A Novel Improved Whale Optimization Algorithm for Global Optimization and Engineering Applications
Abstract
:1. Introduction
2. Whale Optimization Algorithm
2.1. Encircling Prey
2.2. Bubble-Net Attacking
2.3. Search for Prey
3. Improved Whale Optimization Algorithm
3.1. Sine–Tent–Cosine Map
3.2. Gaining–Sharing Knowledge Based Algorithm
3.3. Dynamic Opposition-Based Learning
Algorithm 1 Function DOBL |
|
3.4. DGSWOA Algorithm Description
Algorithm 2 DGSWOA Algorithm |
|
3.5. Complexity Analysis
4. Experimental Design and Results Analysis
4.1. Parameter Settings
4.2. Benchmark Functions
4.3. Impact of Different Strategies on the Algorithm
4.4. Optimization Results Comparison
4.4.1. Algorithm Performance Criteria Analysis
4.4.2. Wilcoxon Signed-Rank Test Results
5. Engineering Application
5.1. Three-Bar Truss Design
5.2. Pressure Vessel Design
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Algorithms | Iteration | Population | Details |
---|---|---|---|
WOA | 500 | 30 | |
PSO | 500 | 30 | |
GA | 500 | 30 | Roulette wheel selection, a mutation probability of 0.1, and uniform crossover with a crossover probability of 1 |
GWO | 500 | 30 | |
BOA | 500 | 30 | , power exponent = 0.1, sensory modality = 0.1 |
SOA | 500 | 30 | |
LWOA | 500 | 30 | |
MSWOA | 500 | 30 | |
DGSWOA | 500 | 30 |
F | Functions | Dimension | Search Range |
---|---|---|---|
Sphere Function | 2, 3, 5, 10, 20, 40 | [−5 to 5] | |
Separable Ellipsoidal Function | 2, 3, 5, 10, 20, 40 | [−5 to 5] | |
Rastrigin Function | 2, 3, 5, 10, 20, 40 | [−5 to 5] | |
Büche–Rastrigin Function | 2, 3, 5, 10, 20, 40 | [−5 to 5] | |
Linear Slope | 2, 3, 5, 10, 20, 40 | [−5 to 5] | |
Attractive Sector Function | 2, 3, 5, 10, 20, 40 | [−5 to 5] | |
Step Ellipsoidal Function | 2, 3, 5, 10, 20, 40 | [−5 to 5] | |
Rosenbrock Function, original | 2, 3, 5, 10, 20, 40 | [−5 to 5] | |
Rosenbrock Function, rotated | 2, 3, 5, 10, 20, 40 | [−5 to 5] | |
Ellipsoidal Function | 2, 3, 5, 10, 20, 40 | [−5 to 5] | |
Discus Function | 2, 3, 5, 10, 20, 40 | [−5 to 5] | |
Bent Cigar Function | 2, 3, 5, 10, 20, 40 | [−5 to 5] | |
Sharp Ridge Function | 2, 3, 5, 10, 20, 40 | [−5 to 5] | |
Different Powers Function | 2, 3, 5, 10, 20, 40 | [−5 to 5] | |
Rastrigin Function | 2, 3, 5, 10, 20, 40 | [−5 to 5] | |
Weierstrass Function | 2, 3, 5, 10, 20, 40 | [−5 to 5] | |
Schaffer’s F7 Function | 2, 3, 5, 10, 20, 40 | [−5 to 5] | |
Schaffer’s F7 Function, moderately ill-conditioned | 2, 3, 5, 10, 20, 40 | [−5 to 5] | |
Composite Griewank–Rosenbrock Function F8F2 | 2, 3, 5, 10, 20, 40 | [−5 to 5] | |
Schwefel Function | 2, 3, 5, 10, 20, 40 | [−5 to 5] | |
Gallagher’s Gaussian 101-me Peaks Function | 2, 3, 5, 10, 20, 40 | [−5 to 5] | |
Gallagher’s Gaussian 21-hi Peaks Function | 2, 3, 5, 10, 20, 40 | [−5 to 5] | |
Katsuura Function | 2, 3, 5, 10, 20, 40 | [−5 to 5] | |
Lunacek bi-Rastrigin Function | 2, 3, 5, 10, 20, 40 | [−5 to 5] |
Function | Criteria | WOA | SWOA | GWOA | DWOA | DGSWOA |
---|---|---|---|---|---|---|
Mean | −9.18 | −9.17 | −9.19 × | −9.15 | −9.18 | |
Std | 3.88 | 5.67 × | 3.83 × | 5.79 | 4.12 | |
Best | −9.23 | −9.23 | −9.26 × | −9.22 | −9.26 | |
Worst | −9.11 | −9.13 × | −9.13 × | −9.02 | −9.10 | |
rank | 2 | 4 | 1 | 5 | 3 | |
Mean | 7.90 | 9.22 | 9.30 | 5.61 × | 7.23 | |
Std | 3.92 | 5.12 | 6.70 | 1.33 × | 2.31 | |
Best | 3.22 | 3.70 | 5.43 | 2.03 × | 5.72 | |
Worst | 1.67 | 2.63 | 2.63 | 6.99 × | 1.23 | |
rank | 3 | 4 | 5 | 1 | 2 | |
Mean | 6.94 | 7.58 | 7.35 | 8.02 | 6.91 × | |
Std | 9.72 | 1.08 | 8.73 × | 1.56 | 9.24 | |
Best | 5.06 × | 5.37 | 5.97 | 6.36 | 5.59 | |
Worst | 8.12 × | 9.15 | 9.15 | 1.12 | 8.51 | |
rank | 2 | 4 | 3 | 5 | 1 | |
Mean | 10.00 | 1.06 | 9.89 | 9.99 | 9.39 × | |
Std | 1.24 | 1.35 | 2.23 | 1.66 | 9.63 × | |
Best | 8.05 | 9.31 | 5.14 × | 6.89 | 7.70 | |
Worst | 1.19 | 1.29 | 1.29 | 1.21 | 1.05 × | |
rank | 4 | 5 | 2 | 3 | 1 | |
Mean | 5.19 | 5.18 | 5.20 | 5.17 × | 5.19 | |
Std | 6.38 | 3.74 | 9.33 | 3.68 × | 7.29 | |
Best | 5.15 × | 5.15 × | 5.15 × | 5.15 × | 5.15 × | |
Worst | 5.33 | 5.45 | 5.45 | 5.27 × | 5.39 | |
rank | 3 | 2 | 5 | 1 | 4 | |
Mean | 1.06 | 9.96 | 9.95 | 1.04 | 9.40 × | |
Std | 1.22 | 6.94 | 5.86 × | 1.02 | 5.93 | |
Best | 8.71 | 8.70 | 8.68 | 9.13 | 8.50 × | |
Worst | 1.26 | 1.08 | 1.08 | 1.26 | 1.02 × | |
rank | 5 | 3 | 2 | 4 | 1 | |
Mean | −7.01 | −7.00 | −7.44 | −7.41 | −7.68 × | |
Std | 5.74 | 3.70 × | 4.70 | 5.50 | 3.87 | |
Best | −8.06 | −7.77 | −7.94 | −8.19 × | −8.16 | |
Worst | −6.17 | −6.36 | −6.36 | −6.42 | −6.88 × | |
rank | 4 | 5 | 2 | 3 | 1 | |
Mean | 1.93 | 9.61 | −9.08 × | −6.03 | −3.79 | |
Std | 1.25 | 1.96 | 3.23 × | 5.97 | 7.36 | |
Best | −1.00 | −1.23 | −1.31 | −1.32 × | −1.16 | |
Worst | 2.39 | 4.66 | −3.03 × | −3.03 × | 9.40 | |
rank | 4 | 5 | 1 | 2 | 3 | |
Mean | −3.47 | −3.48 | −3.51 × | −3.45 | −3.49 | |
Std | 4.37 | 4.54 | 2.79 × | 6.72 | 4.07 | |
Best | −3.56 × | −3.55 | −3.56 | −3.55 | −3.56 | |
Worst | −3.39 | −3.47 × | −3.47 × | −3.35 | −3.43 | |
rank | 4 | 3 | 1 | 5 | 2 | |
Mean | 9.12 | 8.36 | 8.91 | 1.27 | 7.51 × | |
Std | 3.50 × | 6.20 | 5.25 | 7.66 | 4.45 | |
Best | 4.48 | 9.03 | 1.22 | 5.29 | 7.13 × | |
Worst | 1.58 × | 1.92 | 1.92 | 3.34 | 1.66 | |
rank | 4 | 2 | 3 | 5 | 1 | |
Mean | −3.99 | −3.68 | −4.14 | −4.54 | −4.79 × | |
Std | 5.68 × | 1.09 | 1.10 | 6.99 | 9.72 | |
Best | −5.13 | −4.77 | −6.27 | −5.56 | −6.32 × | |
Worst | −3.34 × | −2.49 | −2.49 | −2.81 | −3.03 | |
rank | 4 | 5 | 3 | 2 | 1 | |
Mean | 4.48 | 3.01 × | 6.12 | 3.75 | 5.00 | |
Std | 5.34 | 2.77 | 6.07 | 1.81 × | 3.32 | |
Best | 1.11 × | 1.80 | 4.25 | 1.07 | 3.40 | |
Worst | 1.88 | 2.32 | 2.32 | 5.80 × | 1.29 | |
rank | 3 | 1 | 5 | 2 | 4 | |
Mean | 1.10 | 9.89 | 1.19 | 1.19 | 8.12 × | |
Std | 3.80 × | 4.71 | 6.02 | 4.30 | 5.91 | |
Best | 5.56 | 3.80 | −1.72 | 4.35 | −3.90 × | |
Worst | 1.57 × | 1.87 | 1.87 | 2.00 | 1.64 | |
rank | 3 | 2 | 5 | 4 | 1 | |
Mean | −5.73 | −5.72 | −5.74 × | −5.74 | −5.74 | |
Std | 3.38 | 2.35 × | 2.96 | 3.29 | 2.46 | |
Best | −5.78 | −5.77 | −5.77 | −5.78 | −5.79 × | |
Worst | −5.65 | −5.70 | −5.70 | −5.68 | −5.71 × | |
rank | 4 | 5 | 1 | 3 | 2 | |
Mean | 1.57 × | 1.77 | 1.99 | 1.94 | 1.80 | |
Std | 7.15 × | 9.95 | 1.24 | 8.13 | 1.23 | |
Best | 3.01 | 5.80 | 1.13 | 7.08 | −7.62 × | |
Worst | 2.43 × | 5.08 | 5.08 | 3.78 | 3.43 | |
rank | 1 | 2 | 5 | 4 | 3 | |
Mean | −2.55 | −2.56 | −2.53 | −2.54 | −2.56 × | |
Std | 1.51 × | 1.89 | 1.97 | 2.75 | 2.31 | |
Best | −2.57 | −2.59 | −2.57 | −2.59 | −2.59 × | |
Worst | −2.52 × | −2.51 | −2.51 | −2.49 | −2.51 | |
rank | 3 | 2 | 5 | 4 | 1 | |
Mean | −3.73 × | −3.70 | −3.70 | −3.70 | −3.69 | |
Std | 6.09 | 5.98 | 3.91 | 5.33 | 3.40 × | |
Best | −3.85 × | −3.80 | −3.77 | −3.82 | −3.75 | |
Worst | −3.62 | −3.64 × | −3.64 × | −3.62 | −3.63 | |
rank | 1 | 3 | 4 | 2 | 5 | |
Mean | −3.30 | −3.22 | −3.36 | −3.36 | −3.37 × | |
Std | 1.70 | 1.38 | 1.72 | 1.91 | 7.92 × | |
Best | −3.51 | −3.39 | −3.60 × | −3.57 | −3.49 | |
Worst | −2.92 | −2.91 | −3.02 | −3.02 | −3.23 × | |
rank | 4 | 5 | 3 | 2 | 1 | |
Mean | 4.13 | 4.10 | 4.13 | 4.06 × | 4.06 | |
Std | 5.43 | 3.52 | 3.48 | 3.76 × | 4.11 | |
Best | 4.07 | 4.05 | 4.09 | 4.05 × | 4.05 | |
Worst | 4.23 | 4.21 | 4.21 | 4.06 × | 4.07 | |
rank | 4 | 3 | 5 | 1 | 2 | |
Mean | 1.85 | 1.85 | 1.85 | 1.85 | 1.85 × | |
Std | 2.44 × | 3.33 | 3.30 | 2.81 | 3.25 | |
Best | 1.85 | 1.85 | 1.85 × | 1.85 | 1.85 | |
Worst | 1.86 × | 1.86 | 1.86 | 1.86 | 1.86 | |
rank | 5 | 2 | 4 | 3 | 1 | |
Mean | 3.13 × | 3.14 | 3.15 | 3.15 | 3.14 | |
Std | 1.37 × | 2.58 | 2.01 | 2.86 | 1.98 | |
Best | 3.11 | 3.11 × | 3.13 | 3.13 | 3.11 | |
Worst | 3.17 × | 3.18 | 3.18 | 3.22 | 3.17 | |
rank | 1 | 2 | 5 | 4 | 3 | |
Mean | 4.94 | 4.90 | 4.92 | 4.94 | 4.58 × | |
Std | 5.92 | 3.21 | 4.68 | 5.72 | 5.73 × | |
Best | 4.50 | 4.49 | 4.53 | 4.53 | 4.48 × | |
Worst | 6.55 | 6.10 | 6.10 | 6.52 | 4.68 × | |
rank | 5 | 2 | 3 | 4 | 1 | |
Mean | 2.11 | 2.11 | 2.11 × | 2.11 | 2.12 | |
Std | 2.88 | 3.16 | 3.41 | 3.53 | 2.59 × | |
Best | 2.11 | 2.11 | 2.11 × | 2.11 | 2.11 | |
Worst | 2.12 × | 2.12 | 2.12 | 2.12 | 2.12 | |
rank | 4 | 3 | 1 | 2 | 5 | |
Mean | 1.15 | 1.15 | 1.12 | 1.12 | 1.11 × | |
Std | 4.00 × | 4.46 | 4.81 | 5.36 | 5.06 | |
Best | 1.07 | 1.08 | 1.03 | 1.05 | 1.03 × | |
Worst | 1.21 | 1.20 | 1.20 | 1.24 | 1.19 × | |
rank | 4 | 5 | 3 | 2 | 1 | |
Average Rank | 3.38 | 3.29 | 3.21 | 3.04 | 2.08 | |
Combined Rank | 5 | 4 | 3 | 2 | 1 |
F | Algorithm | Mean | Std | Best | Worst | Rank | p-Value | State |
---|---|---|---|---|---|---|---|---|
PSO | −9.26 | 2.04 | −9.26 | −9.26 | 8 | 1.86 | + | |
GA | −9.26 | 2.22 | −9.26 | −9.26 | 7 | 1.86 | + | |
GWO | −9.26 × | 1.52 × | −9.26 | −9.26 × | 1 | 1.35 | ≈ | |
WOA | −9.26 | 6.15 | −9.26 | −9.26 | 4 | 1.00 | ≈ | |
BOA | −9.17 | 8.30 | −9.26 | −8.92 | 9 | 1.86 | + | |
SOA | −9.26 | 1.58 | −9.26 | −9.26 | 5 | 9.31 | + | |
LWOA | −9.26 | 2.20 | −9.26 | −9.26 | 6 | 1.86 | + | |
MSWOA | −9.26 | 6.00 | −9.26 × | −9.26 | 3 | 5.43 | ≈ | |
DGSWOA | −9.26 | 2.00 | −9.26 | −9.26 | 2 | |||
PSO | 2.78 | 1.93 | 2.76 | 2.85 | 7 | 1.86 | + | |
GA | 2.77 | 8.55 | 2.76 | 2.80 | 3 | 5.78 | + | |
GWO | 2.77 | 5.96 | 2.76 | 2.78 | 4 | 2.61 | + | |
WOA | 2.77 | 3.59 | 2.76 | 2.78 | 2 | 2.34 | + | |
BOA | 2.88 | 4.15 | 2.76 | 5.10 | 9 | 1.86 | + | |
SOA | 2.78 | 2.28 | 2.76 | 2.86 | 5 | 2.69 | + | |
LWOA | 2.78 | 2.10 | 2.76 | 2.85 | 6 | 1.30 | + | |
MSWOA | 2.79 | 3.05 | 2.76 | 2.88 | 8 | 3.15 | + | |
DGSWOA | 2.76 × | 1.35 × | 2.76 × | 2.77 × | 1 | |||
PSO | 2.17 | 4.56 | 2.10 | 2.25 | 6 | 8.33 | + | |
GA | 2.20 | 6.19 | 2.10 | 2.35 | 7 | 1.86 | + | |
GWO | 2.14 | 3.57 | 2.09 | 2.20 | 4 | 7.99 | + | |
WOA | 2.10 | 1.57 × | 2.09 | 2.15 × | 2 | 3.64 | + | |
BOA | 2.29 | 1.33 | 2.11 | 2.60 | 9 | 9.31 | + | |
SOA | 2.24 | 2.18 | 2.09 | 2.90 | 8 | 6.91 | + | |
LWOA | 2.14 | 3.44 | 2.09 | 2.20 | 5 | 2.35 | + | |
MSWOA | 2.10 | 2.98 | 2.09 × | 2.19 | 3 | 4.03 | − | |
DGSWOA | 2.10 × | 2.18 | 2.09 | 2.21 | 1 | |||
PSO | 2.23 | 7.99 | 2.10 | 2.49 | 5 | 1.86 | + | |
GA | 2.30 | 8.45 | 2.17 | 2.48 | 8 | 3.73 | + | |
GWO | 2.24 | 2.07 | 2.10 | 2.99 | 7 | 6.92 | + | |
WOA | 2.11 × | 1.76 × | 2.09 | 2.16 × | 1 | 5.56 | ≈ | |
BOA | 2.24 | 1.40 | 2.09 | 2.60 | 6 | 2.08 | + | |
