ-values, after application of

ICrA to IMG A , are presented in Table 5.

As can be seen from the Table 5, the high μC,C values (μC,C = 0.98) are obtained

for the following group of GAs pairs:

• G A50 ↔ G A80 , G A50 ↔ G A110 , G A60 ↔ G A110 ,

G A70 ↔ G A150 , G A80 ↔ G A110 , and G A110 ↔ G A150 .

These pairs are in strong positive consonance, i.e. the listed above GAs have very

similar or identical performance. Therefore, considering the discussed here model

parameter identification problem, the ICrA results show that we can apply the GA

with a population of 50 chromosomes instead of a GA with a population of 80 or

110 chromosomes. In this manner we can decrease twice the computation efforts,

especially in the case when we use a GA with a population of 50 or 70 chromosomes

instead of a GA with a population of 110 or 150 chromosomes. Moreover, in the

same time we reserve the solution accuracy.

The next group of criteria pairs that are still in strong positive consonance (μC,C =

0.96) are as follows:

• G A30 ↔ G A40 , G A50 ↔ G A60 , G A90 ↔ G A100 ,

G A60 ↔ G A80 , G A90 ↔ G A110 ,



InterCriteria Analysis of Genetic Algorithms Performance



257



Table 5 Genetic algorithms relations sorted by μC,C , νC,C values

GA pairs



μ, ν



GA pairs



μ, ν



GA pairs



μ, ν



G A50 ↔ G A80



0.98, 0.00



G A40 ↔ G A110



0.91, 0.09



G A30 ↔ G A90



0.87, 0.13



G A50 ↔ G A110



0.98, 0.00



G A60 ↔ G A200



0.91, 0.07



G A40 ↔ G A90



0.87, 0.13



G A60 ↔ G A110



0.98, 0.00



G A70 ↔ G A90



0.91, 0.09



G A40 ↔ G A200



0.87, 0.13



G A70 ↔ G A150



0.98, 0.02



G A100 ↔ G A110



0.91, 0.09



G A70 ↔ G A100



0.87, 0.13



G A80 ↔ G A110



0.98, 0.02



G A100 ↔ G A200



0.91, 0.09



G A70 ↔ G A200



0.87, 0.13



G A110 ↔ G A150



0.98, 0.02



G A110 ↔ G A200



0.91, 0.09



G A90 ↔ G A200



0.87, 0.13



G A30 ↔ G A40



0.96, 0.04



G A5 ↔ G A20



0.89, 0.09



G A5 ↔ G A30



0.84, 0.13



G A30 ↔ G A70



0.96, 0.04



G A5 ↔ G A70



0.89, 0.09



G A5 ↔ G A40



0.84, 0.13



G A40 ↔ G A70



0.96, 0.04



G A5 ↔ G A110



0.89, 0.09



G A5 ↔ G A90



0.84, 0.13



G A50 ↔ G A60



0.96, 0.00



G A20 ↔ G A80



0.89, 0.11



G A5 ↔ G A200



0.84, 0.13



G A50 ↔ G A150



0.96, 0.02



G A20 ↔ G A150



0.89, 0.11



G A5 ↔ G A10



0.82, 0.16



G A60 ↔ G A80



0.96, 0.02



G A30 ↔ G A60



0.89, 0.09



G A20 ↔ G A90



0.82, 0.18



G A60 ↔ G A150



0.96, 0.02



G A40 ↔ G A50



0.89, 0.09



G A30 ↔ G A100



0.82, 0.18



G A70 ↔ G A110



0.96, 0.04



G A40 ↔ G A80



0.89, 0.11



G A30 ↔ G A200



0.82, 0.18



G A80 ↔ G A150



0.96, 0.04



G A50 ↔ G A100



0.89, 0.09



G A40 ↔ G A100



0.82, 0.18



G A90 ↔ G A100



0.96, 0.04



G A50 ↔ G A200



0.89, 0.09



G A5 ↔ G A100



0.80, 0.18



G A90 ↔ G A110



0.96, 0.04



G A60 ↔ G A100



0.89, 0.09



G A20 ↔ G A100



0.78, 0.22



G A30 ↔ G A80



0.93, 0.07



G A80 ↔ G A100



0.89, 0.11



G A10 ↔ G A40



0.78, 0.22



G A30 ↔ G A150



0.93, 0.07



G A80 ↔ G A200



0.89, 0.11



G A10 ↔ G A70



0.78, 0.22



G A40 ↔ G A150



0.93, 0.07



G A100 ↔ G A150



0.89, 0.11



G A10 ↔ G A30



0.78, 0.22



G A50 ↔ G A70



0.93, 0.04



G A150 ↔ G A200



0.89, 0.11



G A10 ↔ G A150



0.76, 0.24



G A50 ↔ G A90



0.93, 0.04



G A5 ↔ G A50



0.87, 0.09



G A10 ↔ G A20



0.73, 0.27



G A60 ↔ G A70



0.93, 0.04



G A5 ↔ G A60



0.87, 0.09



G A10 ↔ G A110



0.73, 0.27



G A60 ↔ G A90



0.93, 0.04



G A5 ↔ G A80



0.87, 0.11



G A10 ↔ G A50



0.71, 0.27



G A70 ↔ G A80



0.93, 0.07



G A20 ↔ G A30



0.87, 0.13



G A10 ↔ G A60



0.71, 0.27



G A80 ↔ G A90



0.93, 0.07



G A20 ↔ G A40



0.87, 0.13



G A10 ↔ G A80



0.71, 0.29



G A90 ↔ G A150



0.93, 0.07



G A20 ↔ G A50



0.87, 0.11



G A10 ↔ G A90



0.69, 0.31



G A5 ↔ G A150



0.91, 0.07



G A20 ↔ G A60



0.87, 0.11



G A10 ↔ G A200



0.69, 0.31



G A30 ↔ G A50



0.91, 0.07



G A20 ↔ G A70



0.87, 0.13



G A10 ↔ G A100



0.64, 0.36



G A30 ↔ G A110



0.91, 0.09



G A20 ↔ G A110



0.87, 0.13



G A40 ↔ G A60



0.91, 0.07



G A20 ↔ G A200



0.87, 0.13



G A40 ↔ G A70 , G A70 ↔ G A110 , G A30 ↔ G A70 ,

G A50 ↔ G A150 , G A60 ↔ G A150 , and G A80 ↔ G A150 .

For the pairs of the first row it is clear that these GAs will show similar performance. These GAs have closer population sizes—30–40, 50–60, etc. The similar

performance of the GAs in the second and third rows could be explained similarly.

The interesting results from ICrA are in the last row. The GAs with populations of

50, 60 or 80 chromosomes have very similar performance compared to the GA with a



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