Modified Artificial Gorilla Troop Optimization Algorithm for Solving Constrained Engineering Optimization Problems
Abstract
:1. Introduction
2. Gorilla Troops Optimizer (GTO)
2.1. Exploration Stage
2.2. Exploitation Stage
2.2.1. Following the Silverback
2.2.2. Competition for Adult Females
3. Modified Gorilla Troops Optimizer (MGTO)
3.1. Convergence Strategy of Contraction Control Factors
3.2. Sine Cosine Interaction Fusion Strategy Based on Closeness
3.3. Identification Strategies of Individual Differences in Gorillas
3.4. Implementation of the MGTO Algorithm
Algorithm 1: Pseudocode of MGTO algorithm |
Initialize the population and set corresponding parameters β,w, and p, set the population size N and the maximum number of iterations T. |
Calculate the fitness value of the initialized gorilla. |
%Main Loop |
While (t <= maximum iteration) |
Update C, L using Equations (2) and (4). |
%Exploration phase |
For (each gorilla(Xi)) do |
Use Equation (1) for position updates. |
End for |
Calculate the fitness values of gorilla; if GX is better than X, replace them. |
Set XSilverback as the position of silverback(best position). |
Use Equations (14) and (15) to update U and CAN. |
For (each gorilla(Xi)) do |
Use Equations (16)–(19) for position updates. |
End for |
Calculate the fitness values of gorilla; if GX is better than X, replace them. |
%Exploitation phase |
For (each gorilla(Xi)) do |
If (|C| ≥ 1) then |
Update the position gorilla using Equation (7). |
Else |
Update the position gorilla using Equation (10). |
End if |
End for |
Calculate the fitness values of the gorilla and replace them after comparison. |
For (each gorilla(Xi)) do |
If (Gamma > 0) then |
Update using Equations (24) and (25). |
Else |
Update using Equations (29) and (30). |
End if |
End for |
Calculate the fitness values of the gorilla and replace them after comparison. |
For (each gorilla(Xi)) do |
For (1 to J dimension, J is a random integer between 1 and the total dimension) do |
Use Equations (31)–(33) for position updates. |
End for |
End for |
Calculate the fitness values of the gorilla and replace them after comparison. |
For (each gorilla(Xi)) do |
Use Equation (37) for position updates. |
End for |
Calculate the fitness values of the gorilla and replace them after comparison. |
End while |
Return Xsilverback and its fitness value. |
3.5. Complexity Analysis
4. Experimental Results and Discussion
4.1. Experiments on 23 Standard Benchmark Functions
4.1.1. Result Statistics and Convergence Curve Analysis of 23 Standard Data Functions
4.1.2. Analysis of Wilcoxon Rank Sum Test Results
4.2. Experiments on 30 CEC2014 and 10 CEC2020 Benchmark Function
Analysis of Wilcoxon Rank-Sum Test Results
4.3. Experimental Analysis between Exploration and Exploitation
5. Constrained Engineering Design Problems
5.1. Pressure Vessel Design Problem
5.2. Speed Reducer Design Problem
5.3. Welded Beam Design Problem
5.4. Tension/Compression Spring Design Problem
5.5. Cantilever Beam Design Problem
5.6. Multiple Disc Clutch Brake Problem
5.7. Car Crashworthiness Design
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Algorithm | Parameters | Value |
---|---|---|
MGTO/GTO | p | 0.03 |
β | 3 | |
w | 0.8 | |
SCA | α | 2 |
ROA | C | 0.1 |
WOA | Coefficient vectors | 1 |
Coefficient vectors | [−1, 1] | |
Helical parameter b | 0.75 | |
Helical parameter l | [−1, 1] | |
RSA | 0.1 | |
β | 0.005 | |
SHO | \ | \ |
SOA | b | 1 |
AOA | MOP_Max | 1 |
MOP_Min | 0.2 | |
A | 5 | |
Mu | 0.499 | |
HBA | β | 6 |
C | 2 |
Type | F | dim | Range | Fmin |
---|---|---|---|---|
Unimodal benchmark functions | 30/500 | [−100, 100] | 0 | |
30/500 | [−10, 10] | 0 | ||
30/500 | [−100, 100] | 0 | ||
30/500 | [−100, 100] | 0 | ||
30/500 | [−30, 30] | 0 | ||
30/500 | [−100, 100] | 0 | ||
30/500 | [−1.28, 1.28] | 0 | ||
Multimodal benchmark functions | 30/500 | [−500, 500] | −418.9829 × dim | |
30/500 | [−5.12, 5.12] | 0 | ||
30/500 | [−32, 32] | 0 | ||
30/500 | [−600, 600] | 0 | ||
30/500 | [−50, 50] | 0 | ||
30/500 | [−50, 50] | 0 | ||
Fixed-dimension multimodal benchmark functions | 2 | [−65, 65] | 1 | |
4 | [−5, 5] | 0.00030 | ||
2 | [−5, 5] | −1.0316 | ||
2 | [−5, 5] | 0.398 | ||
5 | [−2, 2] | 3 | ||
3 | [−1, 2] | −3.86 | ||
6 | [0, 1] | −3.32 | ||
4 | [0, 10] | −10.1532 | ||
4 | [0, 10] | −10.4028 | ||
4 | [0, 10] | −10.5363 |
F | dim | Metric | MGTO | GTO | SCA | ROA | WOA | RSA | SHO | SOA | AOA | HBA |
---|---|---|---|---|---|---|---|---|---|---|---|---|
F1 | 30 | min | 0 | 0 | 3.02 × 10−3 | 0 | 2.36 × 10−84 | 0 | 0 | 1.76 × 10−14 | 1.32 × 10−169 | 9.41 × 10−144 |
mean | 0 | 0 | 1.90 × 101 | 0 | 5.85 × 10−72 | 0 | 0 | 6.04 × 10−12 | 4.81 × 10−26 | 1.61 × 10−135 | ||
std | 0 | 0 | 3.51 × 101 | 0 | 3.20 × 10−71 | 0 | 0 | 1.12 × 10−11 | 1.56 × 10−25 | 4.90 × 10−135 | ||
500 | min | 0 | 0 | 1.34 × 105 | 0 | 1.48 × 10−81 | 0 | 0 | 1.34 × 10−2 | 5.92 × 10−1 | 1.40 × 10−119 | |
mean | 0 | 0 | 2.19 × 105 | 0 | 9.05 × 10−70 | 0 | 0 | 1.20 × 10−1 | 6.51 × 10−1 | 3.42 × 10−112 | ||
std | 0 | 0 | 4.83 × 104 | 0 | 4.94 × 10−69 | 0 | 0 | 1.03 × 10−1 | 4.14 × 10−2 | 1.46 × 10−111 | ||
F2 | 30 | min | 0 | 5.75 × 10−208 | 3.05 × 10−4 | 2.97 × 10−192 | 1.50 × 10−57 | 0 | 0 | 1.45 × 10−9 | 0 | 2.52 × 10−76 |
mean | 0 | 1.00 × 10−192 | 1.75 × 10−2 | 1.37 × 10−164 | 2.03 × 10−51 | 0 | 0 | 1.23 × 10−8 | 0 | 7.34 × 10−71 | ||
std | 0 | 0 | 2.42 × 10−2 | 0 | 6.84 × 10−51 | 0 | 0 | 1.10 × 10−8 | 0 | 3.83 × 10−70 | ||
500 | min | 0 | 3.06 × 10−199 | 5.04 × 101 | 3.00 × 10−187 | 7.43 × 10−56 | 0 | 0 | 2.62 × 10−3 | 5.63 × 10−13 | 2.68 × 10−63 | |
mean | 0 | 1.24 × 10−189 | 1.22 × 102 | 2.35 × 10−159 | 4.11 × 10−48 | 0 | 0 | 6.53 × 10−3 | 1.51 × 10−3 | 4.29 × 10−61 | ||
std | 0 | 0 | 5.60 × 101 | 1.29 × 10−158 | 1.43 × 10−47 | 0 | 0 | 2.81 × 10−3 | 1.74 × 10−3 | 8.32 × 10−61 | ||
F3 | 30 | min | 0 | 0 | 1.73 × 102 | 0 | 1.17 × 104 | 0 | 0 | 2.50 × 10−7 | 3.81 × 10−152 | 2.75 × 10−108 |
mean | 0 | 0 | 7.70 × 103 | 1.58 × 10−312 | 4.67 × 104 | 0 | 0 | 6.28 × 10−4 | 7.40 × 10−3 | 8.30 × 10-97 | ||