SOA | 2.34 | 3.06 | 2.09 | 3.10 | 9 | 4.42 | + | |
LWOA | 2.18 | 4.59 | 2.10 | 2.25 | 4 | 6.15 | + | |
MSWOA | 2.11 | 3.98 | 2.09 × | 2.19 | 2 | 5.23 | ≈ | |
DGSWOA | 2.11 | 2.87 | 2.09 | 2.21 | 3 | |||
PSO | 5.18 | 1.84 | 5.16 | 5.23 | 6 | 1.86 | + | |
GA | 5.25 | 5.01 | 5.17 | 5.35 | 7 | 1.86 | + | |
GWO | 5.15 × | 7.11 × | 5.15 × | 5.15 × | 1 | NaN | NaN | |
WOA | 5.15 × | 7.11 × | 5.15 × | 5.15 × | 1 | NaN | NaN | |
BOA | 5.61 | 3.66 | 5.16 | 6.82 | 9 | NaN | NaN | |
SOA | 5.26 | 2.69 | 5.15 | 6.15 | 8 | NaN | NaN | |
LWOA | 5.15 × | 7.11 × | 5.15 × | 5.15 × | 1 | NaN | NaN | |
MSWOA | 5.15 | 2.39 | 5.15 | 5.15 | 5 | NaN | NaN | |
DGSWOA | 5.15 × | 7.11 × | 5.15 × | 5.15 × | 1 | |||
PSO | 8.35 | 2.23 | 8.35 | 8.36 | 7 | 1.86 | + | |
GA | 8.37 | 1.90 | 8.35 | 8.42 | 8 | 1.86 | + | |
GWO | 8.35 | 1.12 | 8.35 | 8.35 | 4 | 5.84 | ≈ | |
WOA | 8.35 | 2.04 | 8.35 | 8.35 | 2 | 5.29 | ≈ | |
BOA | 8.52 | 6.37 | 8.35 | 1.18 | 9 | 1.86 | + | |
SOA | 8.35 | 2.51 | 8.35 | 8.35 | 5 | 1.86 | + | |
LWOA | 8.35 | 4.98 | 8.35 | 8.35 | 6 | 1.86 | + | |
MSWOA | 8.35 × | 2.71 × | 8.35 × | 8.35 × | 1 | 4.42 | − | |
DGSWOA | 8.35 | 1.25 | 8.35 | 8.35 | 3 | |||
PSO | −8.39 | 6.61 | −8.39 | −8.38 | 2 | 4.62 | + | |
GA | −8.39 × | 3.53 × | −8.39 | −8.39 × | 1 | 2.62 | ≈ | |
GWO | −8.36 | 6.13 | −8.39 | −8.10 | 7 | 1.55 | + | |
WOA | −8.39 | 2.09 | −8.39 × | −8.38 | 3 | 1.58 | ≈ | |
BOA | −7.88 | 4.80 | −8.36 | −6.73 | 9 | 1.86 | + | |
SOA | −8.32 | 8.16 | −8.39 | −8.09 | 8 | 4.97 | + | |
LWOA | −8.39 | 8.46 | −8.39 | −8.38 | 4 | 5.04 | ≈ | |
MSWOA | −8.37 | 1.79 | −8.39 | −8.34 | 6 | 5.55 | + | |
DGSWOA | −8.38 | 3.16 | −8.39 | −8.22 | 5 | |||
PSO | −1.35 | 1.90 | −1.35 | −1.35 | 6 | 1.06 | + | |
GA | −1.35 | 1.13 | −1.35 | −1.35 | 8 | 4.66 | + | |
GWO | −1.35 | 1.78 | −1.35 | −1.34 | 7 | 8.79 | ≈ | |
WOA | −1.35 | 5.01 | −1.35 | −1.35 | 3 | 9.84 | ≈ | |
BOA | −1.30 | 5.56 | −1.35 | −1.10 | 9 | 1.86 | + | |
SOA | −1.35 × | 1.28 × | −1.35 | −1.35 × | 1 | 2.21 | − | |
LWOA | −1.35 | 2.52 | −1.35 | −1.35 | 4 | 1.77 | ≈ | |
MSWOA | −1.35 | 3.73 | −1.35 × | −1.35 | 5 | 2.13 | ≈ | |
DGSWOA | −1.35 | 4.39 | −1.35 | −1.35 | 2 | |||
PSO | −3.59 | 1.90 | −3.59 | −3.59 | 4 | 1.86 | + | |
GA | −3.59 | 8.38 | −3.59 | −3.59 | 7 | 9.31 | + | |
GWO | −3.59 | 1.64 | −3.59 | −3.59 | 5 | 1.30 | + | |
WOA | −3.59 | 2.11 | −3.59 × | −3.59 | 2 | 1.77 | ≈ | |
BOA | −3.43 | 2.20 | −3.59 | −2.73 | 9 | 1.86 | + | |
SOA | −3.59 | 7.93 | −3.59 | −3.59 | 8 | 3.73 | + | |
LWOA | −3.59 | 1.22 | −3.59 | −3.59 | 3 | 1.86 | + | |
MSWOA | −3.59 | 2.75 | −3.59 | −3.59 | 6 | 1.86 | + | |
DGSWOA | −3.59 × | 9.34 × | −3.59 | −3.59 × | 1 | |||
PSO | −7.61 | 1.98 | −7.86 | −7.21 | 6 | 1.68 | + | |
GA | −7.54 | 6.26 | −7.90 | −5.10 | 7 | 8.72 | + | |
GWO | −7.74 | 7.51 | −7.89 | −7.68 | 4 | 3.54 | + | |
WOA | −7.83 | 6.92 | −7.90 | −7.65 | 2 | 8.55 | ≈ | |
BOA | 4.25 | 1.18 | −7.88 | 5.75 | 9 | 3.73 | + | |
SOA | −7.34 | 7.33 | −7.90 × | −5.60 | 8 | 3.45 | + | |
LWOA | −7.72 | 1.80 | −7.89 | −7.03 | 5 | 1.89 | + | |
MSWOA | −7.76 | 1.78 | −7.90 | −7.06 | 3 | 4.05 | + | |
DGSWOA | −7.85 × | 4.78 × | −7.90 | −7.71 × | 1 | |||
PSO | −9.85 | 2.13 | −1.01 | −9.26 | 6 | 4.04 | ≈ | |
GA | −9.93 | 1.60 | −1.01 | −9.50 × | 2 | 8.24 | ≈ | |
GWO | −9.65 | 1.85 | −1.00 | −9.22 | 7 | 2.35 | + | |
WOA | −9.91 | 1.58 × | −1.01 | −9.44 | 3 | 9.84 | ≈ | |
BOA | 1.21 | 2.54 | −9.37 | 1.05 | 9 | 1.86 | + | |
SOA | 4.80 | 6.75 | −1.01 | 3.64 | 8 | 6.08 | + | |
LWOA | −9.90 | 1.64 | −1.01 | −9.37 | 5 | 5.29 | ≈ | |
MSWOA | −9.96 × | 2.42 | −1.01 × | −9.27 | 1 | 5.49 | ≈ | |
DGSWOA | −9.91 | 1.84 | −1.01 | −9.44 | 4 | |||
PSO | 2.98 | 2.44 | 2.95 | 3.06 | 7 | 3.79 | + | |
GA | 2.96 | 1.40 | 2.95 × | 3.00 | 3 | 5.29 | ≈ | |
GWO | 2.96 | 1.88 | 2.95 | 3.04 | 4 | 1.24 | ≈ | |
WOA | 2.96 | 6.73 | 2.95 | 2.98 | 2 | 1.24 | ≈ | |
BOA | 3.06 | 2.70 | 2.96 | 4.26 | 9 | 1.86 | + | |
SOA | 2.97 | 1.60 | 2.95 | 3.01 | 5 | 2.93 | + | |
LWOA | 2.97 | 1.74 | 2.95 | 3.02 | 6 | 2.08 | + | |
MSWOA | 2.99 | 1.83 | 2.95 | 3.97 | 8 | 2.71 | ≈ | |
DGSWOA | 2.96 × | 5.56 × | 2.95 | 2.98 × | 1 | |||
PSO | −5.10 | 5.06 | −5.17 | −5.00 | 4 | 9.61 | ≈ | |
GA | −5.09 | 6.96 | −5.17 × | −4.86 | 5 | 6.36 | ≈ | |
GWO | −4.95 | 2.66 | −5.17 | −4.26 | 6 | 3.48 | + | |
WOA | −5.14 × | 2.61 × | −5.17 | −5.07 × | 1 | 2.45 | ≈ | |
BOA | −3.03 | 1.09 | −4.93 | −1.37 | 9 | 1.86 | + | |
SOA | −4.18 | 1.34 | −5.17 | −1.19 | 8 | 1.72 | + | |
LWOA | −5.12 | 3.39 | −5.16 | −5.03 | 3 | 3.49 | ≈ | |
MSWOA | −4.60 | 5.61 | −5.17 | −3.63 | 7 | 6.92 | + | |
DGSWOA | −5.12 | 5.06 | −5.17 | −4.97 | 2 | |||
PSO | −5.79 | 5.35 | −5.79 | −5.79 | 8 | 1.86 | + | |
GA | −5.79 | 1.56 | −5.79 | −5.79 | 7 | 1.86 | + | |
GWO | −5.79 | 6.55 | −5.79 | −5.79 | 5 | 3.28 | ≈ | |
WOA | −5.79 | 3.77 | −5.79 | −5.79 | 2 | 5.70 | ≈ | |
BOA | −5.70 | 6.02 | −5.78 | −5.51 | 9 | 1.86 | + | |
SOA | −5.79 | 5.02 | −5.79 | −5.79 | 3 | 5.98 | ≈ | |
LWOA | −5.79 | 1.30 | −5.79 | −5.79 | 6 | 1.86 | + | |
MSWOA | −5.79 × | 3.09 × | −5.79 × | −5.79 × | 1 | 1.58 | − | |
DGSWOA | −5.79 | 3.69 | −5.79 | −5.79 | 4 | |||
PSO | −4.40 | 4.83 | −4.48 | −4.28 | 6 | 9.22 | + | |
GA | −4.42 | 6.21 | −4.48 | −4.20 | 5 | 3.22 | + | |
GWO | −4.43 | 8.75 | −4.48 | −4.04 | 4 | 2.05 | ≈ | |
WOA | −4.44 | 3.63 | −4.48 | −4.37 × | 2 | 3.84 | + | |
BOA | −2.89 | 7.26 | −4.34 | −1.84 | 9 | 1.86 | + | |
SOA | −4.30 | 3.21 | −4.48 | −3.18 | 7 | 1.34 | + | |
LWOA | −4.43 | 3.53 × | −4.47 | −4.34 | 3 | 7.11 | + | |
MSWOA | −4.14 | 3.15 | −4.48 | −3.18 | 8 | 1.99 | + | |
DGSWOA | −4.45 × | 6.24 | −4.48 × | −4.13 | 1 | |||
PSO | −2.60 | 2.31 | −2.60 | −2.60 | 4 | 1.86 | + | |
GA | −2.60 | 2.87 | −2.60 | −2.60 | 3 | 2.35 | + | |
GWO | −2.60 | 1.42 | −2.60 × | −2.59 | 5 | 7.15 | ≈ | |
WOA | −2.60 × | 2.46 × | −2.60 | −2.60 × | 1 | 5.29 | ≈ | |
BOA | −2.54 | 4.77 | −2.60 | −2.44 | 9 | 1.86 | + | |
SOA | −2.60 | 5.37 | −2.60 | −2.60 | 8 | 1.86 | + | |
LWOA | −2.60 | 6.84 | −2.60 | −2.60 | 7 | 9.31 | + | |
MSWOA | −2.60 | 7.14 | −2.60 | −2.60 | 6 | 5.05 | + | |
DGSWOA | −2.60 | 4.18 | −2.60 | −2.60 | 2 | |||
PSO | −3.86 | 6.35 | −3.87 | −3.84 | 8 | 1.86 | + | |
GA | −3.87 | 2.10 | −3.87 | −3.86 | 5 | 1.86 | + | |
GWO | −3.87 × | 9.71 × | −3.87 | −3.87 × | 1 | 1.06 | − | |
WOA | −3.87 | 1.07 | −3.87 | −3.87 | 3 | 8.08 | ≈ | |
BOA | −3.62 | 1.18 | −3.82 | −3.33 | 9 | 1.86 | + | |
SOA | −3.87 | 1.41 | −3.87 | −3.80 | 7 | 1.86 | + | |
LWOA | −3.87 | 3.69 | −3.87 | −3.86 | 6 | 1.86 | + | |
MSWOA | −3.87 | 2.71 | −3.87 | −3.86 | 4 | 3.86 | + | |
DGSWOA | −3.87 | 3.66 | −3.87 × | −3.87 | 2 | |||
PSO | −3.84 | 1.47 × | −3.86 | −3.80 × | 5 | 1.77 | ≈ | |
GA | −3.85 × | 2.02 | −3.87 × | −3.79 | 1 | 3.64 | − | |
GWO | −3.77 | 7.32 | −3.86 | −3.56 | 8 | 1.06 | + | |
WOA | −3.82 | 2.85 | −3.87 | −3.76 | 6 | 1.37 | + | |
BOA | −2.91 | 9.34 | −3.73 | −4.05 | 9 | 1.86 | + | |
SOA | −3.80 | 5.74 | −3.87 | −3.69 | 7 | 1.37 | + | |
LWOA | −3.84 | 1.97 | −3.87 | −3.79 | 3 | 7.30 | ≈ | |
MSWOA | −3.85 | 1.83 | −3.87 | −3.80 | 2 | 2.13 | ≈ | |
DGSWOA | −3.84 | 3.35 | −3.87 | −3.72 | 4 | |||
PSO | 4.05 | 3.80 | 4.05 | 4.05 | 8 | 1.86 | + | |
GA | 4.05 | 6.21 | 4.05 | 4.05 | 9 | 1.86 | + | |
GWO | 4.05 | 5.00 | 4.05 × | 4.05 | 5 | 4.60 | + | |
WOA | 4.05 | 6.68 | 4.05 | 4.05 | 2 | 1.52 | ≈ | |
BOA | 4.05 | 1.82 | 4.05 | 4.05 | 3 | 4.66 | + | |
SOA | 4.05 | 5.39 | 4.05 | 4.05 | 7 | 1.30 | + | |
LWOA | 4.05 | 3.60 | 4.05 | 4.05 | 6 | 3.73 | + | |
MSWOA | 4.05 | 3.97 | 4.05 | 4.05 | 4 | 4.42 | + | |
DGSWOA | 4.05 × | 3.19 × | 4.05 | 4.05 × | 1 | |||
PSO | 1.83 | 1.33 | 1.83 | 1.84 | 4 | 1.30 | + | |
GA | 1.83 | 1.60 | 1.83 | 1.84 | 5 | 1.86 | + | |
GWO | 1.83 | 4.22 | 1.83 | 1.85 | 7 | 1.64 | + | |
WOA | 1.83 | 5.43 | 1.83 | 1.83 | 2 | 3.74 | + | |
BOA | 1.84 | 4.21 | 1.83 | 1.85 | 9 | 1.86 | + | |
SOA | 1.84 | 3.86 | 1.83 | 1.84 | 8 | 6.15 | + | |
LWOA | 1.83 | 1.15 | 1.83 | 1.84 | 3 | 6.91 | + | |
MSWOA | 1.83 | 2.95 | 1.83 × | 1.84 | 6 | 4.73 | + | |
DGSWOA | 1.83 × | 1.39 × | 1.83 | 1.83 × | 1 | |||
PSO | 3.11 | 4.24 | 3.11 | 3.11 | 4 | 1.86 | + | |
GA | 3.11 | 4.39 | 3.11 | 3.11 | 5 | 1.86 | + | |
GWO | 3.11 | 3.50 | 3.11 × | 3.13 | 7 | 3.87 | ≈ | |
WOA | 3.11 | 8.13 | 3.11 × | 3.11 | 2 | 9.43 | ≈ | |
BOA | 3.11 | 8.67 | 3.11 | 3.11 | 6 | 1.86 | + | |
SOA | 3.11 | 2.56 | 3.11 | 3.11 | 8 | 1.02 | + | |
LWOA | 3.11 | 1.98 | 3.11 | 3.11 | 3 | 1.86 | + | |
MSWOA | 3.11 | 3.43 | 3.11 | 3.11 | 9 | 4.71 | + | |
DGSWOA | 3.11 × | 1.86 × | 3.11 × | 3.11 × | 1 | |||
PSO | 4.30 | 5.59 | 4.30 | 4.30 | 5 | 5.59 | + | |
GA | 4.30 | 7.10 | 4.30 | 4.30 | 7 | 1.86 | + | |
GWO | 4.30 | 3.72 | 4.30 | 4.31 | 8 | 9.31 | + | |
WOA | 4.30 | 1.72 | 4.30 | 4.30 | 3 | 8.08 | ≈ | |
BOA | 4.30 | 1.64 | 4.30 | 4.30 | 6 | 3.73 | + | |
SOA | 4.31 | 4.45 | 4.30 | 4.55 | 9 | 9.35 | ≈ | |
LWOA | 4.30 | 2.44 | 4.30 | 4.30 | 4 | 3.24 | + | |
MSWOA | 4.30 × | 6.44 × | 4.30 × | 4.30 × | 1 | 1.23 | − | |
DGSWOA | 4.30 | 1.73 | 4.30 | 4.30 | 2 | |||
PSO | 2.11 | 1.59 | 2.11 | 2.11 | 6 | 3.73 | + | |
GA | 2.11 | 3.03 | 2.11 | 2.12 | 9 | 1.86 | + | |
GWO | 2.11 | 3.00 | 2.10 | 2.11 | 4 | 6.64 | + | |
WOA | 2.11 | 1.15 | 2.10 | 2.11 | 2 | 1.45 | + | |
BOA | 2.11 | 1.87 | 2.10 | 2.11 | 8 | 1.86 | + | |
SOA | 2.11 | 2.00 | 2.10 | 2.11 | 5 | 9.31 | + | |
LWOA | 2.11 | 1.88 | 2.11 | 2.11 | 7 | 1.86 | + | |
MSWOA | 2.11 | 1.30 | 2.10 | 2.11 | 3 | 1.04 | + | |
DGSWOA | 2.10 × | 4.42 × | 2.10 × | 2.11 × | 1 | |||
PSO | 4.85 | 5.70 | 4.77 | 5.01 | 3 | 8.01 | + | |
GA | 4.86 | 6.47 | 4.78 | 4.99 | 4 | 1.86 | + | |
GWO | 4.91 | 1.00 | 4.76 | 5.05 | 7 | 3.79 | + | |
WOA | 4.87 | 8.00 | 4.77 | 5.02 | 5 | 5.14 | + | |
BOA | 4.80 | 3.07 | 4.76 × | 4.89 × | 2 | 2.62 | + | |
SOA | 4.88 | 1.06 | 4.77 | 5.09 | 6 | 2.09 | + | |
LWOA | 4.92 | 6.94 | 4.79 | 5.01 | 8 | 1.02 | + | |
MSWOA | 4.96 | 5.67 | 4.77 | 5.04 | 9 | 1.86 | + | |
DGSWOA | 4.79 × | 2.43 × | 4.77 | 4.90 | 1 |
F | Algorithm | Mean | Std | Best | Worst | Rank | p-Value | State |
---|---|---|---|---|---|---|---|---|
PSO | −9.26 | 3.52 | −9.26 | −9.25 | 8 | 1.86 | + | |
GA | −9.26 | 4.29 | −9.26 | −9.26 | 7 | 1.86 | + | |
GWO | −9.26 | 2.71 | −9.26 | −9.26 | 5 | 7.61 | − | |
WOA | −9.26 | 1.46 | −9.26 | −9.26 × | 3 | 7.00 | ≈ | |
BOA | −8.93 | 2.16 | −9.20 | −8.45 | 9 | 1.86 | + | |
SOA | −9.26 | 8.89 | −9.26 | −9.26 | 4 | 9.31 | + | |
LWOA | −9.26 | 3.68 × | −9.26 × | −9.26 | 6 | 1.86 | + | |
MSWOA | −9.26 | 1.34 | −9.26 | −9.26 | 2 | 5.16 | ≈ | |
DGSWOA | −9.26 × | 1.62 | −9.26 | −9.26 | 1 | |||
PSO | 3.40 | 5.22 | 2.77 | 4.57 | 5 | 3.73 | + | |
GA | 2.81 | 6.12 | 2.76 × | 3.07 | 2 | 4.05 | + | |
GWO | 3.49 | 7.00 | 2.79 | 5.34 | 6 | 1.86 | + | |
WOA | 2.82 | 8.56 | 2.76 | 3.19 | 3 | 4.60 | + | |
BOA | 7.02 | 5.78 | 2.89 | 3.05 | 9 | 1.86 | + | |
SOA | 3.93 | 1.46 | 2.76 | 7.26 | 8 | 4.71 | + | |
LWOA | 3.10 | 2.32 | 2.77 | 3.66 | 4 | 3.73 | + | |
MSWOA | 3.72 | 1.78 | 2.76 | 7.69 | 7 | 2.37 | + | |
DGSWOA | 2.79 × | 4.09 × | 2.76 | 3.00 × | 1 | |||
PSO | 2.56 | 1.68 | 2.26 | 2.88 | 6 | 5.59 | + | |
GA | 2.64 | 1.67 | 2.33 | 3.08 | 9 | 1.86 | + | |
GWO | 2.41 | 1.79 | 2.20 | 3.09 | 4 | 1.42 | + | |
WOA | 2.29 | 9.78 | 2.09 | 2.56 | 2 | 7.06 | + | |
BOA | 2.62 | 3.67 | 2.21 | 3.61 | 8 | 1.86 | + | |
SOA | 2.59 | 3.66 | 2.16 | 3.26 | 7 | 1.68 | + | |
LWOA | 2.34 | 8.31 | 2.14 × | 2.51 | 3 | 1.68 | + | |
MSWOA | 2.49 | 3.40 | 2.09 | 3.21 | 5 | 1.13 | + | |
DGSWOA | 2.21 × | 5.74 × | 2.10 | 2.35 × | 1 | |||
PSO | 2.90 | 2.93 | 2.28 | 3.57 | 8 | 3.73 | + | |
GA | 3.00 | 2.59 | 2.34 | 3.44 | 9 | 3.73 | + | |
GWO | 2.63 | 2.78 | 2.20 | 3.32 | 5 | 7.99 | + | |
WOA | 2.39 | 1.43 | 2.13 | 2.92 | 2 | 7.30 | ≈ | |
BOA | 2.81 | 2.52 | 2.42 | 3.37 | 6 | 1.86 | + | |
SOA | 2.90 | 4.79 | 2.30 | 3.74 | 7 | 1.68 | + | |
LWOA | 2.54 | 1.72 | 2.12 | 2.79 | 3 | 1.40 | + | |
MSWOA | 2.55 | 3.29 | 2.20 × | 3.80 | 4 | 2.77 | + | |
DGSWOA | 2.36 × | 6.65 × | 2.20 | 2.55 | 1 | |||
PSO | 5.33 | 7.95 | 5.22 | 5.57 | 6 | 1.86 | + | |
GA | 5.60 | 1.48 | 5.31 | 5.88 | 8 | 1.86 | + | |
GWO | 5.15 × | 7.11 × | 5.15 × | 5.15 × | 1 | NaN | NaN | |
WOA | 5.15 × | 7.11 × | 5.15 × | 5.15 × | 1 | NaN | NaN | |
BOA | 6.53 | 5.84 | 5.24 | 7.51 | 9 | NaN | NaN | |
SOA | 5.34 | 3.45 | 5.15 | 6.15 | 7 | NaN | NaN | |
LWOA | 5.15 × | 7.11 × | 5.15 × | 5.15 × | 1 | NaN | NaN | |
MSWOA | 5.19 | 1.79 | 5.15 | 6.15 | 5 | NaN | NaN | |
DGSWOA | 5.15 × | 7.11 × | 5.15 × | 5.15 × | 1 | |||
PSO | 8.43 | 5.40 | 8.36 | 8.58 | 5 | 1.86 | + | |
GA | 8.54 | 1.01 | 8.39 | 8.75 | 7 | 1.86 | + | |
GWO | 8.35 | 2.88 | 8.35 × | 8.36 | 3 | 6.26 | ≈ | |
WOA | 8.35 × | 9.61 × | 8.35 | 8.35 × | 1 | 8.39 | ≈ | |
BOA | 1.15 | 2.58 | 8.42 | 1.12 | 9 | 1.86 | + | |
SOA | 8.53 | 3.19 | 8.35 | 9.42 | 6 | 5.72 | + | |
LWOA | 8.37 | 9.02 | 8.35 | 8.39 | 4 | 5.59 | + | |
MSWOA | 8.58 | 3.91 | 8.35 | 9.37 | 8 | 1.86 | + | |
DGSWOA | 8.35 | 1.50 | 8.35 | 8.35 | 2 | |||
PSO | −8.37 | 1.59 | −8.38 | −8.32 | 6 | 1.86 | + | |
GA | −8.38 | 6.26 | −8.39 | −8.36 | 3 | 8.14 | + | |
GWO | −8.37 | 3.51 | −8.39 × | −8.19 | 5 | 1.68 | + | |
WOA | −8.38 | 4.13 | −8.39 | −8.36 | 2 | 6.19 | + | |
BOA | −7.13 | 7.16 | −8.31 | −5.24 | 9 | 1.86 | + | |
SOA | −8.24 | 2.36 | −8.39 | −7.10 | 8 | 5.59 | + | |
LWOA | −8.38 | 3.86 | −8.39 | −8.37 | 4 | 3.73 | + | |
MSWOA | −8.30 | 8.09 | −8.39 | −8.12 | 7 | 1.86 | + | |
DGSWOA | −8.39 × | 6.03 × | −8.39 | −8.38 × | 1 | |||
PSO | −1.33 | 1.31 | −1.35 | −1.30 | 8 | 1.86 | + | |
GA | −1.34 | 4.96 | −1.35 | −1.34 | 7 | 4.66 | + | |
GWO | −1.35 | 6.72 | −1.35 | −1.35 | 5 | 2.08 | + | |
WOA | −1.35 | 4.47 | −1.35 | −1.35 × | 3 | 4.52 | ≈ | |
BOA | 3.94 | 9.13 | −1.28 | 3.72 | 9 | 1.86 | + | |
SOA | −1.35 | 1.12 | −1.35 | −1.35 | 4 | 1.13 | + | |
LWOA | −1.35 | 1.39 | −1.35 | −1.35 | 6 | 1.64 | + | |
MSWOA | −1.35 × | 5.48 | −1.35 × | −1.35 | 1 | 5.56 | ≈ | |
DGSWOA | −1.35 | 4.06 × | −1.35 | −1.35 | 2 | |||
PSO | −3.58 | 1.06 | −3.59 | −3.54 | 8 | 1.86 | + | |
GA | −3.59 | 4.81 | −3.59 | −3.57 | 6 | 1.86 | + | |
GWO | −3.59 | 9.74 | −3.59 | −3.59 | 3 | 3.73 | + | |
WOA | −3.59 | 2.94 | −3.59 × | −3.59 | 2 | 2.37 | + | |
BOA | −2.31 | 4.59 | −3.51 | −1.65 | 9 | 1.86 | + | |
SOA | −3.58 | 2.10 | −3.59 | −3.52 | 7 | 8.01 | + | |
LWOA | −3.59 | 2.49 | −3.59 | −3.58 | 5 | 1.86 | + | |
MSWOA | −3.59 | 2.45 | −3.59 | −3.59 | 4 | 1.86 | + | |
DGSWOA | −3.59 × | 1.83 × | −3.59 | −3.59 × | 1 | |||
PSO | −2.72 | 3.72 | −7.70 | 6.71 | 7 | 1.19 | + | |
GA | −5.89 | 2.51 | −7.78 | 1.33 | 5 | 7.32 | ≈ | |
GWO | 6.02 | 2.80 | −7.63 | 1.56 | 8 | 3.15 | + | |
WOA | −6.93 × | 8.64 × | −7.80 | −4.82 × | 1 | 9.52 | ≈ | |
BOA | 1.88 | 2.06 | −3.44 | 8.52 | 9 | 1.86 | + | |
SOA | −6.00 | 1.54 | −7.84 | −4.01 | 4 | 3.10 | + | |
LWOA | −5.04 | 1.87 | −7.26 | 1.14 | 6 | 5.14 | + | |
MSWOA | −6.55 | 1.36 | −7.90 × | −4.03 | 3 | 2.99 | ≈ | |
DGSWOA | −6.88 | 1.07 | −7.82 | −2.25 | 2 | |||
PSO | −9.42 × | 5.50 | −1.00 | −8.00 | 1 | 7.00 | ≈ | |
GA | −8.56 | 1.23 | −1.00 | −5.98 | 5 | 1.86 | + | |
GWO | −8.33 | 5.18 | −9.90 | −7.50 | 6 | 4.66 | + | |
WOA | −9.37 | 6.12 | −1.00 | −8.02 | 4 | 8.71 | ≈ | |
BOA | −6.65 | 3.68 × | −7.67 | −5.81 | 8 | 1.86 | + | |
SOA | −6.64 | 2.81 | −1.01 × | 5.14 | 9 | 1.42 | + | |
LWOA | −9.41 | 7.78 | −1.00 | −6.64 | 3 | 2.45 | ≈ | |
MSWOA | −7.75 | 1.30 | −1.00 | −3.21 | 7 | 6.91 | + | |
DGSWOA | −9.41 | 3.96 | −1.01 | −8.47 × | 2 | |||
PSO | 2.38 | 1.75 | 4.33 | 7.08 | 8 | 1.86 | + | |
GA | 3.33 | 3.89 | 2.99 | 4.53 | 6 | 1.30 | + | |
GWO | 2.99 × | 4.09 × | 2.98 | 3.00 × | 1 | 2.45 | ≈ | |
WOA | 3.01 | 7.53 | 2.95 | 3.38 | 3 | 7.77 | ≈ | |
BOA | 2.07 | 2.72 | 1.78 | 1.14 | 9 | 1.86 | + | |
SOA | 3.13 | 2.04 | 2.95 | 4.04 | 5 | 1.70 | + | |
LWOA | 6.12 | 3.16 | 3.10 | 1.97 | 7 | 1.86 | + | |
MSWOA | 3.03 | 1.25 | 2.95 × | 3.45 | 4 | 7.46 | ≈ | |
DGSWOA | 3.00 | 3.15 | 2.96 | 3.15 | 2 | |||
PSO | −3.95 | 5.12 | −4.81 | −2.82 | 7 | 1.86 | + | |
GA | −4.87 | 2.63 | −5.14 | −4.11 | 2 | 9.84 | ≈ | |
GWO | −4.73 | 3.40 | −4.84 | −2.90 | 4 | 5.59 | + | |
WOA | −4.82 | 2.22 | −5.16 | −4.06 | 3 | 1.35 | ≈ | |
BOA | −7.24 | 1.54 | −3.75 | 3.79 | 9 | 1.86 | + | |
SOA | −3.90 | 1.50 | −5.14 | −3.87 | 8 | 1.55 | + | |
LWOA | −4.64 | 2.69 | −5.05 | −3.97 | 5 | 3.15 | + | |
MSWOA | −4.24 | 1.52 | −5.17 × | −2.72 | 6 | 2.89 | ≈ | |
DGSWOA | −4.90 × | 1.21 × | −5.15 | −4.67 × | 1 | |||
PSO | −5.78 | 4.32 | −5.79 | −5.77 | 7 | 1.86 | + | |
GA | −5.79 | 7.07 | −5.79 | −5.79 | 5 | 1.86 | + | |
GWO | −5.79 | 1.46 | −5.79 | −5.71 | 6 | 9.19 | ≈ | |
WOA | −5.79 × | 1.81 × | −5.79 | −5.79 × | 1 | 7.30 | ≈ | |
BOA | −5.60 | 1.22 | −5.78 | −5.17 | 9 | 1.86 | + | |
SOA | −5.77 | 4.23 | −5.79 | −5.62 | 8 | 1.86 | + | |
LWOA | −5.79 | 4.98 | −5.79 | −5.79 | 4 | 1.86 | + | |
MSWOA | −5.79 | 2.85 | −5.79 | −5.79 | 3 | 9.22 | + | |
DGSWOA | −5.79 | 2.07 | −5.79 × | −5.79 | 2 | |||
PSO | −4.03 | 1.55 | −4.28 | −3.77 | 8 | 3.73 | + | |
GA | −4.29 | 7.54 | −4.42 | −4.12 | 4 | 3.71 | ≈ | |
GWO | −4.26 | 7.50 | −4.43 | −4.13 | 5 | 8.79 | ≈ | |
WOA | −4.30 | 5.83 | −4.47 | −4.22 × | 2 | 9.84 | ≈ | |
BOA | −2.22 | 6.50 | −3.46 | −1.23 | 9 | 1.86 | + | |
SOA | −4.13 | 2.99 | −4.46 | −3.07 | 7 | 6.64 | + | |
LWOA | −4.29 | 5.31 × | −4.36 | −4.14 | 3 | 4.40 | ≈ | |
MSWOA | −4.24 | 2.73 | −4.48 × | −3.13 | 6 | 8.39 | ≈ | |
DGSWOA | −4.31 × | 7.62 | −4.47 | −4.13 | 1 | |||
PSO | −2.60 | 2.30 | −2.60 | −2.59 | 5 | 3.24 | + | |
GA | −2.60 | 3.27 | −2.60 | −2.59 | 4 | 2.56 | + | |
GWO | −2.60 | 5.33 | −2.60 | −2.58 | 6 | 4.18 | + | |
WOA | −2.60 | 2.97 | −2.60 | −2.59 | 2 | 9.61 | ≈ | |
BOA | −2.48 | 6.69 | −2.56 | −2.25 | 9 | 1.86 | + | |
SOA | −2.59 | 1.04 | −2.60 | −2.56 | 8 | 1.64 | + | |
LWOA | −2.60 | 1.64 | −2.60 | −2.59 | 3 | 1.99 | + | |
MSWOA | −2.60 | 8.83 | −2.60 × | −2.56 | 7 | 1.55 | + | |
DGSWOA | −2.60 × | 9.62 × | −2.60 | −2.60 × | 1 | |||
PSO | −3.82 | 1.88 | −3.85 | −3.77 | 7 | 1.86 | + | |
GA | −3.86 | 6.55 | −3.87 | −3.84 | 5 | 3.15 | + | |
GWO | −3.86 | 4.36 × | −3.87 | −3.85 | 3 | 1.82 | + | |
WOA | −3.87 × | 4.45 | −3.87 × | −3.86 × | 1 | 8.71 | ≈ | |
BOA | −3.38 | 2.42 | −3.80 | −2.90 | 9 | 1.86 | + | |
SOA | −3.82 | 5.10 | −3.87 | −3.68 | 8 | 8.86 | + | |
LWOA | −3.86 | 8.13 | −3.87 | −3.84 | 4 | 7.06 | + | |
MSWOA | −3.84 | 4.05 | −3.87 | −3.73 | 6 | 1.24 | ≈ | |
DGSWOA | −3.86 | 5.27 | −3.87 | −3.85 | 2 | |||
PSO | −3.71 | 5.95 | −3.82 | −3.59 | 7 | 4.66 | + | |
GA | −3.84 | 1.92 | −3.86 | −3.80 | 3 | 9.19 | ≈ | |
GWO | −3.84 | 3.45 | −3.86 | −3.70 | 2 | 5.03 | ≈ | |
WOA | −3.85 × | 5.90 × | −3.87 | −3.84 × | 1 | 5.78 | − | |
BOA | −2.10 | 6.50 | −3.33 | −9.05 | 9 | 1.86 | + | |
SOA | −3.61 | 2.22 | −3.87 | −3.16 | 8 | 7.99 | + | |
LWOA | −3.81 | 1.96 | −3.86 | −3.77 | 5 | 1.85 | + | |
MSWOA | −3.80 | 7.37 | −3.87 × | −3.55 | 6 | 7.32 | ≈ | |
DGSWOA | −3.83 | 3.73 | −3.87 | −3.73 | 4 | |||
PSO | 4.07 | 1.32 | 4.05 | 4.11 | 9 | 1.86 | + | |
GA | 4.06 | 1.27 | 4.05 | 4.09 | 8 | 5.59 | + | |
GWO | 4.05 | 1.60 | 4.05 | 4.05 | 5 | 8.33 | + | |
WOA | 4.05 | 1.83 | 4.05 | 4.06 | 4 | 2.02 | + | |
BOA | 4.05 | 4.72 | 4.05 | 4.07 | 6 | 9.31 | + | |
SOA | 4.05 | 6.16 | 4.05 | 4.05 | 3 | 2.21 | + | |
LWOA | 4.06 | 5.34 | 4.05 | 4.07 | 7 | 1.86 | + | |
MSWOA | 4.05 × | 6.32 | 4.05 × | 4.05 | 1 | 3.82 | ≈ | |
DGSWOA | 4.05 | 5.90 × | 4.05 | 4.05 × | 2 | |||
PSO | 1.84 | 2.94 | 1.83 | 1.85 | 5 | 3.86 | + | |
GA | 1.84 | 3.47 | 1.83 | 1.85 | 7 | 2.76 | + | |
GWO | 1.84 | 3.66 | 1.84 | 1.85 | 6 | 4.41 | + | |
WOA | 1.84 × | 2.47 | 1.83 | 1.84 | 1 | 7.92 | ≈ | |
BOA | 1.85 | 5.25 | 1.83 | 1.86 | 9 | 1.86 | + | |
SOA | 1.84 | 5.43 | 1.83 × | 1.86 | 8 | 3.90 | + | |
LWOA | 1.84 | 2.90 | 1.83 | 1.84 | 3 | 8.71 | + | |
MSWOA | 1.84 | 4.30 | 1.84 | 1.85 | 4 | 2.08 | + | |
DGSWOA | 1.84 | 1.81 × | 1.83 | 1.84 × | 2 | |||
PSO | 3.11 | 2.23 × | 3.11 | 3.11 × | 2 | 3.60 | ≈ | |
GA | 3.11 | 1.40 | 3.11 | 3.11 | 6 | 7.99 | + | |
GWO | 3.12 | 9.60 | 3.11 × | 3.13 | 7 | 2.05 | + | |
WOA | 3.11 | 1.99 | 3.11 | 3.11 | 5 | 2.99 | ≈ | |
BOA | 3.11 | 1.48 | 3.11 | 3.11 | 3 | 4.16 | ≈ | |
SOA | 3.12 | 7.43 | 3.11 | 3.13 | 9 | 2.55 | + | |
LWOA | 3.11 | 1.49 | 3.11 | 3.11 | 4 | 5.23 | ≈ | |
MSWOA | 3.12 | 6.71 | 3.11 | 3.13 | 8 | 1.86 | + | |
DGSWOA | 3.11 × | 2.76 | 3.11 | 3.11 | 1 | |||
PSO | 4.30 | 1.31 | 4.30 | 4.30 | 3 | 1.53 | + | |
GA | 4.30 | 7.89 | 4.30 | 4.33 | 5 | 9.31 | + | |
GWO | 4.46 | 1.00 | 4.30 | 4.56 | 9 | 1.86 | + | |
WOA | 4.31 | 1.51 | 4.30 | 4.37 | 7 | 1.30 | + | |
BOA | 4.30 | 4.12 | 4.30 | 4.32 | 4 | 1.40 | + | |