std | 0 | 0 | 5.35 × 103 | 0 | 1.54 × 104 | 0 | 0 | 2.58 × 10−3 | 1.50 × 10−2 | 3.25 × 10−96 | ||
500 | min | 0 | 0 | 4.64 × 106 | 1.57 × 10−313 | 1.58 × 107 | 0 | 0 | 5.93 × 103 | 1.36 × 101 | 3.03 × 10−75 | |
mean | 0 | 0 | 7.02 × 106 | 1.25 × 10−261 | 3.13 × 107 | 0 | 0 | 1.43 × 105 | 3.12 × 101 | 1.41 × 10−64 | ||
std | 0 | 0 | 1.39 × 106 | 0 | 1.18 × 107 | 0 | 0 | 1.07 × 105 | 1.53 × 101 | 6.28 × 10−64 | ||
F4 | 30 | min | 0 | 3.03 × 10−208 | 1.46 × 101 | 1.85 × 10−189 | 2.99 | 0 | 0 | 1.20 × 10−4 | 3.00 × 10−61 | 1.53 × 10−61 |
mean | 0 | 2.36 × 10−192 | 3.47 × 101 | 3.13 × 10−170 | 5.09 × 101 | 0 | 0 | 3.97 × 10−3 | 2.27 × 10−2 | 2.89 × 10−57 | ||
std | 0 | 0 | 9.51 | 0 | 2.91 × 101 | 0 | 0 | 8.09 × 10−3 | 2.09 × 10−2 | 1.22 × 10−56 | ||
500 | min | 0 | 2.43 × 10−203 | 9.83 × 101 | 1.03 × 10−189 | 3.54 × 101 | 0 | 0 | 9.71 × 101 | 1.54 × 10−1 | 1.39 × 10−30 | |
mean | 0 | 3.89 × 10−188 | 9.90 × 101 | 1.86 × 10-159 | 8.51 × 101 | 0 | 0 | 9.88 × 101 | 1.80 × 10−1 | 3.38 × 10−28 | ||
std | 0 | 0 | 2.77 × 10−1 | 1.02 × 10−158 | 1.89 × 101 | 0 | 0 | 5.54 × 10−1 | 1.58 × 10−2 | 5.74 × 10−28 | ||
F5 | 30 | min | 1.30 × 10−10 | 4.41 × 10−6 | 5.03 × 101 | 2.87 × 101 | 2.72 × 101 | 9.87 × 10−26 | 2.87 × 101 | 2.70 × 101 | 2.78 × 101 | 2.29 × 101 |
mean | 2.55 × 10−7 | 1.60 | 2.19 × 104 | 2.87 × 101 | 2.79 × 101 | 2.51 × 101 | 2.88 × 101 | 2.83 × 101 | 2.85 × 101 | 2.42 × 101 | ||
std | 4.72 × 10−7 | 6.10 | 3.92 × 104 | 1.76 × 10−2 | 5.15 × 10−1 | 1.00 × 101 | 1.10 × 10−1 | 6.06 × 10−1 | 3.21 × 10−1 | 1.11 | ||
500 | min | 3.30 × 10−8 | 7.75 × 10−5 | 9.07 × 108 | 4.94 × 102 | 4.96 × 102 | 4.99 × 102 | 4.98 × 102 | 5.48 × 102 | 4.99 × 102 | 4.95 × 102 | |
mean | 2.56 × 10−4 | 1.48 | 2.00 × 109 | 4.94 × 102 | 4.96 × 102 | 4.99 × 102 | 4.99 × 102 | 9.52 × 102 | 4.99 × 102 | 4.98 × 102 | ||
std | 4.00 × 10−4 | 2.89 | 5.16 × 108 | 2.32 × 10−1 | 4.35 × 10−1 | 0.00 × 100 | 1.33 × 10−1 | 4.06 × 102 | 7.94 × 10−2 | 7.46 × 10−1 | ||
F6 | 30 | min | 6.04 × 10−16 | 6.47 × 10−9 | 4.58 | 1.02 × 10−1 | 5.67 × 10−2 | 6.36 | 3.14 × 10−2 | 2.31 | 2.47 | 2.53 × 10−6 |
mean | 2.71 × 10−11 | 2.86 × 10−7 | 3.69 × 101 | 6.11 × 10−1 | 3.65 × 10−1 | 7.26 | 3.32 | 3.25 | 3.12 | 2.52 × 10−2 | ||
std | 6.58 × 10−11 | 5.21 × 10−7 | 6.69 × 101 | 3.16 × 10−1 | 2.35 × 10−1 | 3.30 × 10−1 | 2.49 | 5.10 × 10−1 | 2.54 × 10−1 | 7.63 × 10−2 | ||
500 | min | 1.99 × 10−9 | 1.06 × 10−3 | 1.06 × 105 | 5.66 × 10−1 | 1.39 × 101 | 1.25 × 102 | 1.16 × 102 | 1.14 × 102 | 1.13 × 102 | 9.44 × 101 | |
mean | 9.03 × 10−7 | 4.33 × 10−1 | 2.03 × 105 | 8.85 | 3.27 × 101 | 1.25 × 102 | 1.23 × 102 | 1.16 × 102 | 1.16 × 102 | 9.78 × 101 | ||
std | 1.15 × 10−6 | 3.85 × 10−1 | 7.01 × 104 | 4.51 | 9.46 | 0 | 2.35 | 9.19 × 10−1 | 1.35 | 2.15 | ||
F7 | 30 | min | 3.12 × 10−7 | 5.48 × 10−6 | 1.06 × 10−2 | 5.41 × 10−6 | 1.51 × 10−4 | 1.35 × 10−5 | 8.03 × 10−6 | 3.44 × 10−4 | 9.78 × 10−7 | 5.16 × 10−5 |
mean | 2.02 × 10−5 | 1.12 × 10−4 | 8.69 × 10−2 | 1.54 × 10−4 | 3.27 × 10−3 | 9.68 × 10−5 | 1.27 × 10−4 | 2.89 × 10−3 | 9.06 × 10−5 | 3.78 × 10−4 | ||
std | 1.79 × 10−5 | 1.01 × 10−4 | 6.18 × 10−2 | 1.52 × 10−4 | 3.47 × 10−3 | 9.60 × 10−5 | 1.90 × 10−4 | 2.40 × 10−3 | 7.89 × 10−5 | 2.91 × 10−4 | ||
500 | min | 2.37 × 10−6 | 5.82 × 10−6 | 7.89 × 103 | 3.17 × 10−6 | 1.73 × 10−4 | 3.83 × 10−6 | 2.47 × 10−6 | 2.51 × 10−2 | 2.05 × 10−6 | 3.72 × 10−5 | |
mean | 2.60 × 10−5 | 8.81 × 10−5 | 1.44 × 104 | 1.11 × 10−4 | 4.26 × 10−3 | 1.72 × 10−4 | 8.06 × 10−5 | 8.87 × 10−2 | 8.52 × 10−5 | 4.28 × 10−4 | ||
std | 2.03 × 10−5 | 6.24 × 10−5 | 3.00 × 103 | 8.38 × 10−5 | 4.84 × 10−3 | 1.61 × 10−4 | 7.64 × 10−5 | 4.69 × 10−2 | 7.23 × 10−5 | 2.90 × 10−4 | ||
F8 | 30 | min | −1.26 × 104 | −1.26 × 104 | −5.08 × 103 | −1.26 × 104 | −1.26 × 104 | −5.66 × 103 | −4.01 × 103 | −6.87 × 103 | −6.73 × 103 | −1.02 × 104 |
mean | −1.26 × 104 | −1.26 × 104 | −3.82 × 103 | −1.25 × 104 | −1.01 × 104 | −5.46 × 103 | −2.66 × 103 | −5.05 × 103 | −5.39 × 103 | −8.59 × 103 | ||
std | 3.29 × 10−6 | 4.27 × 10−5 | 3.30 × 102 | 1.91 × 102 | 1.89 × 103 | 2.16 × 102 | 7.06 × 102 | 7.06 × 102 | 4.46 × 102 | 9.82 × 102 | ||
500 | min | −2.09 × 105 | −2.09 × 105 | −1.72 × 104 | −2.09 × 105 | −2.09 × 105 | −7.61 × 104 | −2.05 × 104 | −3.81 × 104 | −2.64 × 104 | −1.01 × 105 | |
mean | −2.09 × 105 | −2.09 × 105 | −1.52 × 104 | −2.07 × 105 | −1.73 × 105 | −6.42 × 104 | −1.32 × 104 | −2.30 × 104 | −2.27 × 104 | −7.32 × 104 | ||
std | 2.66 × 10−2 | 3.12 × 101 | 9.19 × 102 | 7.21 × 103 | 2.89 × 104 | 5.62 × 103 | 4.83 × 103 | 4.21 × 103 | 1.46 × 103 | 1.35 × 104 | ||
F9 | 30 | min | 0 | 0 | 1.96 × 10−2 | 0 | 0 | 0 | 0 | 8.53 × 10−13 | 0 | 0 |
mean | 0 | 0 | 3.74 × 101 | 0 | 0 | 0 | 0 | 3.19 | 0 | 0 | ||
std | 0 | 0 | 4.58 × 101 | 0 | 0 | 0 | 0 | 5.87 | 0 | 0 | ||
500 | min | 0 | 0 | 4.93 × 102 | 0 | 0 | 0 | 0 | 4.11 × 10−5 | 0 | 0 | |
mean | 0 | 0 | 1.21 × 103 | 0 | 6.06 × 10−14 | 0 | 0 | 7.01 | 7.21 × 10−6 | 0 | ||
std | 0 | 0 | 4.62 × 102 | 0 | 3.32 × 10−13 | 0 | 0 | 9.00 | 7.25 × 10−6 | 0 | ||
F10 | 30 | min | 8.88 × 10−16 | 8.88 × 10−16 | 3.07 × 10−2 | 8.88 × 10−16 | 8.88 × 10−16 | 8.88 × 10−16 | 8.88 × 10−16 | 2.00 × 101 | 8.88 × 10−16 | 8.88 × 10−16 |
mean | 8.88 × 10−16 | 8.88 × 10−16 | 1.24 × 101 | 8.88 × 10−16 | 4.80 × 10−15 | 8.88 × 10−16 | 8.88 × 10−16 | 2.00 × 101 | 8.88 × 10−16 | 8.88 × 10−16 | ||
std | 0 | 0 | 9.42 | 0 | 2.53 × 10−15 | 0 | 0 | 1.62 × 10−3 | 0 | 0 | ||
500 | min | 8.88 × 10−16 | 8.88 × 10−16 | 7.92 | 8.88 × 10−16 | 8.88 × 10−16 | 8.88 × 10−16 | 8.88 × 10−16 | 2.00 × 101 | 7.22 × 10−3 | 8.88 × 10−16 | |
mean | 8.88 × 10−16 | 8.88 × 10−16 | 1.93 × 101 | 8.88 × 10−16 | 4.68 × 10−15 | 8.88 × 10−16 | 3.54 | 2.00 × 101 | 7.91 × 10−3 | 4.64 | ||
std | 0 | 0 | 3.42 | 0 | 2.63 × 10−15 | 0 | 4.27 | 7.17 × 10−5 | 3.77 × 10−4 | 8.56 | ||
F11 | 30 | min | 0 | 0 | 1.40 × 10−4 | 0 | 0 | 0 | 0 | 7.85 × 10−13 | 2.31 × 10−2 | 0 |
mean | 0 | 0 | 1.09 | 0 | 4.49 × 10−3 | 0 | 0 | 2.00 × 10−2 | 2.33 × 10−1 | 0 | ||
std | 0 | 0 | 8.47 × 10−1 | 0 | 2.46 × 10−2 | 0 | 0 | 3.85 × 10−2 | 1.63 × 10−1 | 0 | ||