SOA | 4.39 | 7.71 | 4.30 | 4.54 | 8 | 3.86 | + | |
LWOA | 4.30 | 1.14 | 4.30 | 4.35 | 6 | 2.08 | + | |
MSWOA | 4.30 × | 5.83 | 4.30 × | 4.30 | 1 | 2.21 | − | |
DGSWOA | 4.30 | 4.67 × | 4.30 | 4.30 × | 2 | |||
PSO | 2.11 | 2.53 | 2.11 | 2.12 | 5 | 2.56 | + | |
GA | 2.11 | 3.45 | 2.11 | 2.12 | 8 | 8.33 | + | |
GWO | 2.11 | 4.10 | 2.11 | 2.13 | 7 | 2.08 | + | |
WOA | 2.11 | 2.18 × | 2.10 | 2.11 × | 2 | 1.91 | ≈ | |
BOA | 2.11 | 3.35 | 2.11 | 2.12 | 9 | 1.64 | + | |
SOA | 2.11 | 3.37 | 2.11 | 2.12 | 6 | 1.60 | + | |
LWOA | 2.11 | 2.59 | 2.11 | 2.12 | 4 | 1.34 | + | |
MSWOA | 2.11 | 2.88 | 2.10 | 2.12 | 3 | 3.71 | ≈ | |
DGSWOA | 2.11 × | 2.29 | 2.10 × | 2.11 | 1 | |||
PSO | 5.25 | 1.46 | 4.97 | 5.51 | 7 | 4.66 | + | |
GA | 5.31 | 1.71 | 4.97 | 5.59 | 8 | 1.30 | + | |
GWO | 5.34 | 2.04 | 4.96 | 5.80 | 9 | 1.86 | + | |
WOA | 5.14 | 1.53 | 4.85 | 5.39 | 6 | 1.40 | + | |
BOA | 5.11 | 1.16 | 4.92 | 5.35 | 4 | 1.82 | + | |
SOA | 4.81 | 5.96 | 4.76 × | 4.95 | 2 | 5.72 | − | |
LWOA | 5.11 | 1.32 | 4.82 | 5.30 | 5 | 5.59 | + | |
MSWOA | 4.79 × | 4.33 × | 4.76 | 4.89 × | 1 | 1.86 | − | |
DGSWOA | 4.96 | 8.36 | 4.79 | 5.12 | 3 |
F | Algorithm | Mean | Std | Best | Worst | Rank | p-Value | State |
---|---|---|---|---|---|---|---|---|
PSO | −9.17 | 3.51 | −9.23 | −9.09 | 7 | 1.86 | + | |
GA | −9.25 | 7.64 | −9.26 | −9.23 | 4 | 1.60 | + | |
GWO | −9.25 | 1.33 | −9.26 | −9.21 | 5 | 9.31 | + | |
WOA | −9.26 × | 2.98 × | −9.26 × | −9.25 × | 1 | 6.70 | ≈ | |
BOA | −8.17 | 5.70 | −9.17 | −6.53 | 9 | 1.86 | + | |
SOA | −9.03 | 2.61 | −9.26 | −8.24 | 8 | 6.15 | + | |
LWOA | −9.26 | 3.13 | −9.26 | −9.25 | 3 | 4.05 | + | |
MSWOA | −9.23 | 1.20 | −9.26 | −8.60 | 6 | 8.39 | ≈ | |
DGSWOA | −9.26 | 3.45 | −9.26 | −9.25 | 2 | |||
PSO | 2.01 | 9.76 | 6.11 | 3.82 | 6 | 1.86 | + | |
GA | 3.16 × | 3.62 × | 2.82 × | 4.25 × | 1 | 3.45 | − | |
GWO | 1.66 | 6.58 | 3.65 | 2.40 | 5 | 3.54 | + | |
WOA | 6.58 | 3.90 | 2.95 | 1.98 | 3 | 8.03 | ≈ | |
BOA | 8.58 | 1.19 | 2.48 | 4.74 | 9 | 1.86 | + | |
SOA | 7.45 | 5.78 | 5.60 | 2.29 | 8 | 1.86 | + | |
LWOA | 1.57 | 6.94 | 5.91 | 3.64 | 4 | 5.59 | + | |
MSWOA | 2.97 | 2.96 | 3.00 | 1.20 | 7 | 2.35 | + | |
DGSWOA | 5.32 | 2.39 | 2.94 | 1.15 | 2 | |||
PSO | 4.88 | 5.84 | 3.62 | 5.87 | 8 | 1.86 | + | |
GA | 4.12 | 4.31 | 2.86 | 4.90 | 5 | 8.01 | + | |
GWO | 3.37 | 4.82 | 2.64 | 4.72 | 3 | 1.85 | + | |
WOA | 3.14 × | 3.93 | 2.49 | 3.98 | 1 | 7.30 | ≈ | |
BOA | 6.29 | 1.55 | 3.47 | 1.08 | 9 | 1.86 | + | |
SOA | 4.18 | 1.18 | 2.84 | 8.35 | 6 | 5.97 | + | |
LWOA | 3.45 | 3.07 × | 2.67 | 4.15 | 4 | 5.38 | + | |
MSWOA | 4.22 | 1.60 | 2.50 | 8.66 | 7 | 3.13 | + | |
DGSWOA | 3.17 | 3.35 | 2.43 × | 3.74 × | 2 | |||
PSO | 5.33 | 8.81 | 3.45 | 7.08 | 7 | 1.86 | + | |
GA | 5.40 | 8.18 | 3.33 | 6.67 | 8 | 1.86 | + | |
GWO | 4.18 | 4.84 | 3.49 | 5.24 | 6 | 1.86 | + | |
WOA | 3.48 | 3.93 | 2.61 | 4.36 | 3 | 2.48 | + | |
BOA | 6.84 | 1.56 | 4.55 | 1.00 | 9 | 1.86 | + | |
SOA | 4.09 | 1.11 | 2.84 | 7.88 | 5 | 1.06 | + | |
LWOA | 3.82 | 4.91 | 2.75 | 5.02 | 4 | 7.99 | + | |
MSWOA | 3.43 | 4.98 | 2.73 | 4.58 | 2 | 1.64 | ≈ | |
DGSWOA | 3.23 × | 2.71 × | 2.61 × | 3.76 × | 1 | |||
PSO | 6.29 | 2.19 | 5.75 | 6.66 | 7 | 1.86 | + | |
GA | 6.80 | 3.38 | 6.16 | 7.55 | 8 | 1.86 | + | |
GWO | 5.19 | 1.40 | 5.15 × | 5.82 | 4 | 1.80 | ≈ | |
WOA | 5.15 × | 7.11 × | 5.15 × | 5.15 × | 1 | NaN | NaN | |
BOA | 9.14 | 1.15 | 6.46 | 1.18 | 9 | NaN | NaN | |
SOA | 5.90 | 3.35 | 5.15 | 6.15 | 6 | NaN | NaN | |
LWOA | 5.15 × | 7.11 × | 5.15 × | 5.15 × | 1 | NaN | NaN | |
MSWOA | 5.49 | 4.71 | 5.15 | 6.15 | 5 | NaN | NaN | |
DGSWOA | 5.15 × | 7.11 × | 5.15 × | 5.15 × | 1 | |||
PSO | 9.28 | 3.32 | 8.57 | 9.71 | 6 | 1.86 | + | |
GA | 8.99 | 2.38 | 8.59 | 9.58 | 5 | 1.86 | + | |
GWO | 8.41 | 4.68 | 8.37 | 8.48 | 3 | 1.89 | + | |
WOA | 8.39 | 3.43 | 8.35 | 8.48 | 2 | 3.09 | ≈ | |
BOA | 5.56 | 8.12 | 9.05 | 3.43 | 9 | 1.86 | + | |
SOA | 3.61 | 8.10 | 8.46 | 3.80 | 7 | 1.86 | + | |
LWOA | 8.57 | 9.29 | 8.42 | 8.73 | 4 | 5.59 | + | |
MSWOA | 4.48 | 1.67 | 8.37 | 9.35 | 8 | 1.86 | + | |
DGSWOA | 8.38 × | 2.83 × | 8.35 × | 8.47 × | 1 | |||
PSO | −8.07 | 1.32 | −8.29 | −7.77 | 7 | 1.86 | + | |
GA | −8.35 | 2.49 | −8.38 | −8.25 | 3 | 8.08 | ≈ | |
GWO | −8.29 | 3.54 | −8.36 | −8.21 | 5 | 1.86 | + | |
WOA | −8.33 | 3.78 | −8.38 | −8.25 | 4 | 6.06 | ≈ | |
BOA | −4.78 | 1.22 | −7.24 | −2.38 | 9 | 1.86 | + | |
SOA | −8.14 | 2.64 | −8.38 | −7.22 | 6 | 3.86 | + | |
LWOA | −8.35 | 2.63 | −8.38 | −8.30 | 2 | 9.84 | ≈ | |
MSWOA | −7.97 | 8.81 | −8.39 | −3.51 | 8 | 3.05 | + | |
DGSWOA | −8.35 × | 2.05 × | −8.39 × | −8.31 × | 1 | |||
PSO | −6.58 | 3.33 | −1.24 | 1.32 | 7 | 1.86 | + | |
GA | −1.31 | 1.39 × | −1.34 | −1.26 | 2 | 8.08 | ≈ | |
GWO | −1.28 | 8.81 | −1.35 | −1.09 | 5 | 4.28 | ≈ | |
WOA | −1.34 × | 2.13 | −1.35 | −1.27 × | 1 | 6.06 | ≈ | |
BOA | 1.92 | 2.49 | −2.94 | 9.82 | 9 | 1.86 | + | |
SOA | 3.75 | 2.22 | −1.34 | 1.23 | 8 | 6.15 | + | |
LWOA | −1.30 | 2.51 | −1.34 | −1.23 | 4 | 3.39 | ≈ | |
MSWOA | −1.26 | 3.20 | −1.35 × | 4.64 | 6 | 1.00 | ≈ | |
DGSWOA | −1.31 | 5.42 | −1.35 | −1.19 | 3 | |||
PSO | −2.85 | 3.17 | −3.33 | −2.04 | 8 | 1.86 | + | |
GA | −3.55 | 1.78 | −3.58 | −3.48 | 6 | 1.86 | + | |
GWO | −3.58 | 1.20 | −3.59 | −3.55 | 3 | 2.61 | + | |
WOA | −3.58 | 1.13 | −3.59 | −3.55 | 2 | 3.45 | + | |
BOA | −1.69 | 2.74 | −2.33 | −9.36 | 9 | 1.86 | + | |
SOA | −3.55 | 3.92 | −3.59 | −3.44 | 7 | 2.61 | + | |
LWOA | −3.55 | 1.69 | −3.59 | −3.51 | 5 | 3.73 | + | |
MSWOA | −3.57 | 1.62 | −3.59 × | −3.55 | 4 | 4.97 | + | |
DGSWOA | −3.59 × | 2.98 × | −3.59 | −3.58 × | 1 | |||
PSO | 1.60 | 8.61 | 2.65 | 4.30 | 5 | 6.15 | + | |
GA | 3.20 | 2.10 × | −5.30 | 9.32 × | 2 | 9.68 | ≈ | |
GWO | 2.24 | 3.52 | −1.57 | 1.85 | 7 | 3.79 | + | |
WOA | 2.84 × | 2.53 | −4.70 × | 1.07 | 1 | 6.70 | ≈ | |
BOA | 1.10 | 6.99 | 1.12 | 2.72 | 9 | 1.86 | + | |
SOA | 3.66 | 5.82 | 1.97 | 2.75 | 8 | 4.66 | + | |
LWOA | 5.47 | 2.92 | 1.22 | 1.19 | 4 | 5.01 | + | |
MSWOA | 1.70 | 1.54 | −3.13 | 6.68 | 6 | 6.91 | + | |
DGSWOA | 3.29 | 2.74 | 2.18 | 1.04 | 3 | |||
PSO | −8.19 | 1.09 | −9.59 | −6.00 | 5 | 7.00 | ≈ | |
GA | −8.86 × | 6.07 × | −9.93 × | −7.57 × | 1 | 6.64 | − | |
GWO | −6.59 | 1.34 | −8.92 | −3.75 | 7 | 1.68 | + | |
WOA | −8.31 | 7.98 | −9.89 | −6.24 | 3 | 1.00 | ≈ | |
BOA | 3.37 | 7.73 | −7.93 | 3.27 | 9 | 9.31 | + | |
SOA | −6.44 | 1.91 | −9.39 | −3.52 | 8 | 3.45 | + | |
LWOA | −8.41 | 7.37 | −9.92 | −6.55 | 2 | 4.52 | ≈ | |
MSWOA | −7.03 | 1.72 | −9.86 | −6.73 | 6 | 7.30 | + | |
DGSWOA | −8.26 | 8.14 | −9.84 | −6.53 | 4 | |||
PSO | 3.56 | 2.17 | 3.34 | 8.95 | 7 | 3.73 | + | |
GA | 3.08 | 5.30 | 5.07 | 2.72 | 5 | 1.00 | ≈ | |
GWO | 2.49 | 5.94 | 3.00 × | 3.14 | 3 | 8.08 | ≈ | |
WOA | 7.41 × | 1.50 | 3.13 | 7.53 | 1 | 2.93 | − | |
BOA | 5.86 | 4.03 | 3.91 | 1.57 | 9 | 1.86 | + | |
SOA | 8.08 | 1.43 | 1.94 | 7.59 | 8 | 2.61 | + | |
LWOA | 2.51 | 1.43 | 4.59 | 5.88 | 4 | 1.58 | + | |
MSWOA | 2.50 | 4.22 | 4.22 | 1.24 | 6 | 3.15 | + | |
DGSWOA | 1.23 | 1.23 × | 3.07 | 4.15 × | 2 | |||
PSO | 6.61 | 2.97 | 1.94 | 1.32 | 7 | 1.86 | + | |
GA | 3.42 | 2.21 | −6.67 | 8.61 | 6 | 1.86 | + | |
GWO | −1.42 | 2.18 | −4.56 | 3.25 | 4 | 3.90 | + | |
WOA | −2.79 | 1.30 | −5.05 × | −1.35 | 2 | 5.23 | ≈ | |
BOA | 2.00 | 1.09 | −1.07 | 4.46 | 9 | 1.86 | + | |
SOA | 8.70 | 9.81 | −2.47 | 3.33 | 8 | 3.73 | + | |
LWOA | −1.54 | 1.07 | −3.10 | 8.65 | 3 | 1.86 | + | |
MSWOA | 1.72 | 7.12 | −4.16 | 3.31 | 5 | 8.01 | + | |
DGSWOA | −3.51 × | 8.94 × | −4.82 | −1.34 × | 1 | |||
PSO | −5.73 | 2.04 | −5.77 | −5.68 | 7 | 1.86 | + | |
GA | −5.78 | 4.01 | −5.79 | −5.77 | 4 | 1.02 | + | |
GWO | −5.78 | 1.54 | −5.79 × | −5.73 | 5 | 1.14 | ≈ | |
WOA | −5.79 | 5.13 | −5.79 | −5.77 | 2 | 8.08 | ≈ | |
BOA | −5.09 | 3.13 | −5.56 | −4.56 | 9 | 1.86 | + | |
SOA | −5.64 | 1.30 | −5.79 | −5.06 | 8 | 5.59 | + | |
LWOA | −5.78 | 2.82 | −5.79 | −5.78 | 3 | 6.92 | + | |
MSWOA | −5.77 | 3.91 | −5.79 | −5.61 | 6 | 1.06 | + | |
DGSWOA | −5.79 × | 2.66 × | −5.79 | −5.78 × | 1 | |||
PSO | −1.85 | 5.83 | −3.02 | −7.60 | 8 | 1.86 | + | |
GA | −3.23 | 3.71 | −4.01 | −2.63 | 4 | 7.67 | ≈ | |
GWO | −3.23 | 3.76 | −4.04 | −2.44 | 3 | 6.67 | ≈ | |
WOA | −3.29 | 4.65 | −4.16 | −2.35 | 2 | 3.09 | ≈ | |
BOA | −2.39 | 1.03 | −1.77 | 3.11 | 9 | 1.86 | + | |
SOA | −3.07 | 1.05 | −4.05 | 1.91 | 5 | 1.19 | ≈ | |
LWOA | −3.07 | 3.76 | −4.09 | −2.29 | 6 | 4.03 | + | |
MSWOA | −2.29 | 1.54 | −4.17 × | 1.62 | 7 | 1.13 | + | |
DGSWOA | −3.41 × | 3.36 × | −4.05 | −2.76 × | 1 | |||
PSO | −2.58 | 8.35 | −2.59 | −2.55 | 6 | 3.73 | + | |
GA | −2.57 | 1.15 | −2.60 | −2.55 | 8 | 1.86 | + | |
GWO | −2.58 | 1.44 | −2.60 | −2.54 | 4 | 4.41 | + | |
WOA | −2.59 | 6.53 | −2.60 × | −2.58 | 2 | 7.15 | ≈ | |
BOA | −2.41 | 7.47 | −2.56 | −2.27 | 9 | 1.86 | + | |
SOA | −2.57 | 1.82 | −2.60 | −2.52 | 7 | 2.55 | + | |
LWOA | −2.58 | 8.87 | −2.60 | −2.56 | 5 | 4.66 | + | |
MSWOA | −2.59 | 1.39 | −2.60 | −2.54 | 3 | 8.14 | + | |
DGSWOA | −2.59 × | 5.82 × | −2.60 | −2.58 × | 1 | |||
PSO | −3.70 | 4.20 | −3.78 | −3.62 | 8 | 1.86 | + | |
GA | −3.78 | 2.20 | −3.83 | −3.72 | 5 | 1.86 | + | |
GWO | −3.84 | 1.64 | −3.86 | −3.76 | 3 | 1.23 | + | |
WOA | −3.84 | 1.34 | −3.86 | −3.81 | 2 | 3.84 | + | |
BOA | −3.12 | 1.77 | −3.49 | −2.80 | 9 | 1.86 | + | |
SOA | −3.76 | 8.67 | −3.84 | −3.52 | 6 | 1.86 | + | |
LWOA | −3.82 | 1.68 | −3.85 | −3.78 | 4 | 3.15 | + | |
MSWOA | −3.76 | 6.34 | −3.87 | −3.57 | 7 | 3.54 | + | |
DGSWOA | −3.85 × | 1.13 × | −3.87 × | −3.83 × | 1 | |||
PSO | −3.33 | 1.22 | −3.57 | −3.13 | 8 | 1.86 | + | |
GA | −3.68 | 5.52 | −3.80 | −3.58 × | 5 | 1.02 | + | |
GWO | −3.77 | 7.52 | −3.84 | −3.55 | 3 | 1.35 | ≈ | |
WOA | −3.79 | 7.13 | −3.86 × | −3.51 | 2 | 7.61 | ≈ | |
BOA | −1.67 | 6.19 | −2.89 | −6.64 | 9 | 1.86 | + | |
SOA | −3.41 | 3.29 | −3.83 | −2.46 | 7 | 8.01 | + | |
LWOA | −3.69 | 5.28 × | −3.75 | −3.55 | 4 | 1.68 | + | |
MSWOA | −3.55 | 1.80 | −3.82 | −3.12 | 6 | 5.59 | + | |
DGSWOA | −3.79 × | 5.84 | −3.85 | −3.54 | 1 | |||
PSO | 4.21 | 6.49 | 4.09 | 4.37 | 9 | 1.86 | + | |
GA | 4.17 | 3.30 | 4.09 | 4.22 | 8 | 1.86 | + | |
GWO | 4.06 | 8.60 | 4.05 × | 4.08 | 5 | 2.05 | + | |
WOA | 4.06 | 6.84 | 4.05 | 4.07 | 2 | 4.71 | + | |
BOA | 4.09 | 1.86 | 4.06 | 4.13 | 6 | 1.86 | + | |
SOA | 4.06 | 6.30 | 4.05 | 4.07 | 4 | 1.86 | + | |
LWOA | 4.15 | 3.55 | 4.07 | 4.22 | 7 | 1.86 | + | |
MSWOA | 4.06 | 7.77 | 4.05 | 4.07 | 3 | 1.86 | + | |
DGSWOA | 4.05 × | 4.83 × | 4.05 | 4.05 × | 1 | |||
PSO | 1.86 | 4.83 | 1.85 | 1.86 | 8 | 3.73 | + | |
GA | 1.85 | 2.20 | 1.84 | 1.85 | 7 | 3.54 | + | |
GWO | 1.85 | 1.55 | 1.84 | 1.85 | 4 | 2.69 | + | |
WOA | 1.85 | 1.53 × | 1.84 | 1.85 × | 2 | 2.19 | + | |
BOA | 1.92 | 3.52 | 1.84 | 3.81 | 9 | 1.86 | + | |
SOA | 1.85 | 4.81 | 1.83 × | 1.86 | 5 | 5.01 | + | |
LWOA | 1.85 | 3.18 | 1.84 | 1.85 | 3 | 1.72 | + | |
MSWOA | 1.85 | 6.07 | 1.84 | 1.86 | 6 | 4.18 | + | |
DGSWOA | 1.84 × | 1.73 | 1.84 | 1.85 | 1 | |||
PSO | 3.12 | 5.62 | 3.11 | 3.13 | 5 | 8.14 | + | |
GA | 3.12 | 8.19 | 3.11 | 3.14 | 6 | 1.37 | + | |
GWO | 3.12 | 1.39 | 3.11 | 3.16 | 7 | 3.05 | + | |
WOA | 3.11 | 6.23 | 3.11 | 3.13 | 4 | 9.84 | ≈ | |
BOA | 3.11 | 7.13 | 3.11 × | 3.13 | 3 | 9.35 | ≈ | |
SOA | 3.15 | 3.26 | 3.11 | 3.24 | 9 | 3.79 | + | |
LWOA | 3.11 × | 4.06 × | 3.11 | 3.12 × | 1 | 3.80 | − | |
MSWOA | 3.13 | 1.89 | 3.11 | 3.18 | 8 | 2.99 | + | |
DGSWOA | 3.11 | 4.74 | 3.11 | 3.12 | 2 | |||
PSO | 4.38 | 5.99 | 4.30 | 4.50 × | 3 | 6.99 | ≈ | |
GA | 4.53 | 2.00 | 4.31 | 5.08 | 6 | 4.34 | + | |
GWO | 4.67 | 4.33 | 4.37 | 5.85 | 7 | 6.64 | + | |
WOA | 4.37 | 6.77 | 4.30 × | 4.57 | 2 | 1.28 | − | |
BOA | 4.36 × | 8.21 | 4.30 | 4.68 | 1 | 1.13 | − | |
SOA | 5.33 | 6.30 | 4.36 | 7.06 | 9 | 4.66 | + | |
LWOA | 4.40 | 5.55 × | 4.30 | 4.51 | 4 | 9.52 | ≈ | |
MSWOA | 4.70 | 5.49 | 4.30 | 6.18 | 8 | 1.24 | ≈ | |
DGSWOA | 4.41 | 6.63 | 4.30 | 4.58 | 5 | |||
PSO | 2.11 | 2.79 | 2.11 | 2.12 | 6 | 3.90 | + | |
GA | 2.12 | 3.33 | 2.11 | 2.12 | 7 | 2.55 | + | |
GWO | 2.11 | 3.78 | 2.11 | 2.12 | 4 | 1.19 | ≈ | |
WOA | 2.11 | 2.82 | 2.10 × | 2.12 × | 2 | 9.19 | ≈ | |
BOA | 2.12 | 3.44 | 2.11 | 2.12 | 8 | 3.54 | + | |
SOA | 2.12 | 3.63 | 2.11 | 2.12 | 9 | 1.02 | + | |
LWOA | 2.11 | 2.15 | 2.11 | 2.12 | 5 | 4.41 | + | |
MSWOA | 2.11 × | 2.76 | 2.11 | 2.12 | 1 | 2.34 | − | |
DGSWOA | 2.11 | 1.66 × | 2.11 | 2.12 | 3 | |||
PSO | 7.02 | 4.20 | 6.01 | 7.73 | 9 | 3.73 | + | |
GA | 6.85 | 4.29 | 6.00 | 7.60 | 8 | 5.72 | + | |
GWO | 6.67 | 3.52 | 6.00 | 7.44 | 7 | 5.14 | + | |
WOA | 6.48 | 3.62 | 5.30 | 7.11 | 4 | 8.72 | + | |
BOA | 6.45 | 3.78 | 5.70 | 7.28 | 3 | 1.85 | + | |
SOA | 6.59 | 9.30 | 4.97 × | 7.99 | 5 | 7.67 | ≈ | |
LWOA | 6.39 | 3.69 | 5.48 | 7.06 | 2 | 5.77 | ≈ | |
MSWOA | 6.66 | 7.88 | 5.48 | 8.36 | 6 | 1.28 | + | |
DGSWOA | 6.22 × | 2.85 × | 5.49 | 6.75 × | 1 |
F | Algorithm | Mean | Std | Best | Worst | Rank | p-Value | State |
---|---|---|---|---|---|---|---|---|
PSO | −8.13 | 2.95 | −8.76 | −7.60 | 7 | 1.86 | + | |
GA | −9.06 | 6.50 | −9.16 | −8.93 | 5 | 1.86 | + | |
GWO | −9.13 | 6.23 | −9.22 | −9.01 | 4 | 4.66 | + | |
WOA | −9.16 | 5.14 | −9.26 | −8.98 | 3 | 5.29 | ≈ | |
BOA | −4.18 | 1.20 | −6.35 | −1.53 | 9 | 1.86 | + | |
SOA | −7.94 | 6.07 | −9.02 | −6.38 | 8 | 1.86 | + | |
LWOA | −9.18 × | 3.24 × | −9.24 | −9.12 × | 1 | 2.37 | ≈ | |
MSWOA | −8.80 | 3.56 | −9.24 | −7.75 | 6 | 1.02 | + | |
DGSWOA | −9.17 | 4.85 | −9.26 × | −9.09 | 2 | |||
PSO | 5.73 | 2.01 | 1.56 | 9.64 | 7 | 1.86 | + | |
GA | 5.93 × | 2.97 × | 2.09 | 1.56 × | 1 | 3.60 | ≈ | |
GWO | 4.15 | 3.09 | 5.87 | 1.04 | 6 | 1.86 | + | |
WOA | 1.02 | 8.11 | 2.00 | 3.23 | 3 | 9.61 | ≈ | |
BOA | 5.46 | 3.72 | 5.26 | 1.64 | 9 | 1.86 | + | |
SOA | 1.30 | 1.22 | 2.59 | 4.50 | 8 | 1.86 | + | |
LWOA | 2.03 | 9.04 | 4.27 | 3.77 | 4 | 1.06 | + | |
MSWOA | 3.62 | 1.75 | 1.14 | 8.73 | 5 | 3.73 | + | |
DGSWOA | 7.34 | 5.19 | 1.80 × | 2.85 | 2 | |||
PSO | 1.42 | 1.74 | 1.09 | 1.76 | 5 | 1.86 | + | |
GA | 1.56 | 1.78 | 1.20 | 1.93 | 7 | 1.86 | + | |
GWO | 6.98 × | 1.03 | 4.71 | 9.23 | 1 | 4.77 | ≈ | |
WOA | 7.31 | 9.82 | 4.70 × | 8.85 × | 3 | 7.00 | ≈ | |
BOA | 2.88 | 7.24 | 1.57 | 4.36 | 9 | 1.86 | + | |
SOA | 1.54 | 5.63 | 9.63 | 3.03 | 6 | 1.86 | + | |
LWOA | 8.03 | 7.12 × | 6.78 | 9.19 | 4 | 6.64 | + | |
MSWOA | 1.75 | 8.92 | 5.35 | 5.40 | 8 | 6.15 | + | |
DGSWOA | 7.25 | 1.07 | 5.61 | 9.67 | 2 | |||
PSO | 1.79 | 1.85 | 1.34 | 2.15 | 7 | 1.86 | + | |
GA | 1.86 | 1.92 | 1.53 | 2.31 | 8 | 1.86 | + | |
GWO | 9.22 | 1.98 | 6.02 | 1.45 | 2 | 8.08 | ≈ | |
WOA | 9.21 × | 1.73 | 4.83 × | 1.22 × | 1 | 6.70 | ≈ | |
BOA | 2.53 | 4.09 | 1.70 | 3.40 | 9 | 1.86 | + | |
SOA | 1.47 | 4.60 | 6.28 | 2.64 | 6 | 1.30 | + | |
LWOA | 9.90 | 9.75 × | 7.25 | 1.23 | 4 | 6.99 | ≈ | |
MSWOA | 1.28 | 4.07 | 6.74 | 2.28 | 5 | 9.90 | + | |
DGSWOA | 9.36 | 1.45 | 6.47 | 1.29 | 3 | |||
PSO | 1.03 | 8.34 | 8.17 | 1.19 | 7 | 1.86 | + | |
GA | 1.22 | 7.96 | 1.06 | 1.37 | 8 | 1.86 | + | |
GWO | 6.00 | 4.37 | 5.15 × | 6.98 | 4 | 3.73 | + | |
WOA | 5.19 | 6.63 | 5.15 × | 5.49 | 3 | 6.03 | ≈ | |
BOA | 1.60 | 1.92 | 1.13 | 1.94 | 9 | 1.86 | + | |
SOA | 7.93 | 2.18 | 5.15 | 1.08 | 6 | 8.01 | + | |
LWOA | 5.15 × | 7.11 × | 5.15 × | 5.15 × | 1 | 9.82 | − | |
MSWOA | 7.52 | 1.85 | 5.15 | 1.17 | 5 | 3.54 | + | |
DGSWOA | 5.18 | 4.73 | 5.15 × | 5.38 | 2 | |||
PSO | 1.72 | 2.13 | 1.24 | 2.03 | 7 | 1.86 | + | |
GA | 1.30 | 8.88 | 1.08 | 1.45 | 5 | 3.73 | + | |
GWO | 1.03 | 7.80 | 8.64 | 1.29 | 3 | 1.52 | ≈ | |
WOA | 9.90 × | 8.53 | 8.55 × | 1.17 | 1 | 5.84 | ≈ | |
BOA | 7.77 | 7.42 | 1.27 | 2.95 | 9 | 1.86 | + | |
SOA | 1.09 | 2.59 | 1.13 | 1.15 | 8 | 1.86 | + | |
LWOA | 1.05 | 6.40 | 9.61 | 1.18 | 4 | 8.14 | + | |
MSWOA | 1.72 | 1.19 | 1.07 | 8.00 | 6 | 3.73 | + | |
DGSWOA | 1.00 | 6.11 × | 8.71 | 1.13 × | 2 | |||
PSO | −3.91 | 1.38 | −5.83 | −3.03 | 7 | 1.86 | + | |
GA | −7.58 × | 2.52 × | −8.03 | −6.86 | 1 | 6.06 | ≈ | |
GWO | −7.18 | 7.16 | −8.09 × | −5.34 | 5 | 2.37 | ≈ | |
WOA | −7.45 | 5.05 | −8.04 | −6.11 | 3 | 8.55 | ≈ | |
BOA | 6.05 | 5.48 | −2.55 | 1.83 | 9 | 1.86 | + | |
SOA | −2.44 | 3.42 | −6.65 | 6.40 | 8 | 1.86 | + | |
LWOA | −7.47 | 3.15 | −8.03 | −6.89 × | 2 | 5.84 | ≈ | |
MSWOA | −5.32 | 1.62 | −7.98 | −1.70 | 6 | 1.86 | + | |
DGSWOA | −7.41 | 4.75 | −8.08 | −6.41 | 4 | |||
PSO | 2.46 | 8.62 | 1.13 | 4.45 | 7 | 1.86 | + | |
GA | 2.69 | 7.10 | −6.86 | 1.69 | 4 | 4.42 | + | |
GWO | 3.74 | 1.74 | −1.02 | 6.21 | 5 | 2.37 | + | |
WOA | −5.11 | 9.24 | −1.29 × | 2.40 | 3 | 3.39 | ≈ | |
BOA | 8.36 | 4.74 | 1.85 | 2.06 | 9 | 1.86 | + | |
SOA | 5.12 | 5.39 | 2.77 | 1.74 | 8 | 1.86 | + | |
LWOA | −5.27 | 5.85 | −1.16 | 2.04 | 2 | 1.29 | ≈ | |
MSWOA | 1.94 | 4.79 | −5.17 | 2.55 | 6 | 1.86 | + | |
DGSWOA | −6.40 × | 4.97 × | −1.27 | 5.21 × | 1 | |||
PSO | 1.76 | 1.01 | 1.07 | 4.26 | 9 | 1.86 | + | |
GA | −2.68 | 3.51 | −3.26 | −1.74 | 7 | 1.86 | + | |
GWO | −3.45 | 5.06 | −3.50 | −3.28 | 3 | 1.23 | + | |
WOA | −3.47 | 5.08 | −3.54 | −3.32 | 2 | 6.99 | ≈ | |
BOA | −1.07 | 1.76 | −1.45 | −7.77 | 8 | 1.86 | + | |
SOA | −3.13 | 6.52 | −3.28 | −3.05 | 5 | 1.86 | + | |
LWOA | −2.99 | 2.44 | −3.35 | −2.41 | 6 | 1.86 | + | |
MSWOA | −3.18 | 9.39 | −3.45 | −3.05 | 4 | 1.86 | + | |
DGSWOA | −3.50 × | 4.77 × | −3.59 × | −3.41 × | 1 | |||
PSO | 4.95 | 2.16 | 6.86 | 1.03 | 6 | 3.73 | + | |
GA | 3.08 | 1.26 | 6.01 | 5.50 | 5 | 1.30 | + | |
GWO | 1.14 | 4.64 | 3.77 | 2.28 | 3 | 1.28 | + | |
WOA | 8.57 | 5.58 | 8.94 | 2.79 | 2 | 9.19 | ≈ | |
BOA | 1.75 | 5.42 | 2.09 | 2.63 | 8 | 1.86 | + | |
SOA | 2.17 | 1.29 | 1.87 | 5.99 | 9 | 1.86 | + | |
LWOA | 2.30 | 9.76 | 6.61 | 4.07 | 4 | 2.05 | + | |
MSWOA | 1.30 | 7.39 | 6.73 | 2.81 | 7 | 3.73 | + | |
DGSWOA | 8.04 × | 3.71 × | 8.34 × | 1.53 × | 1 | |||
PSO | −3.84 | 1.68 | −6.63 | 1.80 | 4 | 2.77 | + | |
GA | −5.25 × | 1.33 | −8.80 × | −3.40 | 1 | 3.71 | ≈ | |
GWO | −4.00 | 9.87 | −5.57 | −2.18 | 3 | 1.04 | + | |
WOA | −3.81 | 1.38 | −6.15 | −5.62 | 5 | 1.58 | + | |
BOA | −3.16 | 1.16 | −6.06 | −5.97 | 6 | 3.86 | + | |
SOA | 1.36 | 4.89 | −6.58 | 1.32 | 9 | 6.15 | + | |
LWOA | −6.35 | 2.85 | −5.49 | 7.56 | 8 | 3.54 | + | |
MSWOA | −1.79 | 2.65 | −4.51 | 1.02 | 7 | 1.86 | + | |
DGSWOA | −4.89 | 7.09 × | −6.58 | −3.84 × | 2 | |||
PSO | 1.05 | 2.98 | 5.92 | 1.85 | 7 | 1.86 | + | |
GA | 6.59 | 2.11 | 3.27 | 1.15 | 6 | 1.86 | + | |
GWO | 1.26 | 1.17 | 3.14 × | 4.33 | 4 | 1.34 | + | |
WOA | 3.65 × | 4.12 | 7.67 | 1.96 | 1 | 9.84 | ≈ | |
BOA | 5.17 | 2.12 | 1.57 | 8.79 | 9 | 1.86 | + | |
SOA | 1.32 | 1.09 | 5.31 | 3.84 | 8 | 1.86 | + | |
LWOA | 4.26 | 1.92 × | 1.25 | 8.37 × | 3 | 2.71 | ≈ | |
MSWOA | 6.12 | 9.09 | 1.77 | 4.10 | 5 | 2.55 | + | |
DGSWOA | 4.06 | 4.69 | 7.47 | 2.31 | 2 | |||
PSO | 4.76 | 7.40 | 3.16 | 6.16 | 7 | 1.86 | + | |
GA | 4.06 | 6.95 | 2.80 | 5.43 | 6 | 1.86 | + | |
GWO | 1.64 | 4.42 | 8.10 | 2.55 | 4 | 5.59 | + | |
WOA | 1.36 | 6.21 | −3.92 × | 2.90 | 3 | 2.77 | + | |
BOA | 6.91 | 9.10 | 4.64 | 8.40 | 9 | 1.86 | + | |
SOA | 4.99 | 1.50 | 1.55 | 7.28 | 8 | 1.86 | + | |
LWOA | 1.17 | 3.42 × | 2.97 | 1.80 × | 2 | 4.28 | ≈ | |
MSWOA | 3.83 | 1.31 | 1.91 | 5.88 | 5 | 1.86 | + | |
DGSWOA | 1.08 × | 4.48 | 3.21 | 2.04 | 1 | |||
PSO | −5.33 | 9.86 | −5.54 | −5.17 | 7 | 1.86 | + | |
GA | −5.65 | 3.66 | −5.73 | −5.56 | 5 | 1.30 | + | |
GWO | −5.70 | 4.95 | −5.75 | −5.51 | 4 | 1.30 | + | |
WOA | −5.72 | 3.53 | −5.79 × | −5.61 | 3 | 2.48 | + | |
BOA | −3.84 | 6.05 | −4.77 | −2.32 | 9 | 1.86 | + | |
SOA | −5.33 | 2.41 | −5.65 | −4.52 | 8 | 1.86 | + | |
LWOA | −5.75 × | 1.26 × | −5.78 | −5.72 × | 1 | 3.39 | ≈ | |
MSWOA | −5.61 | 1.51 | −5.76 | −5.14 | 6 | 6.91 | + | |
DGSWOA | −5.74 | 2.79 | −5.78 | −5.68 | 2 | |||
PSO | 7.64 | 1.72 | 2.08 | 1.03 | 8 | 1.86 | + | |
GA | 6.16 | 1.32 | 3.36 | 8.07 | 6 | 9.31 | + | |
GWO | 1.54 | 7.51 × | 7.15 | 3.47 | 2 | 4.66 | − | |
WOA | 1.91 | 8.55 | 3.32 | 3.64 | 3 | 1.64 | ≈ | |
BOA | 1.11 | 3.30 | 4.07 | 1.77 | 9 | 1.86 | + | |
SOA | 7.14 | 3.87 | −1.56 | 1.77 | 7 | 6.91 | + | |
LWOA | 1.48 × | 8.87 | −5.71 | 3.29 × | 1 | 7.61 | − | |
MSWOA | 4.52 | 2.89 | −6.15 × | 1.26 | 5 | 1.58 | + | |
DGSWOA | 2.32 | 1.17 | −3.48 | 4.54 | 4 | |||
PSO | −2.50 | 2.07 | −2.55 | −2.46 | 6 | 1.86 | + | |
GA | −2.50 | 2.20 | −2.55 | −2.46 | 7 | 1.86 | + | |
GWO | −2.54 | 2.94 | −2.59 | −2.46 | 3 | 3.27 | + | |
WOA | −2.56 | 2.30 | −2.59 × | −2.51 | 2 | 9.03 | ≈ | |
BOA | −2.28 | 7.73 | −2.42 | −2.12 | 9 | 1.86 | + | |
SOA | −2.46 | 3.60 | −2.54 | −2.41 | 8 | 1.86 | + | |
LWOA | −2.51 | 2.29 | −2.56 | −2.48 | 5 | 3.15 | + | |