500 | min | 0 | 0 | 2.64 × 102 | 0 | 0 | 0 | 0 | 8.27 × 10−4 | 5.83 × 103 | 0 | |
mean | 0 | 0 | 1.74 × 103 | 0 | 0 | 0 | 0 | 5.30 × 10−2 | 9.15 × 103 | 0 | ||
std | 0 | 0 | 7.17 × 102 | 0 | 0 | 0 | 0 | 7.76 × 10−2 | 2.35 × 103 | 0 | ||
F12 | 30 | min | 2.50 × 10−15 | 7.46 × 10−11 | 9.42 × 10−1 | 6.17 × 10−3 | 3.37 × 10−3 | 4.69 × 10−1 | 1.42 × 10−4 | 1.49 × 10−1 | 4.13 × 10−1 | 7.54 × 10−7 |
mean | 3.67 × 10−12 | 2.23 × 10−8 | 4.99 × 104 | 3.28 × 10−2 | 1.21 × 10−1 | 1.38 | 2.06 × 10−4 | 3.45 × 10−1 | 5.14 × 10−1 | 2.00 × 10−4 | ||
std | 4.44 × 10−12 | 3.29 × 10−8 | 2.08 × 105 | 2.06 × 10−2 | 4.07 × 10−1 | 4.24 × 10−1 | 2.56 × 10−5 | 1.62 × 10−1 | 4.73 × 10−2 | 9.72 × 10−4 | ||
500 | min | 3.07 × 10−15 | 7.19 × 10−8 | 3.77 × 109 | 1.65 × 10−4 | 2.03 × 10−2 | 1.21 | 3.69 × 10−4 | 1.10 | 1.06 | 6.93 × 10−1 | |
mean | 1.77 × 10−9 | 2.47 × 10−4 | 6.19 × 109 | 2.26 × 10−2 | 8.65 × 10−2 | 1.21 | 9.65 × 10−1 | 1.94 | 1.08 | 7.48 × 10−1 | ||
std | 4.59 × 10−9 | 2.85 × 10−4 | 1.30 × 109 | 1.40 × 10−2 | 3.67 × 10−2 | 4.52 × 10−16 | 3.72 × 10−1 | 9.48 × 10−1 | 1.34 × 10−2 | 2.73 × 10−2 | ||
F13 | 30 | min | 2.10 × 10−14 | 6.32 × 10−10 | 2.99 | 1.42 × 10−2 | 1.49 × 10−1 | 2.20 × 10−30 | 2.92 | 1.60 | 2.59 | 1.90 × 10−3 |
mean | 1.89 × 10−10 | 2.10 × 10−3 | 2.64 × 105 | 3.49 × 10−1 | 5.91 × 10−1 | 5.73 × 10−1 | 2.96 | 1.99 | 2.83 | 3.22 × 10−1 | ||
std | 6.57 × 10−10 | 6.90 × 10−3 | 1.12 × 106 | 2.00 × 10−1 | 2.23 × 10−1 | 1.17 | 1.91 × 10−2 | 2.03 × 10−1 | 1.03 × 10−1 | 2.82 × 10−1 | ||
500 | min | 1.55 × 10−10 | 1.58 × 10−6 | 4.36 × 109 | 1.37 × 10−1 | 7.04 | 5.00 × 101 | 4.99 × 101 | 5.42 × 101 | 5.01 × 101 | 4.88 × 101 | |
mean | 1.85 × 10−7 | 6.74 × 10−2 | 9.40 × 109 | 5.30 | 1.84 × 101 | 5.00 × 101 | 5.00 × 101 | 7.32 × 101 | 5.02 × 101 | 4.93 × 101 | ||
std | 3.95 × 10−7 | 1.15 × 10−1 | 2.32 × 109 | 2.88 × 100 | 6.99 | 0 | 1.76 × 10−2 | 1.51 × 101 | 3.81 × 10−2 | 2.79 × 10−1 | ||
F14 | 2 | min | 9.98 × 10−1 | 9.98 × 10−1 | 9.98 × 10−1 | 9.98 × 10−1 | 9.98 × 10−1 | 1.06 | 1.06 | 9.98 × 10−1 | 9.98 × 10−1 | 9.98 × 10−1 |
mean | 9.98 × 10−1 | 9.98 × 10−1 | 1.53 | 4.78 | 2.73 | 4.72 | 9.52 | 2.48 | 9.71 | 1.72 | ||
std | 0 | 0 | 8.92 × 10−1 | 4.56 | 2.98 | 3.55 | 3.97 | 2.46 | 3.65 | 1.89 | ||
F15 | 4 | min | 3.07 × 10−4 | 3.07 × 10−4 | 5.14 × 10−4 | 3.40 × 10−4 | 3.09 × 10−4 | 7.36 × 10−4 | 3.10 × 10−4 | 1.22 × 10−3 | 3.72 × 10−4 | 3.07 × 10−4 |
mean | 3.07 × 10−4 | 4.30 × 10−4 | 9.37 × 10−4 | 9.01 × 10−4 | 6.56 × 10−4 | 2.79 × 10−3 | 3.17 × 10−4 | 1.25 × 10−3 | 1.08 × 10−2 | 7.21 × 10−3 | ||
std | 1.84 × 10−18 | 3.17 × 10−4 | 3.24 × 10−4 | 5.74 × 10−4 | 4.45 × 10−4 | 1.97 × 10−3 | 5.01 × 10−6 | 5.07 × 10−5 | 1.30 × 10−2 | 1.00 × 10−2 | ||
F16 | 2 | min | −1.03 | −1.03 | −1.03 | −1.03 | −1.03 | −1.03 | −1.03 | −1.03 | −1.03 | −1.03 |
mean | −1.03 | −1.03 | −1.03 | −1.03 | −1.03 | −1.03 | −9.48 × 10−1 | −1.03 | −1.03 | −1.03 | ||
std | 6.32 × 10−16 | 6.39 × 10−16 | 5.45 × 10−5 | 4.96 × 10−8 | 1.43 × 10−9 | 5.90 × 10−3 | 1.85 × 10−1 | 2.56 × 10−6 | 1.34 × 10−7 | 6.05 × 10−16 | ||
F17 | 2 | min | 3.98 × 10−1 | 3.98 × 10−1 | 3.98 × 10−1 | 3.98 × 10−1 | 3.98 × 10−1 | 3.99 × 10−1 | 3.98 × 10−1 | 3.98 × 10−1 | 3.98 × 10−1 | 3.98 × 10−1 |
mean | 3.98 × 10−1 | 3.98 × 10−1 | 4.00 × 10−1 | 3.98 × 10−1 | 3.98 × 10−1 | 4.26 × 10−1 | 5.37 × 10−1 | 3.98 × 10−1 | 3.98 × 10−1 | 3.98 × 10−1 | ||
std | 0 | 0 | 1.60 × 10−3 | 9.33 × 10−6 | 1.54 × 10−5 | 3.04 × 10−2 | 4.25 × 10−1 | 8.10 × 10−5 | 1.07 × 10−7 | 0 | ||
F18 | 5 | min | 3.00 | 3.00 | 3.00 | 3.00 | 3.00 | 3.00 | 3.40 | 3.00 | 3.00 | 3.00 |
mean | 3.00 | 3.00 | 3.00 | 3.00 | 3.00 | 5.78 | 2.26 × 101 | 3.00 | 5.70 | 9.30 | ||
std | 1.71 × 10−15 | 1.21 × 10−15 | 4.66 × 10−5 | 9.32 × 10−4 | 1.10 × 10−4 | 8.48 | 3.39 × 101 | 4.74 × 10−4 | 8.24 | 2.09 × 101 | ||
F19 | 3 | min | −3.86 | −3.86 | −3.86 | −3.86 | −3.86 | −3.86 | −3.85 | −3.86 | −3.86 | −3.86 |
mean | −3.86 | −3.86 | −3.85 | −3.76 | −3.86 | −3.79 | −3.46 | −3.85 | −3.85 | −3.86 | ||
std | 2.54 × 10−15 | 2.65 × 10−15 | 4.12 × 10−3 | 1.63 × 10−1 | 5.23 × 10−3 | 5.49 × 10−2 | 4.63 × 10−1 | 7.04 × 10−3 | 3.62 × 10−3 | 2.60 × 10−15 | ||
F20 | 6 | min | −3.32 | −3.32 | −3.16 | −3.28 | −3.32 | −2.98 | −3.11 | −3.19 | −3.22 | −3.32 |
mean | −3.31 | −3.28 | −2.92 | −3.04 | −3.24 | −2.47 | −2.68 | −3.01 | −3.08 | −3.26 | ||
std | 4.11 × 10−2 | 5.70 × 10−2 | 3.30 × 10−1 | 1.61 × 10−1 | 9.60 × 10−2 | 4.39 × 10−1 | 2.38 × 10−1 | 1.68 × 10−1 | 9.54 × 10−2 | 7.68 × 10−2 | ||
F21 | 4 | min | −1.02 × 101 | −1.02 × 101 | −5.44 | −1.02 × 101 | −1.02 × 101 | −5.06 | −8.06 | −1.01 × 101 | −8.70 | −1.02 × 101 |
mean | −1.02 × 101 | −1.02 × 101 | −2.29 | −9.85 | −8.68 | −5.01 | −4.04 | −4.17 | −4.08 | −1.02 × 101 | ||
std | 5.67 × 10−15 | 6.04 × 10−15 | 1.67 | 1.46 | 2.45 | 2.24 × 10−1 | 1.43 | 4.03 | 1.50 | 8.14 × 10−6 | ||
F22 | 4 | min | −1.04 × 101 | −1.04 × 101 | −7.31 | −1.04 × 101 | −1.04 × 101 | −5.09 | −5.96 | −1.04 × 101 | −8.54 | −1.04 × 101 |
mean | −1.04 × 101 | −1.04 × 101 | −2.91 | −1.04 × 101 | −8.12 | −5.09 | −4.40 | −5.64 | −4.08 | −9.07 | ||
std | 8.08 × 10−16 | 8.08 × 10−16 | 1.89 | 7.55 × 10−2 | 3.08 | 8.73 × 10−7 | 1.05 | 4.39 | 1.80 | 3.04 | ||
F23 | 4 | min | −1.05 × 101 | −1.05 × 101 | −8.94 | −1.05 × 101 | −1.05 × 101 | −5.13 | −5.85 | −1.05 × 101 | −9.27 | −1.05 × 101 |
mean | −1.05 × 101 | −1.05 × 101 | −4.25 | −1.03 × 101 | −7.13 | −5.13 | −4.07 | −6.74 | −3.96 | −8.32 | ||
std | 1.98 × 10−15 | 2.84 × 10−15 | 1.83 | 1.02 | 3.10 | 1.86 × 10−6 | 1.28 | 4.19 | 1.96 | 3.47 |
F | dim | MGTO Vs GTO | MGTO Vs SCA | MGTO Vs ROA | MGTO Vs WOA | MGTO Vs RSA | MGTO Vs SHO | MGTO Vs SOA | MGTO Vs AOA | MGTO Vs HBA |
---|---|---|---|---|---|---|---|---|---|---|
F1 | 30 | 1 | 1.73 × 10−6 | 1 | 1.73 × 10−6 | 1 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 |
50 | 1 | 1.73 × 10−6 | 1 | 1.73 × 10−6 | 1 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | |
F2 | 30 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1 | 1.73 × 10−6 | 1.73 × 10−6 | 1 | 1.73 × 10−6 |
50 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | |
F3 | 30 | 1 | 1.73 × 10−6 | 6.25 × 10−2 | 1.73 × 10−6 | 1 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 |
50 | 1 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | |
F4 | 30 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 |
50 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | |
F5 | 30 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 5.31 × 10−5 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 |
50 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | |
F6 | 30 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 |
50 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | |
F7 | 30 | 6.98 × 10−6 | 1.73 × 10−6 | 1.25 × 10−4 | 1.73 × 10−6 | 6.89 × 10−5 | 1.73 × 10−6 | 1.73 × 10−6 | 7.51 × 10−5 | 1.73 × 10−6 |
50 | 3.06 × 10−4 | 1.73 × 10−6 | 6.32 × 10−5 | 1.92 × 10−6 | 1.48 × 10−4 | 1.73 × 10−6 | 1.73 × 10−6 | 2.26 × 10−3 | 6.98 × 10−6 | |
F8 | 30 | 3.61 × 10−3 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 |
50 | 4.73 × 10−6 | 1.73 × 10−6 | 9.32 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | |
F9 | 30 | 1 | 1.73 × 10−6 | 1 | 5.00 × 10−1 | 1 | 1.73 × 10−6 | 1.73 × 10−6 | 1 | 1 |
50 | 1 | 1.73 × 10−6 | 1 | 1 | 1 | 1.73 × 10−6 | 1.73 × 10−6 | 8.86 × 10−5 | 1 | |
F10 | 30 | 1 | 1.73 × 10−6 | 1 | 2.41 × 10−6 | 1 | 1.73 × 10−6 | 1.73 × 10−6 | 1 | 5.00 × 10−1 |
50 | 1 | 1.73 × 10−6 | 1 | 3.22 × 10−5 | 1 | 1.73 × 10−6 | 1.72 × 10−6 | 1.73 × 10−6 | 9.77 × 10−4 | |
F11 | 30 | 1 | 1.73 × 10−6 | 1 | 5.00 × 10−1 | 1 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1 |
50 | 1 | 1.73 × 10−6 | 1 | 1 | 1 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1 | |
F12 | 30 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 |
50 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | |
F13 | 30 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.48 × 10−2 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 |
50 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | |
F14 | 2 | 2.50 × 10−2 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.72 × 10−1 |
F15 | 4 | 4.49 × 10−2 | 1.73 × 10−6 | 1.64 × 10−5 | 2.16 × 10−5 | 1.73 × 10−6 | 1.73 × 10−6 | 2.13 × 10−6 | 6.34 × 10−6 | 8.32 × 10−6 |
F16 | 2 | 1 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1 |
F17 | 2 | 1 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1 |
F18 | 5 | 4.81 × 10−1 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 5.93 × 10−2 |
F19 | 6 | 1 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1 |
F20 | 3 | 1.25 × 10−1 | 1.73 × 10−6 | 1.73 × 10−6 | 8.47 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 7.57 × 10−4 |
F21 | 4 | 1 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.25 × 10−1 |
F22 | 4 | 1 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 7.81 × 10−3 |
F23 | 4 | 1 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 3.13 × 10−2 |
CEC2014 | Metric | MGTO | GTO | SCA | ROA | WOA | RSA | SHO | SOA | AOA | HBA |
---|---|---|---|---|---|---|---|---|---|---|---|
CEC1 | MIN | 1.04 × 106 | 1.63 × 106 | 2.82 × 108 | 3.52 × 108 | 5.42 × 107 | 6.49 × 108 | 1.53 × 109 | 5.83 × 107 | 4.26 × 108 | 2.22 × 106 |
MEAN | 3.91 × 106 | 7.97 × 106 | 4.96 × 108 | 7.72 × 108 | 2.05 × 108 | 1.11 × 109 | 1.99 × 109 | 1.79 × 108 | 1.19 × 109 | 1.12 × 107 | |
STD | 2.28 × 106 | 4.64 × 106 | 1.68 × 108 | 2.59 × 108 | 9.96 × 107 | 2.42 × 108 | 2.53 × 108 | 9.38 × 107 | 4.08 × 108 | 5.76 × 106 | |
CEC2 | MIN | 4.11 × 103 | 1.36 × 104 | 1.76 × 1010 | 3.19 × 1010 | 4.30 × 109 | 6.54 × 1010 | 7.74 × 1010 | 6.73 × 109 | 4.77 × 1010 | 9.76 × 104 |
MEAN | 2.72 × 104 | 2.83 × 105 | 2.90 × 1010 | 5.94 × 1010 | 7.41 × 109 | 7.37 × 1010 | 8.67 × 1010 | 1.55 × 1010 | 7.06 × 1010 | 1.28 × 107 | |
STD | 2.79 × 104 | 3.27 × 105 | 5.85 × 109 | 1.38 × 1010 | 2.42 × 109 | 4.98 × 109 | 4.91 × 109 | 4.83 × 109 | 1.00 × 1010 | 5.40 × 107 | |
CEC3 | MIN | 1.77 × 103 | 2.62 × 103 | 4.44 × 104 | 5.80 × 104 | 5.48 × 104 | 6.52 × 104 | 9.39 × 104 | 4.83 × 104 | 6.66 × 104 | 5.22 × 103 |
MEAN | 5.44 × 103 | 6.90 × 103 | 7.65 × 104 | 8.84 × 104 | 1.27 × 105 | 7.84 × 104 | 9.21 × 105 | 6.29 × 104 | 8.39 × 104 | 1.06 × 104 | |
STD | 1.87 × 103 | 3.69 × 103 | 1.78 × 104 | 7.90 × 103 | 6.42 × 104 | 7.39 × 103 | 1.33 × 106 | 9.32 × 103 | 8.35 × 103 | 4.16 × 103 | |
CEC4 | MIN | 4.19 × 102 | 4.88 × 102 | 1.72 × 103 | 4.23 × 103 | 8.31 × 102 | 6.30 × 103 | 1.18 × 104 | 8.52 × 102 | 5.07 × 103 | 4.90 × 102 |
MEAN | 5.19 × 102 | 5.43 × 102 | 2.83 × 103 | 9.27 × 103 | 1.39 × 103 | 1.10 × 104 | 1.79 × 104 | 1.47 × 103 | 1.31 × 104 | 5.70 × 102 | |
STD | 3.79 × 101 | 4.79 × 101 | 7.54 × 102 | 3.22 × 103 | 4.24 × 102 | 3.11 × 103 | 3.23 × 103 | 5.36 × 102 | 4.53 × 103 | 5.05 × 101 | |
CEC5 | MIN | 5.20 × 102 | 5.20 × 102 | 5.21 × 102 | 5.21 × 102 | 5.21 × 102 | 5.21 × 102 | 5.21 × 102 | 5.21 × 102 | 5.21 × 102 | 5.21 × 102 |
MEAN | 5.20 × 102 | 5.20 × 102 | 5.21 × 102 | 5.21 × 102 | 5.21 × 102 | 5.21 × 102 | 5.21 × 102 | 5.21 × 102 | 5.21 × 102 | 5.21 × 102 | |
STD | 2.38 × 10−1 | 3.06 × 10−1 | 5.20 × 10−2 | 8.38 × 10−2 | 1.08 × 10−1 | 6.51 × 10−2 | 7.36 × 10−2 | 9.35 × 10−2 | 7.12 × 10−2 | 1.75 × 10−1 | |
CEC6 | MIN | 6.18 × 102 | 6.24 × 102 | 6.35 × 102 | 6.35 × 102 | 6.35 × 102 | 6.38 × 102 | 6.43 × 102 | 6.28 × 102 | 6.36 × 102 | 6.17 × 102 |
MEAN | 6.25 × 102 | 6.30 × 102 | 6.39 × 102 | 6.40 × 102 | 6.39 × 102 | 6.40 × 102 | 6.46 × 102 | 6.34 × 102 | 6.39 × 102 | 6.23 × 102 | |
STD | 2.93 × 100 | 3.72 × 100 | 2.29 × 100 | 2.95 × 100 | 3.27 × 100 | 1.89 × 100 | 1.91 × 100 | 3.57 × 100 | 2.82 × 100 | 4.72 × 100 | |
CEC7 | MIN | 7.00 × 102 | 7.00 × 102 | 8.76 × 102 | 9.58 × 102 | 7.26 × 102 | 1.12 × 103 | 1.34 × 103 | 7.39 × 102 | 1.14 × 103 | 7.00 × 102 |
MEAN | 7.00 × 102 | 7.00 × 102 | 9.62 × 102 | 1.13 × 103 | 7.47 × 102 | 1.33 × 103 | 1.57 × 103 | 8.37 × 102 | 1.35 × 103 | 7.01 × 102 | |
STD | 4.82 × 10−2 | 2.23 × 10−1 | 4.99 × 101 | 9.85 × 101 | 1.40 × 101 | 1.03 × 102 | 8.82 × 101 | 5.37 × 101 | 9.97 × 101 | 2.84 × 10−1 | |
CEC8 | MIN | 8.56 × 102 | 9.10 × 102 | 1.05 × 103 | 1.06 × 103 | 9.92 × 102 | 1.13 × 103 | 1.18 × 103 | 9.77 × 102 | 1.09 × 103 | 8.61 × 102 |