MSWOA | −2.52 | 4.21 | −2.58 | −2.41 | 4 | 4.41 | + | |
DGSWOA | −2.56 × | 1.75 × | −2.59 | −2.51 × | 1 | |||
PSO | −3.45 | 5.42 | −3.59 | −3.37 | 8 | 1.86 | + | |
GA | −3.62 | 4.59 × | −3.71 | −3.56 | 5 | 2.76 | + | |
GWO | −3.72 | 5.68 | −3.80 | −3.56 | 2 | 1.24 | ≈ | |
WOA | −3.72 | 5.50 | −3.84 | −3.61 | 3 | 3.60 | ≈ | |
BOA | −2.75 | 2.59 | −3.37 | −2.16 | 9 | 1.86 | + | |
SOA | −3.55 | 1.00 | −3.70 | −3.29 | 7 | 8.01 | + | |
LWOA | −3.72 × | 4.76 | −3.83 | −3.61 × | 1 | 1.71 | ≈ | |
MSWOA | −3.59 | 8.58 | −3.74 | −3.44 | 6 | 1.30 | + | |
DGSWOA | −3.70 | 5.76 | −3.85 × | −3.61 | 4 | |||
PSO | −2.29 | 2.23 | −2.74 | −1.88 | 8 | 1.86 | + | |
GA | −3.10 | 1.65 | −3.46 | −2.79 | 5 | 3.24 | + | |
GWO | −3.33 | 2.12 | −3.62 | −2.80 | 4 | 3.82 | ≈ | |
WOA | −3.38 | 1.55 × | −3.63 | −3.04 | 2 | 9.19 | ≈ | |
BOA | −1.03 | 3.10 | −1.80 | −6.12 | 9 | 1.86 | + | |
SOA | −2.78 | 4.01 | −3.54 | −1.97 | 7 | 9.31 | + | |
LWOA | −3.36 | 1.60 | −3.62 | −3.05 × | 3 | 5.29 | ≈ | |
MSWOA | −3.02 | 2.95 | −3.55 | −2.35 | 6 | 4.42 | + | |
DGSWOA | −3.38 × | 1.61 | −3.64 × | −2.96 | 1 | |||
PSO | 4.71 | 8.51 | 4.50 | 4.82 | 9 | 1.86 | + | |
GA | 4.50 | 7.68 | 4.22 | 4.63 | 8 | 1.86 | + | |
GWO | 4.12 | 6.13 | 4.05 | 4.28 | 4 | 8.33 | + | |
WOA | 4.14 | 5.73 | 4.06 | 4.25 | 5 | 8.01 | + | |
BOA | 4.28 | 5.69 | 4.14 | 4.39 | 6 | 1.86 | + | |
SOA | 4.07 | 1.77 × | 4.06 | 4.07 | 3 | 1.30 | + | |
LWOA | 4.42 | 7.68 | 4.20 | 4.56 | 7 | 1.86 | + | |
MSWOA | 4.07 | 2.38 | 4.06 | 4.07 | 2 | 8.33 | + | |
DGSWOA | 4.06 × | 5.37 | 4.05 × | 4.07 × | 1 | |||
PSO | 5.47 | 2.83 | 1.87 | 1.18 | 7 | 1.86 | + | |
GA | 1.86 | 2.00 × | 1.85 | 1.86 | 5 | 2.35 | + | |
GWO | 1.86 | 2.56 | 1.85 | 1.86 | 3 | 3.48 | + | |
WOA | 1.85 | 2.74 | 1.85 | 1.86 × | 2 | 2.45 | ≈ | |
BOA | 8.34 | 7.82 | 1.87 | 3.37 | 8 | 1.86 | + | |
SOA | 9.24 | 1.43 | 1.85 | 6.55 | 9 | 1.86 | + | |
LWOA | 1.86 | 2.59 | 1.85 | 1.86 | 4 | 6.19 | + | |
MSWOA | 3.53 | 7.73 | 1.85 | 4.50 | 6 | 2.05 | + | |
DGSWOA | 1.85 × | 3.58 | 1.84 × | 1.86 | 1 | |||
PSO | 3.26 | 3.59 | 3.19 | 3.33 | 7 | 1.86 | + | |
GA | 3.28 | 5.62 | 3.18 | 3.41 | 8 | 9.31 | + | |
GWO | 3.18 | 5.30 | 3.12 | 3.37 | 4 | 1.72 | + | |
WOA | 3.14 | 2.49 | 3.11 | 3.19 × | 3 | 8.08 | ≈ | |
BOA | 3.18 | 6.26 | 3.11 | 3.38 | 5 | 9.93 | + | |
SOA | 3.32 | 1.47 | 3.11 | 3.61 | 9 | 2.55 | + | |
LWOA | 3.13 × | 2.84 | 3.11 × | 3.26 | 1 | 7.61 | − | |
MSWOA | 3.24 | 8.03 | 3.12 | 3.41 | 6 | 6.15 | + | |
DGSWOA | 3.14 | 2.39 × | 3.11 | 3.19 | 2 | |||
PSO | 6.28 | 6.52 | 5.11 | 7.75 | 5 | 3.73 | + | |
GA | 6.76 | 6.45 | 5.20 | 8.00 | 7 | 1.86 | + | |
GWO | 4.98 | 5.43 | 4.52 | 6.61 | 4 | 4.97 | + | |
WOA | 4.87 | 4.16 | 4.45 | 6.40 | 3 | 2.21 | ≈ | |
BOA | 6.67 | 1.19 | 4.50 | 1.02 | 6 | 5.59 | + | |
SOA | 8.00 | 2.12 | 4.50 | 1.12 | 9 | 6.15 | + | |
LWOA | 4.80 | 3.98 | 4.31 × | 6.61 | 2 | 3.28 | ≈ | |
MSWOA | 7.11 | 1.88 | 4.44 | 1.08 | 8 | 8.01 | + | |
DGSWOA | 4.73 × | 2.58 × | 4.34 | 5.43 × | 1 | |||
PSO | 2.12 | 3.06 | 2.11 | 2.13 | 5 | 6.91 | + | |
GA | 2.12 | 3.27 | 2.12 | 2.13 | 8 | 2.61 | + | |
GWO | 2.12 | 4.79 | 2.11 × | 2.13 | 4 | 2.02 | + | |
WOA | 2.11 | 3.80 | 2.11 | 2.12 | 2 | 3.39 | ≈ | |
BOA | 2.12 | 3.50 | 2.12 | 2.13 | 9 | 5.59 | + | |
SOA | 2.12 | 4.34 | 2.11 | 2.13 | 7 | 1.02 | + | |
LWOA | 2.12 | 3.16 | 2.11 | 2.13 | 6 | 1.02 | + | |
MSWOA | 2.12 | 3.18 | 2.11 | 2.12 | 3 | 8.71 | + | |
DGSWOA | 2.11 × | 2.88 × | 2.11 | 2.12 × | 1 | |||
PSO | 1.54 | 1.04 | 1.33 | 1.73 | 9 | 1.86 | + | |
GA | 1.32 | 1.11 | 1.00 | 1.47 | 8 | 9.31 | + | |
GWO | 1.15 | 6.89 | 9.93 | 1.25 | 3 | 2.99 | + | |
WOA | 1.17 | 5.73 × | 1.07 | 1.26 | 4 | 9.52 | + | |
BOA | 1.19 | 8.82 | 9.84 | 1.34 | 6 | 6.29 | + | |
SOA | 1.17 | 1.34 | 8.53 | 1.37 | 5 | 2.08 | + | |
LWOA | 1.15 | 9.49 | 9.28 | 1.30 | 2 | 3.84 | + | |
MSWOA | 1.20 | 1.24 | 8.71 | 1.40 | 7 | 6.08 | + | |
DGSWOA | 1.10 × | 7.40 | 8.38 × | 1.20 × | 1 |
F | Algorithm | Mean | Std | Best | Worst | Rank | p-Value | State |
---|---|---|---|---|---|---|---|---|
PSO | −3.27 | 7.25 | −4.27 | −1.65 | 8 | 1.86 | + | |
GA | −7.66 | 2.57 | −8.30 | −7.17 | 5 | 1.86 | + | |
GWO | −8.29 | 2.35 | −8.63 | −7.49 | 4 | 5.49 | ≈ | |
WOA | −8.32 | 3.22 | −8.82 | −7.35 | 3 | 8.03 | ≈ | |
BOA | −7.02 | 2.58 | −1.56 | −3.47 | 9 | 1.86 | + | |
SOA | −4.47 | 1.36 | −6.49 | −1.74 | 7 | 1.86 | + | |
LWOA | −8.65 × | 2.06 × | −8.94 | −8.15 × | 1 | 8.03 | ≈ | |
MSWOA | −6.78 | 8.85 | −8.08 | −4.28 | 6 | 3.73 | + | |
DGSWOA | −8.49 | 3.54 | −9.08 × | −7.58 | 2 | |||
PSO | 5.53 | 1.19 | 3.36 | 8.83 | 7 | 1.86 | + | |
GA | 1.96 | 6.23 | 7.79 | 3.17 | 5 | 1.86 | + | |
GWO | 1.79 | 7.22 | 8.21 | 2.91 | 4 | 7.99 | + | |
WOA | 1.11 | 5.08 | 5.40 | 2.61 | 2 | 7.67 | ≈ | |
BOA | 1.91 | 1.19 | 2.73 | 4.70 | 9 | 1.86 | + | |
SOA | 6.86 | 4.39 | 1.50 | 1.81 | 8 | 1.86 | + | |
LWOA | 1.42 | 5.04 | 6.69 | 3.09 | 3 | 2.56 | + | |
MSWOA | 4.19 | 3.95 | 6.73 | 1.82 | 6 | 3.73 | + | |
DGSWOA | 9.48 × | 2.99 × | 4.49 × | 1.65 × | 1 | |||
PSO | 4.79 | 5.37 | 3.21 | 5.82 | 6 | 1.86 | + | |
GA | 4.71 | 4.68 | 3.85 | 5.78 | 5 | 1.86 | + | |
GWO | 2.49 | 3.63 | 1.59 × | 3.35 | 2 | 5.38 | − | |
WOA | 2.84 | 3.39 | 2.11 | 3.79 | 4 | 2.62 | ≈ | |
BOA | 7.82 | 1.42 | 4.05 | 1.04 | 9 | 1.86 | + | |
SOA | 5.79 | 1.33 | 2.89 | 8.23 | 7 | 1.86 | + | |
LWOA | 2.16 × | 2.58 × | 1.67 | 2.72 × | 1 | 3.15 | − | |
MSWOA | 6.16 | 1.46 | 3.53 | 9.29 | 8 | 1.86 | + | |
DGSWOA | 2.74 | 3.35 | 1.94 | 3.57 | 3 | |||
PSO | 5.83 | 4.92 | 4.34 | 6.90 | 8 | 1.86 | + | |
GA | 5.20 | 4.21 | 4.17 | 5.87 | 7 | 1.86 | + | |
GWO | 3.68 | 3.77 | 3.22 | 4.75 | 4 | 1.35 | ≈ | |
WOA | 3.41 | 4.05 | 2.70 | 4.24 | 2 | 3.49 | ≈ | |
BOA | 5.98 | 9.22 | 3.19 | 7.60 | 9 | 9.31 | + | |
SOA | 4.65 | 1.01 | 3.11 | 6.53 | 6 | 6.92 | + | |
LWOA | 2.80 × | 2.46 × | 2.27 | 3.35 × | 1 | 4.66 | − | |
MSWOA | 3.97 | 8.90 | 2.05 × | 5.71 | 5 | 1.97 | + | |
DGSWOA | 3.51 | 4.63 | 2.49 | 4.50 | 3 | |||
PSO | 2.22 | 1.37 | 1.91 | 2.45 | 7 | 1.86 | + | |
GA | 2.56 | 1.57 | 2.26 | 2.95 | 8 | 1.86 | + | |
GWO | 1.13 | 1.12 | 8.98 | 1.34 | 4 | 1.86 | + | |
WOA | 7.47 | 9.52 | 5.45 | 9.07 | 3 | 2.80 | ≈ | |
BOA | 3.17 | 3.02 | 2.56 | 3.65 | 9 | 1.86 | + | |
SOA | 2.06 | 4.65 | 1.26 | 2.85 | 6 | 1.86 | + | |
LWOA | 5.86 × | 7.18 × | 5.15 × | 8.13 × | 1 | 6.92 | − | |
MSWOA | 1.49 | 3.47 | 8.62 | 2.08 | 5 | 1.86 | + | |
DGSWOA | 7.32 | 1.07 | 5.31 | 1.00 | 2 | |||
PSO | 8.21 | 2.37 | 4.27 | 1.33 | 7 | 1.86 | + | |
GA | 7.70 | 2.01 | 3.34 | 1.17 | 6 | 1.86 | + | |
GWO | 3.08 | 2.50 | 1.44 | 1.09 | 4 | 1.71 | ≈ | |
WOA | 2.10 × | 9.20 | 1.44 | 5.84 | 1 | 2.99 | ≈ | |
BOA | 2.21 | 4.12 | 1.42 | 2.86 | 9 | 1.86 | + | |
SOA | 1.50 | 7.25 | 3.50 | 2.97 | 8 | 1.86 | + | |
LWOA | 2.33 | 4.74 × | 1.59 | 3.13 × | 3 | 1.09 | ≈ | |
MSWOA | 6.57 | 4.90 | 3.69 | 1.78 | 5 | 1.86 | + | |
DGSWOA | 2.12 | 6.44 | 1.38 × | 4.80 | 2 | |||
PSO | 1.97 | 4.53 | 1.21 | 2.86 | 7 | 1.86 | + | |
GA | 1.25 | 3.90 | 3.44 | 2.10 | 5 | 1.86 | + | |
GWO | −3.07 | 2.09 | −7.03 × | 3.62 | 2 | 8.55 | ≈ | |
WOA | −2.29 | 2.39 | −6.18 | 5.34 | 4 | 3.09 | ≈ | |
BOA | 3.26 | 6.69 | 1.99 | 4.65 | 9 | 1.86 | + | |
SOA | 2.42 | 8.61 | 2.25 | 4.12 | 8 | 1.86 | + | |
LWOA | −3.83 × | 1.82 × | −6.34 | 2.53 × | 1 | 6.36 | ≈ | |
MSWOA | 1.57 | 7.76 | 1.60 | 3.52 | 6 | 1.86 | + | |
DGSWOA | −2.76 | 2.19 | −6.49 | 2.68 | 3 | |||
PSO | 3.35 | 9.39 | 1.51 | 5.31 | 8 | 1.86 | + | |
GA | 9.86 | 3.43 | 3.03 | 1.59 | 5 | 1.86 | + | |
GWO | 1.75 | 8.05 | 1.01 | 3.49 | 4 | 1.46 | + | |
WOA | 1.42 | 8.26 | 1.12 | 3.52 | 3 | 3.84 | + | |
BOA | 3.85 | 1.01 | 2.34 | 5.86 | 9 | 1.86 | + | |
SOA | 1.98 | 8.20 | 4.12 | 3.82 | 7 | 1.86 | + | |
LWOA | 8.23 × | 4.35 × | 1.90 | 1.77 × | 1 | 2.05 | ≈ | |
MSWOA | 1.64 | 7.42 | 1.61 | 2.89 | 6 | 1.86 | + | |
DGSWOA | 1.02 | 6.42 | −6.77 × | 2.43 | 2 | |||
PSO | 2.82 | 7.58 | 9.46 | 4.20 | 9 | 1.86 | + | |
GA | 1.24 | 4.98 | 4.96 | 2.50 | 8 | 1.86 | + | |
GWO | −2.83 × | 1.61 | −3.19 × | −2.57 × | 1 | 4.77 | ≈ | |
WOA | −2.81 | 1.49 | −3.17 | −2.52 | 2 | 7.61 | ≈ | |
BOA | −6.29 | 5.91 | −7.83 | −4.82 | 6 | 1.86 | + | |
SOA | −2.38 | 1.54 × | −2.43 | −2.36 | 5 | 1.86 | + | |
LWOA | 5.58 | 1.27 | −1.95 | 2.93 | 7 | 1.86 | + | |
MSWOA | −2.41 | 3.11 | −2.50 | −2.37 | 4 | 1.86 | + | |
DGSWOA | −2.79 | 1.39 | −3.13 | −2.55 | 3 | |||
PSO | 5.81 | 1.62 | 2.68 | 9.24 | 6 | 1.86 | + | |
GA | 2.98 | 1.07 | 1.10 | 4.85 | 5 | 1.86 | + | |
GWO | 7.37 | 3.61 | 2.61 | 1.93 | 3 | 1.20 | + | |
WOA | 6.33 | 4.28 | 1.35 × | 1.94 | 2 | 7.46 | ≈ | |
BOA | 3.33 | 1.38 | 1.55 | 6.61 | 9 | 1.86 | + | |
SOA | 1.52 | 9.03 | 1.59 | 3.95 | 8 | 1.86 | + | |
LWOA | 1.48 | 5.41 | 4.45 | 2.77 | 4 | 5.59 | + | |
MSWOA | 6.22 | 6.21 | 1.03 | 3.10 | 7 | 1.86 | + | |
DGSWOA | 5.37 × | 1.90 × | 1.57 | 9.30 × | 1 | |||
PSO | 5.56 | 3.07 | −4.83 | 1.19 | 5 | 5.72 | + | |
GA | −1.34 × | 1.32 × | −3.37 | 1.53 × | 1 | 3.13 | − | |
GWO | −1.81 | 1.86 | −2.89 | 5.49 | 2 | 8.79 | ≈ | |
WOA | 1.30 | 2.08 | −2.65 | 6.53 | 4 | 5.98 | ≈ | |
BOA | 6.85 | 3.02 | −1.80 | 1.68 | 9 | 1.86 | + | |
SOA | 2.88 | 1.21 | 5.37 | 4.19 | 8 | 1.86 | + | |
LWOA | 7.76 | 3.42 | −3.27 | 1.40 | 6 | 9.31 | + | |
MSWOA | 1.29 | 1.13 | 4.71 | 3.52 | 7 | 5.59 | + | |
DGSWOA | 8.72 | 2.38 | −3.42 × | 6.40 | 3 | |||
PSO | 7.23 | 1.24 | 4.22 | 8.99 | 7 | 1.86 | + | |
GA | 5.00 | 9.81 | 2.44 | 6.43 | 6 | 1.86 | + | |
GWO | 1.06 | 5.09 | 3.21 | 2.69 | 4 | 1.64 | + | |
WOA | 8.30 | 4.23 | 9.57 × | 1.87 | 3 | 5.98 | ≈ | |
BOA | 9.21 | 1.49 | 6.10 | 1.30 | 9 | 1.86 | + | |
SOA | 7.49 | 1.35 | 5.16 | 1.07 | 8 | 1.86 | + | |
LWOA | 4.95 × | 1.54 × | 2.39 | 8.65 × | 1 | 4.34 | − | |
MSWOA | 4.19 | 1.56 | 1.75 | 7.16 | 5 | 1.86 | + | |
DGSWOA | 7.68 | 4.05 | 2.10 | 1.73 | 2 | |||
PSO | 1.30 | 9.36 | 1.10 | 1.47 | 9 | 1.86 | + | |
GA | 1.07 | 9.45 | 8.75 | 1.20 | 6 | 1.86 | + | |
GWO | 5.05 | 7.40 | 3.56 | 6.24 | 3 | 7.30 | + | |
WOA | 5.29 | 1.32 | 2.20 | 8.31 | 4 | 4.18 | + | |
BOA | 1.25 | 6.02 × | 1.13 | 1.36 | 8 | 1.86 | + | |
SOA | 1.15 | 8.13 | 9.80 | 1.33 | 7 | 1.86 | + | |
LWOA | 3.91 × | 7.91 | 2.58 | 5.79 × | 1 | 5.70 | ≈ | |
MSWOA | 9.18 | 1.48 | 6.44 | 1.18 | 5 | 1.86 | + | |
DGSWOA | 4.04 | 1.24 | 1.54 × | 7.18 | 2 | |||
PSO | −3.98 | 2.89 | −4.62 | −3.56 | 8 | 1.86 | + | |