MEAN | 9.02 × 102 | 9.33 × 102 | 1.08 × 103 | 1.12 × 103 | 1.03 × 103 | 1.16 × 103 | 1.22 × 103 | 1.03 × 103 | 1.15 × 103 | 8.92 × 102 | |
STD | 2.92 × 101 | 1.97 × 101 | 2.46 × 101 | 2.94 × 101 | 4.83 × 101 | 1.93 × 101 | 4.28 × 101 | 2.84 × 101 | 3.53 × 101 | 2.38 × 101 | |
CEC9 | MIN | 1.01 × 103 | 1.03 × 103 | 1.18 × 103 | 1.20 × 103 | 1.14 × 103 | 1.21 × 103 | 1.29 × 103 | 1.08 × 103 | 1.20 × 103 | 9.84 × 102 |
MEAN | 1.06 × 103 | 1.08 × 103 | 1.23 × 103 | 1.25 × 103 | 1.24 × 103 | 1.25 × 103 | 1.32 × 103 | 1.14 × 103 | 1.24 × 103 | 1.03 × 103 | |
STD | 2.35 × 101 | 2.50 × 101 | 2.83 × 101 | 2.85 × 101 | 6.58 × 101 | 2.10 × 101 | 2.56 × 101 | 3.20 × 101 | 2.15 × 101 | 2.99 × 101 | |
CEC10 | MIN | 1.69 × 103 | 3.28 × 103 | 7.32 × 103 | 6.98 × 103 | 5.74 × 103 | 7.44 × 103 | 8.82 × 103 | 5.51 × 103 | 6.55 × 103 | 2.82 × 103 |
MEAN | 2.78 × 103 | 4.74 × 103 | 8.00 × 103 | 7.69 × 103 | 6.45 × 103 | 7.90 × 103 | 9.91 × 103 | 7.02 × 103 | 7.39 × 103 | 4.09 × 103 | |
STD | 4.72 × 102 | 1.10 × 103 | 4.09 × 102 | 7.01 × 102 | 7.26 × 102 | 5.58 × 102 | 7.55 × 102 | 8.43 × 102 | 6.20 × 102 | 1.25 × 103 | |
CEC11 | MIN | 1.23 × 103 | 1.57 × 103 | 2.26 × 103 | 1.85 × 103 | 1.59 × 103 | 2.26 × 103 | 2.99 × 103 | 1.70 × 103 | 1.71 × 103 | 1.27 × 103 |
MEAN | 1.63 × 103 | 2.01 × 103 | 2.56 × 103 | 2.56 × 103 | 2.22 × 103 | 2.61 × 103 | 3.48 × 103 | 2.25 × 103 | 2.11 × 103 | 1.99 × 103 | |
STD | 1.75 × 102 | 3.45 × 102 | 2.54 × 102 | 2.59 × 102 | 3.67 × 102 | 2.28 × 102 | 2.77 × 102 | 3.19 × 102 | 2.84 × 102 | 4.29 × 102 | |
CEC12 | MIN | 1.20 × 103 | 1.20 × 103 | 1.20 × 103 | 1.20 × 103 | 1.20 × 103 | 1.20 × 103 | 1.20 × 103 | 1.20 × 103 | 1.20 × 103 | 1.20 × 103 |
MEAN | 1.20 × 103 | 1.20 × 103 | 1.20 × 103 | 1.20 × 103 | 1.20 × 103 | 1.20 × 103 | 1.20 × 103 | 1.20 × 103 | 1.20 × 103 | 1.20 × 103 | |
STD | 1.37 × 10−1 | 2.15 × 10−1 | 2.91 × 10−1 | 3.49 × 10−1 | 5.20 × 10−1 | 4.10 × 10−1 | 7.98 × 10−1 | 3.41 × 10−1 | 2.77 × 10−1 | 3.64 × 10−1 | |
CEC13 | MIN | 1.30 × 103 | 1.30 × 103 | 1.30 × 103 | 1.30 × 103 | 1.30 × 103 | 1.30 × 103 | 1.30 × 103 | 1.30 × 103 | 1.30 × 103 | 1.30 × 103 |
MEAN | 1.30 × 103 | 1.30 × 103 | 1.30 × 103 | 1.30 × 103 | 1.30 × 103 | 1.30 × 103 | 1.30 × 103 | 1.30 × 103 | 1.30 × 103 | 1.30 × 103 | |
STD | 6.59 × 10−2 | 1.02 × 10−1 | 1.58 × 10−1 | 1.08 | 1.89 × 10−1 | 6.43 × 10−1 | 1.13 | 1.64 × 10−1 | 1.19 | 9.69 × 10−2 | |
CEC14 | MIN | 1.40 × 103 | 1.40 × 103 | 1.40 × 103 | 1.40 × 103 | 1.40 × 103 | 1.41 × 103 | 1.43 × 103 | 1.40 × 103 | 1.41 × 103 | 1.40 × 103 |
MEAN | 1.40 × 103 | 1.40 × 103 | 1.40 × 103 | 1.41 × 103 | 1.40 × 103 | 1.41 × 103 | 1.44 × 103 | 1.40 × 103 | 1.43 × 103 | 1.40 × 103 | |
STD | 6.10 × 10−2 | 2.36 × 10−1 | 6.06 × 10−1 | 8.30 | 2.40 × 10−1 | 5.84 | 1.06 × 101 | 1.03 | 9.46 | 2.04 × 10−1 | |
CEC15 | MIN | 1.50 × 103 | 1.50 × 103 | 1.51 × 103 | 1.51 × 103 | 1.50 × 103 | 1.76 × 103 | 3.23 × 103 | 1.50 × 103 | 1.58 × 103 | 1.50 × 103 |
MEAN | 1.50 × 103 | 1.50 × 103 | 1.59 × 103 | 2.20 × 103 | 1.51 × 103 | 5.83 × 103 | 2.19 × 104 | 1.66 × 103 | 5.27 × 103 | 1.50 × 103 | |
STD | 4.57 × 10−1 | 1.49 | 4.45 × 102 | 1.51 × 103 | 5.63 | 3.46 × 103 | 2.19 × 104 | 8.45 × 102 | 5.14 × 103 | 5.89 × 10−1 | |
CEC16 | MIN | 1.60 × 103 | 1.60 × 103 | 1.60 × 103 | 1.60 × 103 | 1.60 × 103 | 1.60 × 103 | 1.60 × 103 | 1.60 × 103 | 1.60 × 103 | 1.60 × 103 |
MEAN | 1.60 × 103 | 1.60 × 103 | 1.60 × 103 | 1.60 × 103 | 1.60 × 103 | 1.60 × 103 | 1.60 × 103 | 1.60 × 103 | 1.60 × 103 | 1.60 × 103 | |
STD | 3.06 × 10−1 | 3.86 × 10−1 | 2.39 × 10−1 | 3.20 × 10−1 | 3.69 × 10−1 | 2.15 × 10−1 | 2.86 × 10−1 | 3.03 × 10−1 | 3.05 × 10−1 | 3.51 × 10−1 | |
CEC17 | MIN | 1.77 × 103 | 1.96 × 103 | 8.48 × 103 | 3.77 × 103 | 7.57 × 103 | 2.59 × 105 | 6.07 × 105 | 5.17 × 103 | 2.89 × 104 | 2.24 × 103 |
MEAN | 2.39 × 103 | 2.61 × 103 | 6.86 × 104 | 4.35 × 105 | 2.41 × 105 | 4.84 × 105 | 6.05 × 106 | 1.06 × 105 | 3.95 × 105 | 9.16 × 103 | |
STD | 3.66 × 102 | 6.66 × 102 | 7.75 × 104 | 3.62 × 105 | 3.35 × 105 | 1.17 × 105 | 8.34 × 106 | 1.82 × 105 | 1.76 × 105 | 1.04 × 104 | |
CEC18 | MIN | 1.81 × 103 | 1.82 × 103 | 5.30 × 103 | 2.51 × 103 | 2.02 × 103 | 8.98 × 103 | 2.19 × 105 | 2.36 × 103 | 1.95 × 103 | 1.97 × 103 |
MEAN | 1.85 × 103 | 1.90 × 103 | 3.55 × 104 | 1.20 × 104 | 9.68 × 103 | 1.47 × 105 | 2.12 × 107 | 1.48 × 104 | 1.09 × 104 | 9.75 × 103 | |
STD | 2.46 × 101 | 5.33 × 101 | 3.22 × 104 | 8.69 × 103 | 9.10 × 103 | 2.36 × 105 | 2.98 × 107 | 1.31 × 104 | 8.97 × 103 | 7.50 × 103 | |
CEC19 | MIN | 1.90 × 103 | 1.90 × 103 | 1.90 × 103 | 1.90 × 103 | 1.90 × 103 | 1.91 × 103 | 1.92 × 103 | 1.90 × 103 | 1.90 × 103 | 1.90 × 103 |
MEAN | 1.90 × 103 | 1.90 × 103 | 1.91 × 103 | 1.91 × 103 | 1.91 × 103 | 1.92 × 103 | 1.97 × 103 | 1.90 × 103 | 1.95 × 103 | 1.90 × 103 | |
STD | 9.62 × 10−1 | 1.37 | 1.26 | 1.19 × 101 | 1.43 | 1.48 × 101 | 3.64 × 101 | 1.02 | 2.95 | 1.68 | |
CEC20 | MIN | 2.01 × 103 | 2.01 × 103 | 2.13 × 103 | 2.13 × 103 | 2.26 × 103 | 6.01 × 103 | 2.93 × 104 | 2.21 × 103 | 4.81 × 103 | 2.08 × 103 |
MEAN | 2.03 × 103 | 2.09 × 103 | 8.79 × 103 | 3.46 × 104 | 1.43 × 104 | 3.85 × 104 | 3.08 × 106 | 1.04 × 104 | 9.69 × 103 | 3.41 × 103 | |
STD | 1.79 × 101 | 8.23 × 101 | 5.48 × 103 | 4.51 × 104 | 8.69 × 103 | 1.27 × 105 | 5.11 × 106 | 7.95 × 103 | 5.73 × 103 | 1.87 × 103 | |
CEC21 | MIN | 2.10 × 103 | 2.12 × 103 | 4.33 × 103 | 3.29 × 103 | 1.38 × 104 | 9.73 × 103 | 4.91 × 104 | 3.34 × 103 | 3.75 × 103 | 2.24 × 103 |
MEAN | 2.35 × 103 | 2.44 × 103 | 1.35 × 104 | 1.84 × 105 | 1.18 × 106 | 1.38 × 106 | 6.16 × 106 | 1.37 × 104 | 1.00 × 106 | 2.91 × 103 | |
STD | 1.78 × 102 | 2.34 × 102 | 5.51 × 103 | 8.18 × 105 | 3.05 × 106 | 2.21 × 106 | 1.15 × 107 | 8.29 × 103 | 1.73 × 106 | 4.51 × 102 | |
CEC22 | MIN | 2.20 × 103 | 2.22 × 103 | 2.24 × 103 | 2.23 × 103 | 2.23 × 103 | 2.28 × 103 | 2.29 × 103 | 2.23 × 103 | 2.24 × 103 | 2.21 × 103 |
MEAN | 2.22 × 103 | 2.24 × 103 | 2.30 × 103 | 2.35 × 103 | 2.32 × 103 | 2.43 × 103 | 2.78 × 103 | 2.28 × 103 | 2.43 × 103 | 2.30 × 103 | |