GA | −5.03 | 1.01 | −5.25 | −4.83 | 5 | 1.86 | + | |
GWO | −5.38 | 1.24 | −5.60 | −5.16 | 3 | 3.71 | ≈ | |
WOA | −5.36 | 1.41 | −5.59 | −5.01 | 4 | 7.32 | ≈ | |
BOA | −1.45 | 5.26 | −2.66 | −8.22 | 9 | 1.86 | + | |
SOA | −4.19 | 3.68 | −4.83 | −3.40 | 7 | 1.86 | + | |
LWOA | −5.55 × | 5.41 × | −5.64 | −5.43 × | 1 | 4.42 | − | |
MSWOA | −4.77 | 2.67 | −5.24 | −4.22 | 6 | 1.86 | + | |
DGSWOA | −5.41 | 1.27 | −5.66 × | −5.13 | 2 | |||
PSO | 3.86 | 2.84 | 3.28 | 4.45 | 7 | 1.86 | + | |
GA | 3.07 | 2.55 | 2.18 | 3.58 | 5 | 1.86 | + | |
GWO | 1.50 × | 2.08 | 1.03 × | 2.03 × | 1 | 1.22 | − | |
WOA | 1.73 | 2.35 | 1.32 | 2.27 | 3 | 2.21 | ≈ | |
BOA | 3.92 | 3.86 | 3.21 | 4.90 | 9 | 1.86 | + | |
SOA | 3.86 | 7.12 | 2.20 | 4.91 | 8 | 3.73 | + | |
LWOA | 1.69 | 2.00 × | 1.39 | 2.33 | 2 | 4.05 | − | |
MSWOA | 3.80 | 7.29 | 2.69 | 5.38 | 6 | 1.86 | + | |
DGSWOA | 1.80 | 2.18 | 1.35 | 2.28 | 4 | |||
PSO | −2.39 | 2.84 | −2.47 | −2.35 | 6 | 1.86 | + | |
GA | −2.38 | 2.45 | −2.45 | −2.35 | 7 | 1.86 | + | |
GWO | −2.47 | 3.66 | −2.56 × | −2.36 | 3 | 2.77 | + | |
WOA | −2.47 | 3.19 | −2.56 | −2.41 | 2 | 3.27 | + | |
BOA | −2.19 | 6.82 | −2.32 | −2.04 | 9 | 1.86 | + | |
SOA | −2.38 | 5.97 | −2.47 | −2.24 | 8 | 3.54 | + | |
LWOA | −2.39 | 2.42 × | −2.45 | −2.35 | 5 | 3.73 | + | |
MSWOA | −2.44 | 4.35 | −2.52 | −2.36 | 4 | 2.32 | + | |
DGSWOA | −2.49 × | 2.83 | −2.53 | −2.43 × | 1 | |||
PSO | −3.05 | 4.74 × | −3.15 | −2.96 | 8 | 1.86 | + | |
GA | −3.28 | 5.36 | −3.40 | −3.18 | 5 | 4.42 | + | |
GWO | −3.47 × | 7.32 | −3.60 × | −3.32 × | 1 | 1.37 | − | |
WOA | −3.39 | 7.20 | −3.53 | −3.24 | 3 | 4.90 | ≈ | |
BOA | −2.39 | 1.83 | −2.82 | −2.12 | 9 | 1.86 | + | |
SOA | −3.16 | 1.01 | −3.34 | −2.93 | 7 | 3.73 | + | |
LWOA | −3.45 | 9.38 | −3.59 | −3.25 | 2 | 5.55 | − | |
MSWOA | −3.17 | 1.08 | −3.38 | −3.00 | 6 | 6.15 | + | |
DGSWOA | −3.38 | 6.59 | −3.48 | −3.23 | 4 | |||
PSO | −8.34 | 2.61 | −1.57 | −3.63 | 8 | 1.86 | + | |
GA | −1.80 | 2.34 | −2.48 | −1.42 | 5 | 3.45 | + | |
GWO | −2.43 × | 2.01 | −2.86 | −1.95 × | 1 | 1.68 | − | |
WOA | −2.22 | 2.64 | −2.86 | −1.67 | 3 | 1.24 | ≈ | |
BOA | −4.97 | 1.84 × | −9.34 | −1.90 | 9 | 1.86 | + | |
SOA | −1.10 | 4.77 | −2.08 | −3.86 | 6 | 9.31 | + | |
LWOA | −2.32 | 3.35 | −3.09 × | −1.47 | 2 | 1.06 | − | |
MSWOA | −9.35 | 3.42 | −1.66 | −3.00 | 7 | 1.86 | + | |
DGSWOA | −2.09 | 2.51 | −2.54 | −1.41 | 4 | |||
PSO | 5.32 | 1.25 | 4.96 | 5.51 | 9 | 1.86 | + | |
GA | 4.76 | 6.71 | 4.62 | 4.88 | 8 | 1.86 | + | |
GWO | 4.26 | 1.15 | 4.07 | 4.44 | 4 | 3.73 | + | |
WOA | 4.28 | 8.48 | 4.07 | 4.42 | 5 | 1.86 | + | |
BOA | 4.46 | 5.07 | 4.34 | 4.54 | 6 | 1.86 | + | |
SOA | 4.07 | 2.16 × | 4.07 | 4.07 | 3 | 1.86 | + | |
LWOA | 4.66 | 5.54 | 4.54 | 4.76 | 7 | 1.86 | + | |
MSWOA | 4.07 | 3.40 | 4.07 | 4.07 | 2 | 3.73 | + | |
DGSWOA | 4.07 × | 1.35 | 4.07 × | 4.07 × | 1 | |||
PSO | 1.26 | 3.30 | 5.85 | 1.75 | 9 | 1.86 | + | |
GA | 3.63 | 1.69 | 1.87 | 8.74 | 5 | 3.73 | + | |
GWO | 2.06 | 5.43 | 1.85 × | 4.58 | 3 | 1.71 | ≈ | |
WOA | 2.77 | 2.45 | 1.86 | 1.26 | 4 | 5.43 | ≈ | |
BOA | 4.75 | 2.34 | 1.09 | 9.58 | 8 | 1.86 | + | |
SOA | 3.87 | 2.80 | 1.86 | 1.12 | 7 | 3.73 | + | |
LWOA | 1.88 × | 5.81 × | 1.86 | 2.19 | 1 | 2.21 | ≈ | |
MSWOA | 2.51 | 2.57 | 1.86 | 1.02 | 6 | 3.73 | + | |
DGSWOA | 1.89 | 6.58 | 1.86 | 2.19 × | 2 | |||
PSO | 3.71 | 4.41 × | 3.58 | 3.78 | 8 | 1.86 | + | |
GA | 3.69 | 5.53 | 3.54 | 3.77 | 7 | 1.86 | + | |
GWO | 3.27 | 8.80 | 3.15 | 3.55 | 4 | 9.61 | ≈ | |
WOA | 3.25 | 1.09 | 3.13 × | 3.57 | 3 | 9.84 | ≈ | |
BOA | 3.54 | 1.07 | 3.32 | 3.79 | 5 | 1.86 | + | |
SOA | 3.75 | 1.02 | 3.47 | 3.85 | 9 | 1.86 | + | |
LWOA | 3.23 × | 6.75 | 3.14 | 3.44 | 1 | 7.00 | ≈ | |
MSWOA | 3.60 | 1.26 | 3.33 | 3.79 | 6 | 3.73 | + | |
DGSWOA | 3.23 | 4.53 | 3.15 | 3.34 × | 2 | |||
PSO | 1.12 | 3.77 × | 9.71 | 1.16 | 8 | 1.86 | + | |
GA | 1.06 | 7.33 | 8.14 | 1.15 | 7 | 1.86 | + | |
GWO | 6.50 | 1.76 | 4.54 | 1.05 | 4 | 2.93 | + | |
WOA | 6.01 | 1.20 | 4.91 | 8.98 | 2 | 1.05 | ≈ | |
BOA | 9.29 | 1.21 | 6.53 | 1.13 | 6 | 1.86 | + | |
SOA | 1.16 | 5.45 | 9.68 | 1.24 | 9 | 1.86 | + | |
LWOA | 6.10 | 1.67 | 4.69 | 9.94 | 3 | 1.35 | ≈ | |
MSWOA | 9.16 | 1.70 | 6.38 | 1.18 | 5 | 3.73 | + | |
DGSWOA | 5.43 × | 7.97 | 4.35 × | 6.94 × | 1 | |||
PSO | 2.13 | 3.50 | 2.12 | 2.14 | 6 | 6.15 | + | |
GA | 2.13 | 4.62 | 2.12 | 2.14 | 5 | 2.55 | + | |
GWO | 2.12 | 6.49 | 2.11 | 2.13 | 3 | 2.21 | + | |
WOA | 2.12 | 3.73 | 2.11 | 2.13 × | 2 | 9.52 | + | |
BOA | 2.13 | 5.21 | 2.12 | 2.14 | 9 | 3.73 | + | |
SOA | 2.13 | 2.98 × | 2.12 | 2.13 | 7 | 3.73 | + | |
LWOA | 2.13 | 3.19 | 2.12 | 2.14 | 8 | 3.73 | + | |
MSWOA | 2.12 | 3.68 | 2.11 | 2.13 | 4 | 1.86 | + | |
DGSWOA | 2.12 × | 4.51 | 2.11 × | 2.13 | 1 | |||
PSO | 4.06 | 2.45 | 3.54 | 4.54 | 9 | 1.86 | + | |
GA | 3.00 | 2.05 | 2.51 | 3.33 | 8 | 1.86 | + | |
GWO | 2.33 | 1.25 | 2.04 | 2.55 | 2 | 8.71 | + | |
WOA | 2.33 | 1.00 × | 2.11 | 2.55 | 3 | 9.30 | + | |
BOA | 2.47 | 1.43 | 2.15 | 2.70 | 6 | 8.01 | + | |
SOA | 2.57 | 1.51 | 2.22 | 2.82 | 7 | 9.31 | + | |
LWOA | 2.46 | 1.47 | 2.19 | 2.71 | 5 | 9.98 | + | |
MSWOA | 2.43 | 1.34 | 2.16 | 2.66 | 4 | 2.35 | + | |
DGSWOA | 2.25 × | 1.06 | 2.02 × | 2.41 × | 1 |
F | Algorithm | Mean | Std | Best | Worst | Rank | p-Value | State |
---|---|---|---|---|---|---|---|---|
PSO | 1.27 | 1.54 | 1.02 | 1.60 | 9 | 1.86 | + | |
GA | 6.47 | 1.48 | 2.67 | 8.55 | 6 | 1.86 | + | |
GWO | −4.59 | 9.33 | −6.74 | −2.50 | 3 | 6.99 | ≈ | |
WOA | −4.41 | 1.24 | −6.11 | −1.79 | 4 | 6.19 | + | |
BOA | 9.57 | 9.23 | 7.39 | 1.10 | 8 | 1.86 | + | |
SOA | 7.11 | 1.62 | 2.83 | 9.70 | 7 | 1.86 | + | |
LWOA | −5.88 × | 6.92 × | −7.26 | −4.52 × | 1 | 5.23 | ≈ | |
MSWOA | 3.38 | 1.87 | −1.09 | 6.74 | 5 | 1.86 | + | |
DGSWOA | −5.13 | 1.45 | −7.29 × | −1.58 | 2 | |||
PSO | 3.81 | 5.86 | 2.55 | 5.47 | 7 | 1.86 | + | |
GA | 2.97 | 5.25 | 1.70 | 3.91 | 6 | 1.86 | + | |
GWO | 8.32 | 3.92 | 4.63 | 2.73 | 3 | 3.27 | + | |
WOA | 6.76 | 2.05 | 3.60 | 1.25 | 2 | 7.77 | ≈ | |
BOA | 8.86 | 2.15 | 5.08 | 1.57 | 9 | 1.86 | + | |
SOA | 4.93 | 2.42 | 1.22 | 1.08 | 8 | 1.86 | + | |
LWOA | 8.56 | 2.83 | 3.49 | 1.30 | 4 | 2.77 | + | |
MSWOA | 2.94 | 1.67 | 7.99 | 6.89 | 5 | 1.86 | + | |
DGSWOA | 6.74 × | 1.87 × | 2.78 × | 1.09 × | 1 | |||
PSO | 1.42 | 9.88 | 1.23 | 1.62 | 9 | 1.86 | + | |
GA | 1.14 | 6.80 | 1.02 | 1.27 | 5 | 1.86 | + | |
GWO | 6.23 × | 4.68 × | 5.34 | 7.32 × | 1 | 3.05 | − | |
WOA | 7.20 | 5.58 | 6.19 | 8.37 | 4 | 2.37 | ≈ | |
BOA | 1.20 | 5.47 | 1.08 | 1.29 | 7 | 1.86 | + | |
SOA | 1.19 | 9.97 | 9.89 | 1.39 | 6 | 1.86 | + | |
LWOA | 6.49 | 7.51 | 5.27 × | 8.00 | 2 | 1.55 | − | |
MSWOA | 1.20 | 9.69 | 9.97 | 1.36 | 8 | 1.86 | + | |
DGSWOA | 6.96 | 6.12 | 5.93 | 8.23 | 3 | |||
PSO | 1.71 | 1.15 | 1.48 | 1.98 | 9 | 1.86 | + | |
GA | 1.16 | 4.81 | 1.03 | 1.24 | 8 | 1.86 | + | |
GWO | 7.13 × | 3.87 × | 6.29 | 8.00 × | 1 | 9.22 | − | |
WOA | 7.69 | 4.95 | 6.54 | 8.56 | 2 | 1.24 | ≈ | |
BOA | 1.06 | 3.94 | 9.62 | 1.14 | 7 | 1.86 | + | |
SOA | 1.02 | 7.90 | 8.48 | 1.14 | 6 | 1.86 | + | |
LWOA | 8.33 | 7.26 | 6.52 | 1.00 | 4 | 7.61 | + | |
MSWOA | 9.65 | 7.54 | 8.02 | 1.10 | 5 | 2.61 | + | |
DGSWOA | 7.85 | 6.59 | 5.95 × | 8.97 | 3 | |||
PSO | 5.21 | 2.10 × | 4.60 | 5.57 | 7 | 1.86 | + | |
GA | 5.48 | 3.07 | 4.57 | 5.99 | 8 | 1.86 | + | |
GWO | 3.07 | 2.66 | 2.49 | 3.56 | 4 | 1.86 | + | |
WOA | 1.99 | 2.88 | 1.45 | 2.46 | 2 | 2.89 | ≈ | |
BOA | 6.43 | 4.77 | 5.16 | 7.14 | 9 | 1.86 | + | |
SOA | 4.63 | 7.63 | 2.42 | 6.50 | 6 | 1.86 | + | |
LWOA | 1.36 × | 3.38 | 7.60 × | 2.03 × | 1 | 1.30 | − | |
MSWOA | 4.02 | 9.84 | 2.15 | 6.55 | 5 | 1.86 | + | |
DGSWOA | 2.07 | 3.36 | 1.45 | 2.73 | 3 | |||
PSO | 3.15 | 3.19 | 2.48 | 3.90 | 7 | 1.86 | + | |
GA | 2.69 | 4.09 | 1.93 | 3.30 | 6 | 1.86 | + | |
GWO | 4.11 × | 6.23 | 4.68 | 3.15 | 1 | 8.24 | ≈ | |
WOA | 6.21 | 8.12 | 4.47 | 3.42 | 4 | 6.12 | ≈ | |
BOA | 4.73 | 8.75 | 3.24 | 5.78 | 9 | 1.86 | + | |
SOA | 4.05 | 8.85 | 2.41 | 5.79 | 8 | 1.86 | + | |
LWOA | 4.45 | 3.99 × | 4.83 | 1.48 × | 2 | 9.35 | ≈ | |
MSWOA | 2.11 | 8.00 | 5.45 | 3.56 | 5 | 1.86 | + | |
DGSWOA | 4.90 | 7.25 | 4.31 × | 3.42 | 3 | |||
PSO | 8.64 | 9.04 | 6.24 | 1.02 | 9 | 1.86 | + | |
GA | 5.10 | 5.94 | 3.98 | 6.54 | 7 | 1.86 | + | |
GWO | 6.82 × | 2.85 × | 1.83 | 1.32 × | 1 | 4.03 | − | |
WOA | 9.21 | 3.77 | 2.93 | 1.91 | 2 | 9.68 | ≈ | |
BOA | 6.00 | 7.30 | 3.65 | 7.06 | 8 | 1.86 | + | |
SOA | 4.98 | 1.10 | 2.69 | 7.31 | 6 | 1.86 | + | |
LWOA | 1.24 | 3.74 | 4.14 | 2.00 | 4 | 2.56 | + | |
MSWOA | 4.65 | 1.06 | 2.68 | 6.92 | 5 | 1.86 | + | |
DGSWOA | 9.32 | 4.13 | 1.00 × | 1.96 | 3 | |||
PSO | 2.75 | 3.28 | 2.00 | 3.32 | 9 | 1.86 | + | |
GA | 1.09 | 1.52 | 6.76 | 1.45 | 7 | 1.86 | + | |
GWO | 1.44 | 5.23 | 9.21 | 2.92 | 4 | 6.08 | + | |
WOA | 8.63 × | 3.77 × | 3.89 | 1.68 × | 1 | 6.85 | ≈ | |
BOA | 1.30 | 1.46 | 9.79 | 1.60 | 8 | 1.86 | + | |
SOA | 5.77 | 1.20 | 3.16 | 7.95 | 6 | 1.86 | + | |
LWOA | 1.27 | 5.33 | 4.59 | 2.51 | 3 | 4.27 | + | |
MSWOA | 5.65 | 1.21 | 2.63 | 7.75 | 5 | 1.86 | + | |
DGSWOA | 9.43 | 5.42 | 3.58 × | 2.54 | 2 | |||
PSO | 1.51 | 2.14 | 1.07 | 1.92 | 9 | 1.86 | + | |
GA | 1.11 | 2.37 | 6.69 | 1.56 | 8 | 1.86 | + | |
GWO | −1.35 × | 1.52 | −1.72 × | −1.13 | 1 | 2.48 | − | |
WOA | −1.27 | 1.17 | −1.53 | −1.14 | 3 | 6.55 | ≈ | |
BOA | −2.24 | 2.32 | −2.74 | −1.89 | 6 | 1.86 | + | |
SOA | −1.07 | 5.59 × | −1.08 | −1.06 | 5 | 1.86 | + | |
LWOA | 1.14 | 6.17 | 4.31 | 2.59 | 7 | 1.86 | + | |
MSWOA | −1.08 | 1.54 | −1.12 | −1.06 | 4 | 1.86 | + | |
DGSWOA | −1.28 | 9.74 | −1.67 | −1.14 × | 2 | |||
PSO | 2.63 | 4.42 | 1.62 | 3.71 | 8 | 1.86 | + | |
GA | 1.47 | 3.22 | 8.23 | 2.10 | 6 | 1.86 | + | |
GWO | 2.88 | 9.72 | 1.40 | 5.68 | 3 | 2.32 | + | |
WOA | 2.15 | 7.19 × | 1.13 | 4.65 × | 2 | 2.13 | ≈ | |
BOA | 3.13 | 9.09 | 1.29 | 4.90 | 9 | 1.86 | + | |
SOA | 2.06 | 8.06 | 7.39 | 3.59 | 7 | 1.86 | + | |
LWOA | 3.78 | 1.11 | 1.90 | 6.04 | 4 | 1.64 | + | |
MSWOA | 1.08 | 4.09 | 6.15 | 2.22 | 5 | 1.86 | + | |
DGSWOA | 1.89 × | 9.49 | 6.70 × | 4.86 | 1 | |||
PSO | 2.40 | 4.26 | 1.49 | 3.44 | 5 | 1.86 | + | |
GA | 1.21 | 2.52 × | 4.42 × | 1.66 | 4 | 1.14 | ≈ | |
GWO | 9.81 × | 2.68 | 4.71 | 1.59 × | 1 | 1.71 | ≈ | |