STD | 7.22 | 5.64 × 101 | 4.41 × 101 | 7.99 × 101 | 9.39 × 101 | 7.55 × 101 | 2.16 × 102 | 5.77 × 101 | 1.09 × 102 | 8.66 × 101 | |
CEC23 | MIN | 2.50 × 103 | 2.50 × 103 | 2.64 × 103 | 2.50 × 103 | 2.50 × 103 | 2.50 × 103 | 2.50 × 103 | 2.63 × 103 | 2.50 × 103 | 2.50 × 103 |
MEAN | 2.50 × 103 | 2.50 × 103 | 2.65 × 103 | 2.50 × 103 | 2.62 × 103 | 2.50 × 103 | 2.50 × 103 | 2.65 × 103 | 2.50 × 103 | 2.51 × 103 | |
STD | 0 | 0 | 6.76 | 0 | 4.95 × 101 | 0 | 0 | 8.92 | 0 | 2.24 × 101 | |
CEC24 | MIN | 2.51 × 103 | 2.53 × 103 | 2.55 × 103 | 2.60 × 103 | 2.54 × 103 | 2.59 × 103 | 2.60 × 103 | 2.53 × 103 | 2.56 × 103 | 2.52 × 103 |
MEAN | 2.57 × 103 | 2.58 × 103 | 2.56 × 103 | 2.60 × 103 | 2.58 × 103 | 2.60 × 103 | 2.60 × 103 | 2.55 × 103 | 2.59 × 103 | 2.56 × 103 | |
STD | 2.50 × 101 | 2.93 × 101 | 7.07 | 0 | 2.99 × 101 | 4.07 | 0 | 2.46 × 101 | 1.81 × 101 | 3.64 × 101 | |
CEC25 | MIN | 2.63 × 103 | 2.70 × 103 | 2.67 × 103 | 2.70 × 103 | 2.67 × 103 | 2.70 × 103 | 2.70 × 103 | 2.70 × 103 | 2.70 × 103 | 2.67 × 103 |
MEAN | 2.69 × 103 | 2.69 × 103 | 2.70 × 103 | 2.70 × 103 | 2.69 × 103 | 2.70 × 103 | 2.70 × 103 | 2.70 × 103 | 2.70 × 103 | 2.68 × 103 | |
STD | 1.23 × 101 | 1.70 × 101 | 1.44 × 101 | 0 | 1.53 × 101 | 0 | 0 | 1.55 | 3.43 | 2.70 × 101 | |
CEC26 | MIN | 2.70 × 103 | 2.70 × 103 | 2.70 × 103 | 2.70 × 103 | 2.70 × 103 | 2.70 × 103 | 2.70 × 103 | 2.70 × 103 | 2.70 × 103 | 2.70 × 103 |
MEAN | 2.70 × 103 | 2.70 × 103 | 2.70 × 103 | 2.70 × 103 | 2.70 × 103 | 2.70 × 103 | 2.71 × 103 | 2.70 × 103 | 2.71 × 103 | 2.70 × 103 | |
STD | 7.71 × 10−2 | 8.27 × 10−2 | 2.06 × 10−1 | 1.80 × 101 | 1.82 × 10−1 | 7.36 × 10−1 | 1.75 × 101 | 1.36 × 10−1 | 2.45 × 101 | 1.17 × 10−1 | |
CEC27 | MIN | 2.70 × 103 | 2.70 × 103 | 2.72 × 103 | 2.90 × 103 | 2.71 × 103 | 2.90 × 103 | 2.90 × 103 | 3.10 × 103 | 2.90 × 103 | 2.90 × 103 |
MEAN | 2.83 × 103 | 2.84 × 103 | 3.05 × 103 | 2.89 × 103 | 3.18 × 103 | 2.90 × 103 | 2.90 × 103 | 3.14 × 103 | 2.92 × 103 | 3.00 × 103 | |
STD | 4.96 × 101 | 9.30 × 101 | 1.43 × 102 | 3.22 × 101 | 1.19 × 102 | 0 | 0 | 5.98 × 101 | 1.02 × 102 | 9.06 × 101 | |
CEC28 | MIN | 3.00 × 103 | 3.00 × 103 | 3.24 × 103 | 3.00 × 103 | 3.00 × 103 | 3.00 × 103 | 3.00 × 103 | 3.17 × 103 | 3.00 × 103 | 3.03 × 103 |
MEAN | 3.00 × 103 | 3.00 × 103 | 3.30 × 103 | 3.00 × 103 | 3.46 × 103 | 3.00 × 103 | 3.00 × 103 | 3.19 × 103 | 3.00 × 103 | 3.22 × 103 | |
STD | 0 | 0 | 5.49 × 101 | 0 | 2.05 × 102 | 0 | 0 | 9.96 × 100 | 0 | 1.44 × 102 | |
CEC29 | MIN | 3.10 × 103 | 3.11 × 103 | 5.34 × 103 | 3.10 × 103 | 3.22 × 103 | 3.10 × 103 | 3.10 × 103 | 3.48 × 103 | 3.10 × 103 | 3.33 × 103 |
MEAN | 3.10 × 103 | 6.88 × 104 | 2.26 × 104 | 2.05 × 105 | 2.99 × 105 | 3.10 × 103 | 3.10 × 103 | 5.62 × 103 | 7.72 × 105 | 8.44 × 105 | |
STD | 0 | 3.59 × 105 | 1.89 × 104 | 7.73 × 105 | 8.25 × 105 | 0 | 0 | 2.70 × 103 | 2.33 × 106 | 1.28 × 106 | |
CEC30 | MIN | 3.20 × 103 | 3.49 × 103 | 4.13 × 103 | 3.73 × 103 | 3.79 × 103 | 3.20 × 103 | 3.20 × 103 | 3.79 × 103 | 4.89 × 103 | 3.46 × 103 |
MEAN | 3.20 × 103 | 3.91 × 103 | 5.17 × 103 | 9.73 × 103 | 6.36 × 103 | 3.20 × 103 | 3.20 × 103 | 4.14 × 103 | 4.88 × 104 | 1.31 × 104 | |
STD | 0 | 4.51 × 102 | 1.07 × 103 | 1.11 × 104 | 1.99 × 103 | 0 | 0 | 2.74 × 102 | 1.06 × 105 | 3.24 × 104 |
CEC2020 | Metric | MGTO | GTO | SCA | ROA | WOA | RSA | SHO | SOA | AOA | HBA |
---|---|---|---|---|---|---|---|---|---|---|---|
CEC1 | MIN | 1.00 × 102 | 1.02 × 102 | 5.21 × 108 | 1.29 × 109 | 5.98 × 106 | 6.48 × 109 | 7.07 × 109 | 1.25 × 107 | 3.59 × 109 | 1.78 × 102 |
MEAN | 8.74 × 102 | 2.57 × 103 | 1.15 × 109 | 4.79 × 109 | 6.72 × 107 | 1.19 × 1010 | 1.62 × 1010 | 4.00 × 108 | 1.01 × 1010 | 4.59 × 103 | |
STD | 5.15 × 102 | 3.18 × 103 | 3.57 × 108 | 3.22 × 109 | 8.06 × 107 | 4.44 × 109 | 5.00 × 109 | 3.69 × 108 | 4.32 × 109 | 3.93 × 103 | |
CEC2 | MIN | 1.15 × 103 | 1.50 × 103 | 2.26 × 103 | 2.09 × 103 | 1.72 × 103 | 2.33 × 103 | 3.04 × 103 | 1.66 × 103 | 1.90 × 103 | 1.47 × 103 |
MEAN | 1.66 × 103 | 2.02 × 103 | 2.55 × 103 | 2.59 × 103 | 2.33 × 103 | 2.78 × 103 | 3.47 × 103 | 2.11 × 103 | 2.29 × 103 | 1.89 × 103 | |
STD | 2.15 × 102 | 3.02 × 102 | 2.51 × 102 | 2.80 × 102 | 3.13 × 102 | 2.46 × 102 | 2.80 × 102 | 2.23 × 102 | 2.70 × 102 | 4.87 × 102 | |
CEC3 | MIN | 7.07 × 102 | 7.26 × 102 | 7.70 × 102 | 7.74 × 102 | 7.55 × 102 | 7.97 × 102 | 8.42 × 102 | 7.55 × 102 | 7.74 × 102 | 7.21 × 102 |
MEAN | 7.39 × 102 | 7.55 × 102 | 7.87 × 102 | 8.16 × 102 | 8.02 × 102 | 8.12 × 102 | 8.73 × 102 | 7.69 × 102 | 8.00 × 102 | 7.39 × 102 | |
STD | 1.46 × 101 | 1.73 × 101 | 1.41 × 101 | 2.89 × 101 | 2.83 × 101 | 1.13 × 101 | 2.26 × 101 | 1.58 × 101 | 1.65 × 101 | 1.47 × 101 | |
CEC4 | MIN | 1.90 × 103 | 1.90 × 103 | 1.90 × 103 | 1.90 × 103 | 1.90 × 103 | 1.90 × 103 | 1.90 × 103 | 1.90 × 103 | 1.90 × 103 | 1.90 × 103 |
MEAN | 1.90 × 103 | 1.90 × 103 | 1.90 × 103 | 1.90 × 103 | 1.90 × 103 | 1.90 × 103 | 1.90 × 103 | 1.90 × 103 | 1.90 × 103 | 1.90 × 103 | |
STD | 0 | 0 | 1.32 | 0 | 4.09 × 10−1 | 0 | 0 | 4.46 × 10−1 | 0 | 0 | |
CEC5 | MIN | 1.78 × 103 | 1.94 × 103 | 1.25 × 104 | 5.46 × 103 | 3.68 × 103 | 3.26 × 105 | 4.12 × 105 | 5.66 × 103 | 9.75 × 103 | 1.87 × 103 |
MEAN | 2.35 × 103 | 2.54 × 103 | 1.02 × 105 | 3.38 × 105 | 2.13 × 105 | 4.84 × 105 | 3.90 × 106 | 1.18 × 105 | 3.63 × 105 | 6.28 × 103 | |
STD | 2.73 × 102 | 5.79 × 102 | 1.16 × 105 | 2.98 × 105 | 3.73 × 105 | 7.88 × 104 | 5.11 × 106 | 1.85 × 105 | 1.72 × 105 | 8.09 × 103 | |
CEC6 | MIN | 1.60 × 103 | 1.60 × 103 | 1.71 × 103 | 1.74 × 103 | 1.71 × 103 | 1.92 × 103 | 2.25 × 103 | 1.66 × 103 | 1.84 × 103 | 1.60 × 103 |
MEAN | 1.64 × 103 | 1.75 × 103 | 1.87 × 103 | 1.92 × 103 | 1.87 × 103 | 2.27 × 103 | 2.75 × 103 | 1.82 × 103 | 2.09 × 103 | 1.81 × 103 | |
STD | 5.06 × 101 | 1.21 × 102 | 9.28 × 101 | 1.25 × 102 | 1.30 × 102 | 1.71 × 102 | 3.37 × 102 | 9.10 × 101 | 1.89 × 102 | 1.87 × 102 | |
CEC7 | MIN | 2.10 × 103 | 2.11 × 103 | 4.96 × 103 | 2.93 × 103 | 8.95 × 103 | 2.35 × 104 | 3.66 × 104 | 3.11 × 103 | 5.39 × 103 | 2.18 × 103 |
MEAN | 2.36 × 103 | 2.64 × 103 | 1.52 × 104 | 2.19 × 105 | 1.06 × 106 | 1.38 × 106 | 3.59 × 106 | 1.80 × 104 | 7.18 × 105 | 3.05 × 103 | |