WOA | 1.07 | 3.53 | 4.63 | 1.74 | 2 | 8.08 | ≈ | |
BOA | 1.72 | 3.43 | 1.14 | 1.43 | 9 | 1.30 | + | |
SOA | 4.17 | 1.66 | 1.16 | 7.87 | 8 | 1.86 | + | |
LWOA | 2.84 | 5.71 | 1.70 | 3.86 | 7 | 1.86 | + | |
MSWOA | 2.64 | 9.54 | 1.14 | 3.89 | 6 | 1.30 | + | |
DGSWOA | 1.08 | 3.28 | 5.14 | 1.77 | 3 | |||
PSO | 4.33 | 6.64 | 3.14 | 5.60 | 7 | 1.86 | + | |
GA | 2.74 | 3.69 | 2.01 | 3.59 | 5 | 1.86 | + | |
GWO | 7.74 | 1.84 | 4.09 | 1.14 | 3 | 8.03 | ≈ | |
WOA | 8.11 | 2.58 | 4.07 | 1.42 | 4 | 1.00 | ≈ | |
BOA | 8.01 | 2.41 | 3.79 | 1.21 | 9 | 1.86 | + | |
SOA | 5.66 | 1.79 | 2.34 | 9.59 | 8 | 1.86 | + | |
LWOA | 4.66 × | 1.45 × | 2.55 × | 8.54 × | 1 | 7.06 | − | |
MSWOA | 3.59 | 9.79 | 1.75 | 5.65 | 6 | 1.86 | + | |
DGSWOA | 6.95 | 2.11 | 3.07 | 1.24 | 2 | |||
PSO | 2.66 | 1.27 | 2.23 | 2.85 | 8 | 1.86 | + | |
GA | 2.40 | 1.10 | 2.14 | 2.63 | 6 | 1.86 | + | |
GWO | 1.24 | 1.01 × | 1.05 | 1.45 | 4 | 1.82 | + | |
WOA | 1.22 | 1.26 | 8.05 | 1.45 | 3 | 2.37 | + | |
BOA | 2.70 | 1.32 | 2.39 | 2.98 | 9 | 1.86 | + | |
SOA | 2.49 | 2.04 | 1.86 | 2.85 | 7 | 1.86 | + | |
LWOA | 9.62 × | 1.09 | 7.39 × | 1.18 × | 1 | 1.13 | − | |
MSWOA | 1.93 | 1.76 | 1.58 | 2.37 | 5 | 1.86 | + | |
DGSWOA | 1.07 | 1.24 | 8.61 | 1.27 | 2 | |||
PSO | −9.04 | 4.37 | −1.87 | −1.43 | 8 | 1.86 | + | |
GA | −3.86 | 2.28 | −4.37 | −3.36 | 5 | 1.86 | + | |
GWO | −4.55 | 2.25 | −4.89 | −4.00 | 3 | 5.70 | ≈ | |
WOA | −4.48 | 1.78 × | −4.90 | −4.14 | 4 | 7.11 | + | |
BOA | 6.74 | 1.44 | −6.62 | 3.83 | 9 | 1.86 | + | |
SOA | −9.64 | 1.24 | −3.83 | 1.33 | 7 | 1.86 | + | |
LWOA | −4.63 × | 2.68 | −5.15 × | −4.08 | 1 | 6.70 | ≈ | |
MSWOA | −2.01 | 9.05 | −3.70 | −3.14 | 6 | 1.86 | + | |
DGSWOA | −4.60 | 1.84 | −4.96 | −4.23 × | 2 | |||
PSO | 1.26 | 8.30 | 1.06 | 1.38 | 9 | 1.86 | + | |
GA | 9.70 | 7.30 | 7.69 | 1.07 | 5 | 1.86 | + | |
GWO | 5.16 × | 4.89 | 4.01 × | 5.93 × | 1 | 1.30 | − | |
WOA | 6.14 | 6.71 | 4.89 | 8.06 | 3 | 2.77 | − | |
BOA | 9.92 | 4.77 × | 8.82 | 1.07 | 6 | 1.86 | + | |
SOA | 10.00 | 1.02 | 8.33 | 1.18 | 7 | 1.86 | + | |
LWOA | 5.67 | 7.67 | 4.51 | 7.25 | 2 | 3.79 | − | |
MSWOA | 1.02 | 9.71 | 7.76 | 1.17 | 8 | 1.86 | + | |
DGSWOA | 6.48 | 4.94 | 5.53 | 7.33 | 4 | |||
PSO | −2.27 | 2.07 | −2.31 | −2.23 | 6 | 1.86 | + | |
GA | −2.26 | 1.95 × | −2.30 | −2.23 | 7 | 1.86 | + | |
GWO | −2.39 | 3.91 | −2.46 | −2.33 | 3 | 4.16 | ≈ | |
WOA | −2.40 | 3.96 | −2.49 × | −2.33 | 2 | 9.84 | ≈ | |
BOA | −2.07 | 5.49 | −2.18 | −1.89 | 9 | 1.86 | + | |
SOA | −2.22 | 5.34 | −2.33 | −2.10 | 8 | 1.86 | + | |
LWOA | −2.30 | 2.48 | −2.37 | −2.26 | 5 | 9.31 | + | |
MSWOA | −2.33 | 4.29 | −2.43 | −2.25 | 4 | 3.24 | + | |
DGSWOA | −2.40 × | 3.40 | −2.48 | −2.33 × | 1 | |||
PSO | −2.55 | 9.47 | −2.87 | −2.41 | 8 | 1.86 | + | |
GA | −3.03 | 6.32 | −3.16 | −2.91 | 5 | 3.73 | + | |
GWO | −3.30 × | 6.98 | −3.47 × | −3.16 × | 1 | 4.97 | − | |
WOA | −3.17 | 4.92 × | −3.27 | −3.07 | 3 | 2.45 | ≈ | |
BOA | −1.43 | 4.14 | −2.30 | −7.21 | 9 | 1.86 | + | |
SOA | −2.62 | 1.70 | −2.90 | −2.24 | 7 | 1.86 | + | |
LWOA | −3.17 | 1.13 | −3.44 | −2.95 | 4 | 6.12 | ≈ | |
MSWOA | −2.68 | 1.75 | −3.03 | −2.19 | 6 | 1.86 | + | |
DGSWOA | −3.19 | 7.50 | −3.40 | −3.06 | 2 | |||
PSO | 1.12 | 3.91 | 2.38 | 1.91 | 8 | 1.86 | + | |
GA | −2.17 | 3.60 | −9.85 | 3.51 | 5 | 1.86 | + | |
GWO | −1.93 × | 2.93 × | −2.44 × | −1.46 × | 1 | 1.37 | − | |
WOA | −1.50 | 3.43 | −2.11 | −8.29 | 4 | 6.41 | ≈ | |
BOA | 1.14 | 5.96 | −5.60 | 2.36 | 9 | 1.86 | + | |
SOA | 3.73 | 7.55 | −9.24 | 1.93 | 6 | 1.86 | + | |
LWOA | −1.52 | 3.34 | −1.99 | −7.84 | 3 | 8.39 | ≈ | |
MSWOA | 5.26 | 7.59 | −1.13 | 1.97 | 7 | 1.86 | + | |
DGSWOA | −1.53 | 3.98 | −2.18 | −6.81 | 2 | |||
PSO | 5.98 | 1.67 | 5.57 | 6.33 | 9 | 1.86 | + | |
GA | 5.00 | 4.89 | 4.84 | 5.06 | 8 | 1.86 | + | |
GWO | 4.42 | 9.23 | 4.07 × | 4.53 | 4 | 3.73 | + | |
WOA | 4.43 | 9.53 | 4.07 | 4.54 | 5 | 1.86 | + | |
BOA | 4.62 | 4.71 | 4.50 | 4.68 | 6 | 1.86 | + | |
SOA | 4.07 | 4.60 × | 4.07 | 4.07 | 3 | 1.86 | + | |
LWOA | 4.80 | 5.67 | 4.62 | 4.91 | 7 | 1.86 | + | |
MSWOA | 4.07 | 6.57 | 4.07 | 4.07 | 2 | 3.54 | + | |
DGSWOA | 4.07 × | 1.92 | 4.07 | 4.07 × | 1 | |||
PSO | 6.79 | 1.02 | 4.71 | 8.38 | 9 | 1.86 | + | |
GA | 1.39 | 4.51 | 6.27 | 2.52 | 7 | 1.86 | + | |
GWO | 1.62 | 8.23 × | 2.89 | 3.90 | 3 | 1.64 | + | |
WOA | 2.02 | 1.34 | 3.05 | 6.44 | 4 | 2.02 | + | |
BOA | 1.75 | 5.38 | 6.86 | 2.90 | 8 | 1.86 | + | |
SOA | 1.25 | 4.41 | 2.28 | 2.08 | 6 | 3.73 | + | |
LWOA | 1.51 | 9.12 | 1.93 × | 3.78 × | 2 | 9.19 | ≈ | |
MSWOA | 9.93 | 4.78 | 1.84 | 2.15 | 5 | 1.86 | + | |
DGSWOA | 1.10 × | 9.54 | 2.17 | 3.88 | 1 | |||
PSO | 3.89 | 1.82 | 3.85 | 3.91 | 9 | 1.86 | + | |
GA | 3.87 | 1.38 × | 3.83 | 3.90 | 7 | 1.86 | + | |
GWO | 3.52 | 1.13 | 3.31 | 3.74 | 3 | 4.52 | ≈ | |
WOA | 3.53 | 1.29 | 3.34 | 3.78 | 4 | 5.84 | ≈ | |
BOA | 3.85 | 1.78 | 3.81 | 3.89 | 5 | 1.86 | + | |
SOA | 3.89 | 2.04 | 3.83 | 3.91 | 8 | 1.86 | + | |
LWOA | 3.44 × | 1.13 | 3.31 | 3.74 × | 1 | 4.73 | − | |
MSWOA | 3.85 | 2.32 | 3.80 | 3.90 | 6 | 1.86 | + | |
DGSWOA | 3.50 | 1.41 | 3.21 × | 3.77 | 2 | |||
PSO | 1.22 | 1.70 | 1.17 | 1.24 | 9 | 1.86 | + | |
GA | 1.19 | 1.63 | 1.15 | 1.22 | 6 | 1.86 | + | |
GWO | 7.83 | 1.29 | 6.11 | 1.15 | 4 | 2.80 | ≈ | |
WOA | 7.72 | 1.16 | 5.66 | 1.02 | 3 | 1.71 | ≈ | |
BOA | 1.20 | 1.88 | 1.16 | 1.24 | 8 | 1.86 | + | |
SOA | 1.20 | 1.41 × | 1.17 | 1.23 | 7 | 1.86 | + | |
LWOA | 6.73 × | 8.87 | 5.43 × | 9.86 × | 1 | 1.75 | − | |
MSWOA | 1.17 | 3.21 | 1.09 | 1.23 | 5 | 1.86 | + | |
DGSWOA | 7.39 | 1.32 | 5.56 | 1.03 | 2 | |||
PSO | 2.14 | 3.61 × | 2.14 | 2.15 | 6 | 1.86 | + | |
GA | 2.14 | 4.56 | 2.13 | 2.15 | 5 | 1.86 | + | |
GWO | 2.13 | 6.55 | 2.12 | 2.14 | 2 | 5.29 | ≈ | |
WOA | 2.14 | 7.57 | 2.12 | 2.14 | 4 | 1.46 | + | |
BOA | 2.15 | 4.24 | 2.14 | 2.16 | 8 | 3.73 | + | |
SOA | 2.15 | 5.55 | 2.14 | 2.16 | 9 | 1.86 | + | |
LWOA | 2.14 | 4.64 | 2.13 | 2.15 | 7 | 3.73 | + | |
MSWOA | 2.14 | 5.01 | 2.12 | 2.14 | 3 | 1.04 | + | |
DGSWOA | 2.13 × | 6.65 | 2.12 × | 2.14 × | 1 | |||
PSO | 1.04 | 4.30 | 9.41 | 1.12 | 9 | 1.86 | + | |
GA | 7.13 | 2.81 | 6.49 | 7.57 | 8 | 1.86 | + | |
GWO | 4.94 | 2.27 | 4.33 | 5.26 | 3 | 2.99 | + | |
WOA | 4.79 | 1.90 × | 4.26 | 5.09 × | 2 | 6.41 | ≈ | |
BOA | 5.28 | 1.98 | 4.94 | 5.64 | 6 | 1.30 | + | |
SOA | 5.23 | 2.23 | 4.64 | 5.52 | 5 | 5.72 | + | |
LWOA | 5.61 | 2.80 | 4.93 | 6.12 | 7 | 1.86 | + | |
MSWOA | 5.16 | 2.33 | 4.52 | 5.53 | 4 | 3.86 | + | |
DGSWOA | 4.76 × | 2.59 | 4.15 × | 5.16 | 1 |
Dim | Rank | PSO | GA | GWO | WOA | BOA | SOA | LWOA | MSWOA | DGSWOA |
---|---|---|---|---|---|---|---|---|---|---|
2 | Average Rank | 5.63 | 5.54 | 5.08 | 2.42 | 8.04 | 6.71 | 4.75 | 4.63 | 1.96 |
Combined Rank | 7 | 6 | 5 | 2 | 9 | 8 | 4 | 3 | 1 | |
3 | Average Rank | 6.17 | 5.79 | 5.04 | 2.58 | 8.00 | 6.63 | 4.38 | 4.54 | 1.63 |
Combined Rank | 7 | 6 | 5 | 2 | 9 | 8 | 3 | 4 | 1 | |
5 | Average Rank | 6.83 | 5.17 | 4.67 | 2.13 | 8.00 | 6.96 | 3.67 | 5.71 | 1.75 |
Combined Rank | 7 | 5 | 4 | 2 | 9 | 8 | 3 | 6 | 1 | |
10 | Average Rank | 6.92 | 5.67 | 3.50 | 2.71 | 8.21 | 7.33 | 3.25 | 5.58 | 1.83 |
Combined Rank | 7 | 6 | 4 | 2 | 9 | 8 | 3 | 5 | 1 | |
20 | Average Rank | 7.50 | 5.79 | 2.92 | 2.96 | 8.25 | 7.13 | 2.83 | 5.46 | 2.17 |
Combined Rank | 8 | 6 | 3 | 4 | 9 | 7 | 2 | 5 | 1 | |
40 | Average Rank | 8.04 | 6.25 | 2.42 | 3.04 | 7.92 | 6.71 | 3.38 | 5.21 | 2.04 |
Combined Rank | 9 | 6 | 2 | 3 | 8 | 7 | 4 | 5 | 1 |
Algorithms | Statistical Results | Optimization Results | ||||
---|---|---|---|---|---|---|
Mean | Std | Best | Worst | |||
PSO | 264.0102172 | 0.089045092 | 263.9064511 | 264.2583806 | 0.78925546 | 0.40775062 |
GA | 264.7136911 | 0.487230295 | 263.9960005 | 265.4198156 | 0.787181601 | 0.420651119 |
GWO | 269.9444207 | 4.131765734 | 264.4659362 | 278.160449 | 0.51189717 | 0.257295503 |
WOA | 268.7030823 | 3.522943015 | 264.1199548 | 277.3260036 | 0.793886107 | 0.441581823 |
BOA | 264.5959808 | 0.480966027 | 263.9142765 | 265.839117 | 0.778680571 | 0.443518559 |
SOA | 265.4164476 | 1.998136218 | 263.903026 | 270.7246175 | 0.781988998 | 0.442365584 |
LWOA | 264.0792459 | 0.129620357 | 263.9051139 | 264.3445435 | 0.787698749 | 0.412843951 |
MSWOA | 263.9713221 | 0.090194172 | 263.8960647 | 264.2718789 | 0.785543396 | 0.417860973 |
DGSWOA | 263.9446738 | 0.038407885 | 263.8967369 | 264.0726374 | 0.786838623 | 0.413931035 |
Algorithms | Statistical Results | Optimization Results | ||||||
---|---|---|---|---|---|---|---|---|
Mean | Std | Best | Worst | R | L | |||
PSO | 30,390.520 | 8083.371 | 17,777.737 | 48,137.525 | 2.309 | 1.513 | 75.372 | 52.845 |
GA | 120,763.889 | 56,080.125 | 30,688.705 | 231,074.092 | 4.381 | 5.577 | 81.543 | 54.552 |
GWO | 10,700.645 | 1500.438 | 8398.811 | 15,708.056 | 1.512 | 0.775 | 69.265 | 12.478 |
WOA | 31,526.721 | 66,876.075 | 8181.402 | 300,155.386 | 1.854 | 2.186 | 70.097 | 18.752 |
BOA | 40,264.568 | 17,383.321 | 10,875.077 | 78,916.257 | 3.117 | 2.756 | 67.930 | 16.939 |
SOA | 83,099.446 | 126,485.649 | 9439.262 | 54,0344.896 | 1.907 | 8.901 | 67.594 | 30.248 |
LWOA | 8483.994 | 164.481 | 8164.971 | 8785.056 | 1.331 | 0.659 | 67.766 | 11.629 |
MSWOA | 24,266.370 | 21,728.982 | 8732.646 | 111,624.903 | 1.364 | 2.449 | 67.386 | 31.039 |
DGSWOA | 8949.740 | 827.810 | 8170.268 | 11,511.884 | 1.388 | 0.691 | 67.851 | 10.505 |
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Liang, Z.; Shu, T.; Ding, Z. A Novel Improved Whale Optimization Algorithm for Global Optimization and Engineering Applications. Mathematics 2024, 12, 636. https://doi.org/10.3390/math12050636
Liang Z, Shu T, Ding Z. A Novel Improved Whale Optimization Algorithm for Global Optimization and Engineering Applications. Mathematics. 2024; 12(5):636. https://doi.org/10.3390/math12050636
Chicago/Turabian StyleLiang, Ziying, Ting Shu, and Zuohua Ding. 2024. "A Novel Improved Whale Optimization Algorithm for Global Optimization and Engineering Applications" Mathematics 12, no. 5: 636. https://doi.org/10.3390/math12050636
APA StyleLiang, Z., Shu, T., & Ding, Z. (2024). A Novel Improved Whale Optimization Algorithm for Global Optimization and Engineering Applications. Mathematics, 12(5), 636. https://doi.org/10.3390/math12050636