STD | 2.07 × 102 | 6.00 × 102 | 1.07 × 104 | 7.49 × 105 | 2.93 × 106 | 2.02 × 106 | 3.57 × 106 | 3.67 × 104 | 1.14 × 106 | 7.36 × 102 | |
CEC8 | MIN | 2.20 × 103 | 2.30 × 103 | 2.35 × 103 | 2.36 × 103 | 2.28 × 103 | 2.74 × 103 | 3.21 × 103 | 2.26 × 103 | 2.66 × 103 | 2.30 × 103 |
MEAN | 2.30 × 103 | 2.30 × 103 | 2.46 × 103 | 2.74 × 103 | 2.52 × 103 | 3.29 × 103 | 3.97 × 103 | 3.02 × 103 | 3.10 × 103 | 2.30 × 103 | |
STD | 1.55 × 101 | 1.61 × 101 | 2.93 × 102 | 3.98 × 102 | 5.31 × 102 | 3.30 × 102 | 4.78 × 102 | 7.18 × 102 | 3.37 × 102 | 1.16 × 101 | |
CEC9 | MIN | 2.50 × 103 | 2.50 × 103 | 2.77 × 103 | 2.72 × 103 | 2.60 × 103 | 2.81 × 103 | 2.86 × 103 | 2.74 × 103 | 2.77 × 103 | 2.74 × 103 |
MEAN | 2.65 × 103 | 2.70 × 103 | 2.79 × 103 | 2.80 × 103 | 2.79 × 103 | 2.90 × 103 | 2.96 × 103 | 2.76 × 103 | 2.86 × 103 | 2.74 × 103 | |
STD | 1.22 × 102 | 1.11 × 102 | 3.66 × 101 | 7.18 × 101 | 5.20 × 101 | 6.80 × 101 | 7.01 × 101 | 4.58 × 101 | 8.25 × 101 | 6.91 × 101 | |
CEC10 | MIN | 2.60 × 103 | 2.90 × 103 | 2.94 × 103 | 2.97 × 103 | 2.91 × 103 | 3.23 × 103 | 3.48 × 103 | 2.92 × 103 | 3.11 × 103 | 2.90 × 103 |
MEAN | 2.92 × 103 | 2.94 × 103 | 2.99 × 103 | 3.22 × 103 | 2.98 × 103 | 3.51 × 103 | 3.90 × 103 | 2.95 × 103 | 3.39 × 103 | 2.93 × 103 | |
STD | 2.15 × 101 | 3.19 × 101 | 3.20 × 101 | 2.13 × 102 | 8.10 × 101 | 2.49 × 102 | 4.14 × 102 | 3.69 × 101 | 2.32 × 102 | 2.30 × 101 |
CEC2014 | MGTO VS GTO | MGTO VS SCA | MGTO VS ROA | MGTO VS WOA | MGTO VS RSA | MGTO VS SHO | MGTO VS SOA | MGTO VS AOA | MGTO VS HBA |
---|---|---|---|---|---|---|---|---|---|
CEC1 | 3.32 × 10−4 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 2.41 × 10−4 |
CEC2 | 2.60 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 |
CEC3 | 3.59 × 10−4 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 2.88 × 10−6 |
CEC4 | 4.28 × 10−2 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 4.65 × 10−1 |
CEC5 | 2.85 × 10−2 | 1.73 × 10−6 | 1.73 × 10−6 | 1.92 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.92 × 10−6 |
CEC6 | 3.88 × 10−4 | 1.73 × 10−6 | 1.73 × 10−6 | 1.92 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.64 × 10−5 | 1.73 × 10−6 | 9.63 × 10−4 |
CEC7 | 9.32 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 |
CEC8 | 5.75 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 8.22 × 10−2 |
CEC9 | 7.34 × 10−1 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 4.29 × 10−6 | 1.73 × 10−6 | 6.98 × 10−6 |
CEC10 | 2.35 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 5.22 × 10−6 |
CEC11 | 1.89 × 10−4 | 1.73 × 10−6 | 1.73 × 10−6 | 2.35 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 2.35 × 10−6 | 2.88 × 10−6 | 2.16 × 10−5 |
CEC12 | 3.82 × 10−1 | 1.73 × 10−6 | 1.92 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.97 × 10−5 | 4.72 × 10−2 |
CEC13 | 1.64 × 10−5 | 1.73 × 10−6 | 1.73 × 10−6 | 1.92 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.02 × 10−5 |
CEC14 | 2.22 × 10−4 | 1.73 × 10−6 | 2.88 × 10−6 | 2.41 × 10−3 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 2.84 × 10−5 |
CEC15 | 1.11 × 10−3 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 8.29 × 10−1 |
CEC16 | 2.58 × 10−3 | 1.73 × 10−6 | 2.88 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.92 × 10−6 | 2.18 × 10−2 |
CEC17 | 4.05 × 10−1 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 4.29 × 10−6 |
CEC18 | 1.85 × 10−2 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 |
CEC19 | 4.20 × 10−4 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 8.47 × 10−6 | 1.73 × 10−6 | 2.05 × 10−4 |
CEC20 | 8.94 × 10−4 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 |
CEC21 | 5.45 × 10−2 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.92 × 10−6 |
CEC22 | 3.39 × 10−1 | 1.73 × 10−6 | 5.75 × 10−6 | 2.35 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 2.13 × 10−6 | 3.32 × 10−4 |
CEC23 | 1 | 1.73 × 10−6 | 1 | 2.56 × 10−6 | 1 | 1 | 1.73 × 10−6 | 1 | 9.77 × 10−4 |
CEC24 | 6.96 × 10−1 | 1.92 × 10−6 | 1 | 1.75 × 10−2 | 1 | 1 | 2.60 × 10−6 | 3.42 × 10−2 | 1.15 × 10−4 |
CEC25 | 1.74 × 10−2 | 1.73 × 10−6 | 2.44 × 10−4 | 4.88 × 10−2 | 2.44 × 10−4 | 2.44 × 10−4 | 2.13 × 10−6 | 2.44 × 10−4 | 2.47 × 10−1 |
CEC26 | 5.04 × 10−1 | 1.73 × 10−6 | 1.92 × 10−6 | 2.88 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 4.29 × 10−6 | 1.73 × 10−6 | 7.81 × 10−1 |
CEC27 | 5.37 × 10−2 | 1.24 × 10−5 | 5.00 × 10−1 | 1.92 × 10−6 | 5.00 × 10−1 | 5.00 × 10−1 | 3.18 × 10−6 | 5.00 × 10−1 | 8.22 × 10−3 |
CEC28 | 1 | 1.73 × 10−6 | 1 | 1.73 × 10−6 | 1 | 1 | 1.73 × 10−6 | 5.00 × 10−1 | 1.73 × 10−6 |
CEC29 | 1.73 × 10−6 | 1.73 × 10−6 | 5.95 × 10−5 | 1.73 × 10−6 | 1 | 1 | 1.73 × 10−6 | 1.22 × 10−4 | 1.73 × 10−6 |
CEC30 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1 | 1 | 1.73 × 10−6 | 5.61 × 10−6 | 1.73 × 10−6 |
CEC2020 | MGTO VS GTO | MGTO VS SCA | MGTO VS ROA | MGTO VS WOA | MGTO VS RSA | MGTO VS SHO | MGTO VS SOA | MGTO VS AOA | MGTO VS HBA |
---|---|---|---|---|---|---|---|---|---|
CEC1 | 4.72 × 10−2 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 7.19 × 10−2 |
CEC2 | 1.48 × 10−4 | 1.73 × 10−6 | 1.73 × 10−6 | 7.69 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 4.45 × 10−5 | 4.29 × 10−6 | 1.25 × 10−2 |
CEC3 | 2.22 × 10−4 | 1.73 × 10−6 | 2.35 × 10−6 | 2.35 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 2.60 × 10−5 | 2.13 × 10−6 | 4.07 × 10−2 |
CEC4 | 1 | 1.22 × 10−4 | 1 | 3.13 × 10−2 | 1 | 1 | 2.50 × 10−1 | 1 | 1 |
CEC5 | 4.72 × 10−2 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.64 × 10−5 |
CEC6 | 2.61 × 10−4 | 1.73 × 10−6 | 4.29 × 10−6 | 3.18 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 8.92 × 10−5 | 1.73 × 10−6 | 1.36 × 10−4 |
CEC7 | 4.11 × 10−3 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.92 × 10−6 | 9.32 × 10−6 |
CEC8 | 2.70 × 10−2 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 6.87 × 10−2 |
CEC9 | 2.58 × 10−3 | 1.24 × 10−5 | 1.73 × 10−6 | 2.88 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 3.72 × 10−5 | 1.92 × 10−6 | 1.11 × 10−3 |
CEC10 | 2.80 × 10−1 | 4.73 × 10−6 | 1.73 × 10−6 | 1.92 × 10−6 | 1.73 × 10−6 | 1.73 × 10−6 | 3.82 × 10−1 | 1.73 × 10−6 | 6.73 × 10−1 |
Algorithm | Ts | Th | R | L | Best Cost |
---|---|---|---|---|---|
MGTO | 0.7424 | 0.3702 | 40.3196 | 200.0000 | 5734.9132 |
MGTOA [29] | 0.754363 | 0.366375 | 40.42809 | 198.5652 | 5752.402458 |
EO [2] | 1.0480 | 0.5114 | 55.3848 | 60.6465 | 6470.6125 |
HBA [28] | 1.2404 | 0.5844 | 65.2252 | 10.0000 | 7141.3612 |
GWO [14] | 0.8125 | 0.4375 | 42.0984 | 176.6366 | 6059.7143 |
HHO [18] | 1.2492 | 0.5810 | 65.2139 | 10.0487 | 7149.8665 |
WOA [19] | 0.8125 | 0.4375 | 42.09845 | 176.6366 | 6059.714335 |
MVO [3] | 1.2269 | 0.5928 | 64.3294 | 14.0578 | 7106.0065 |
ACO [30] | 0.8125 | 0.4375 | 42.10362 | 176.7387 | 6059.0888 |
NGO [31] | 0.7427 | 0.3708 | 40.3199 | 200.0000 | 5735.0462 |
EROA [32] | 0.84343 | 0.400762 | 44.786 | 145.9578 | 5935.7301 |
PSO [13] | 0.8861 | 0.4306 | 46.9699 | 124.3784 | 6024.2816 |
Algorithm | Optimal Values for Variables | Optimal Weight | ||||||
---|---|---|---|---|---|---|---|---|
x1 | x2 | x3 | x4 | x5 | x6 | x7 | ||
MGTO | 3.47641 | 0.7 | 17 | 7.3 | 7.8 | 3.3486 | 5.27678 | 2988.2713 |
MDA [33] | 3.5 | 0.7 | 17 | 7.3 | 7.67039 | 3.54242 | 5.2481 | 3019.5833 |
MFO [34] | 3.497455 | 0.7 | 17 | 7.82775 | 7.712457 | 3.351787 | 5.286352 | 2998.94083 |
CS [35] | 3.5015 | 0.7 | 17 | 7.605 | 7.8181 | 3.352 | 5.2875 | 3000.981 |
RSA [27] | 3.50279 | 0.7 | 17 | 7.30812 | 7.74715 | 3.35067 | 5.28675 | 2996.5157 |
HS [36] | 3.520124 | 0.7 | 17 | 8.37 | 7.8 | 3.36697 | 5.288719 | 3029.002 |
Algorithm | h | l | t | b | Best Weight |
---|---|---|---|---|---|
MGTO | 0.2057 | 3.2531 | 9.03662 | 0.2057 | 1.6952 |
GTO [21] | 0.2094 | 3.21 | 8.9565 | 0.2094 | 1.7087 |
WOA [19] | 0.20536 | 3.48293 | 9.03746 | 0.206276 | 1.730499 |
ROA [16] | 0.200077 | 3.365754 | 9.011182 | 0.206893 | 1.706447 |
GWO [14] | 0.205676 | 3.478377 | 9.03681 | 0.205778 | 1.72624 |
GA [37] | 0.1829 | 4.0483 | 9.3666 | 0.2059 | 1.8242 |
MFO [34] | 0.2057 | 3.4703 | 9.0364 | 0.2057 | 1.72452 |
MVO [3] | 0.205463 | 3.473193 | 9.044502 | 0.205695 | 1.72645 |
GSA [38] | 0.182129 | 3.856979 | 10 | 0.202376 | 1.879952 |
TSA [39] | 0.24415 | 6.223 | 8.2955 | 0.2444 | 2.3824 |
MROA [40] | 0.2062185 | 3.254893 | 9.020003 | 0.206489 | 1.699058 |
Algorithm | d | D | V | Best Weight |
---|---|---|---|---|
MGTO | 0.05 | 0.37443 | 8.546566 | 0.009872 |
SSA [41] | 0.051207 | 0.345215 | 12.00403 | 0.012676 |
ES [9] | 0.051989 | 0.363965 | 10.89052 | 0.012681 |
PSO [13] | 0.051728 | 0.357644 | 11.24454 | 0.012675 |
EROA [32] | 0.053799 | 0.46951 | 5.811 | 0.010614 |
HHO [18] | 0.051796 | 0.359305 | 11.13886 | 0.012665 |
HS [36] | 0.051154 | 0.349871 | 12.07643 | 0.012671 |
AO [42] | 0.0502439 | 0.35262 | 10.5425 | 0.011165 |
DE [12] | 0.051609 | 0.354714 | 11.41083 | 0.01267 |
Algorithm | Optimal Values for Variables | Optimum Weight | ||||
---|---|---|---|---|---|---|
x1 | x2 | x3 | x4 | x5 | ||
MGTO | 6.0142 | 5.3107 | 4.4942 | 3.5010 | 2.15338 | 1.33995647611238 |
WOA [19] | 5.1261 | 5.6188 | 5.0952 | 3.9329 | 2.3219 | 1.37873150673956 |
BWO [43] | 6.2094 | 6.2094 | 6.2094 | 6.2094 | 6.2094 | 1.93736251728534 |
PSO [13] | 6.0040 | 5.2950 | 4.4915 | 3.5125 | 2.1710 | 1.33998298081255 |
GSA [38] | 5.6052 | 4.9553 | 5.6619 | 3.1959 | 3.2026 | 1.41155753917296 |
ERHHO [44] | 6.0509 | 5.2639 | 4.514 | 3.4605 | 2.1878 | 1.3402 |
SCA [6] | 5.1096 | 5.9911 | 5.0150 | 3.7095 | 3.2744 | 1.44143866919587 |
Algorithm | Optimal Values for Variables | Optimum Weight | ||||
---|---|---|---|---|---|---|
x1 | x2 | x3 | x4 | x5 | ||
MGTO | 70 | 90 | 1 | 600 | 2 | 0.235242 |
TLBO [45] | 70 | 90 | 1 | 810 | 3 | 0.313656611 |
WCA [46] | 70 | 90 | 1 | 910 | 3 | 0.313656 |
SCA [6] | 69.516 | 90 | 1 | 1000 | 2 | 0.24019 |
CMVO [47] | 70 | 90 | 1 | 910 | 3 | 0.313656 |
MFO [34] | 70 | 90 | 1 | 910 | 3 | 0.313656 |
Algorithm | MGTO | GTO [21] | ROA [16] | MPA [48] | SOA [17] | HHOCM [49] | MSCSO [50] | MALO [51] |
---|---|---|---|---|---|---|---|---|
x1 | 0.5 | 0.5 | 0.5 | 0.5 | 0.50063 | 0.500164 | 0.50011 | 0.5 |
x2 | 1.2292 | 1.2607 | 1.22942 | 1.22823 | 1.25921 | 1.248612 | 1.22826 | 1.2281 |
x3 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.659558 | 0.50001 | 0.5 |
x4 | 1.20079 | 1.1495 | 1.21197 | 1.2049 | 1.26308 | 1.098515 | 1.20254 | 1.2126 |
x5 | 0.5 | 0.6205 | 0.5 | 0.5 | 0.9377 | 0.757989 | 0.50019 | 0.5 |
x6 | 1.07605 | 0.8860 | 1.37798 | 1.2393 | 1.11573 | 0.767268 | 1.05280 | 1.308 |
x7 | 0.5 | 0.5 | 0.50005 | 0.5 | 0.5 | 0.500055 | 0.50002 | 0.5 |
x8 | 0.345 | 0.34485 | 0.34489 | 0.34498 | 0.334889 | 0.343105 | 0.34499 | 0.3449 |
x9 | 0.345 | 0.344608 | 0.19263 | 0.192 | 0.252275 | 0.192032 | 0.33595 | 0.2804 |
x10 | 0.62110 | 6.202292 | 0.62239 | 0.44035 | 4.3435 | 2.898805 | 0.46117 | 0.4242 |
x11 | 0.64810 | 7.3429 | - | 1.78504 | 16.2208 | - | 1.05012 | 4.6565 |
Best Weight | 23.18916 | 23.4084 | 23.23544 | 23.19982 | 24.42114 | 24.48358 | 23.19085 | 23.2294 |
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You, J.; Jia, H.; Wu, D.; Rao, H.; Wen, C.; Liu, Q.; Abualigah, L. Modified Artificial Gorilla Troop Optimization Algorithm for Solving Constrained Engineering Optimization Problems. Mathematics 2023, 11, 1256. https://doi.org/10.3390/math11051256
You J, Jia H, Wu D, Rao H, Wen C, Liu Q, Abualigah L. Modified Artificial Gorilla Troop Optimization Algorithm for Solving Constrained Engineering Optimization Problems. Mathematics. 2023; 11(5):1256. https://doi.org/10.3390/math11051256
Chicago/Turabian StyleYou, Jinhua, Heming Jia, Di Wu, Honghua Rao, Changsheng Wen, Qingxin Liu, and Laith Abualigah. 2023. "Modified Artificial Gorilla Troop Optimization Algorithm for Solving Constrained Engineering Optimization Problems" Mathematics 11, no. 5: 1256. https://doi.org/10.3390/math11051256
APA StyleYou, J., Jia, H., Wu, D., Rao, H., Wen, C., Liu, Q., & Abualigah, L. (2023). Modified Artificial Gorilla Troop Optimization Algorithm for Solving Constrained Engineering Optimization Problems. Mathematics, 11(5), 1256. https://doi.org/10.3390/math11051256