MTV-MFO: Multi-Trial Vector-Based Moth-Flame Optimization Algorithm
Abstract
:1. Introduction
- The canonical MFO is modified by substituting the transverse orientation of MFO with the MTV approach to enhance the performance of the original MFO.
- In the flag-guided trial vector producer (F-TVP), the flag flame is introduced with the aim of enhancing the exploration ability of the original MFO. Besides that, the best flame is employed to calculate the distance between moth and flames. Additionally, a new spiral function is used to model the flying path of moths.
- In the contingent trial vector producer (C-TVP), two new external archives are employed to increase exploratory capability and diversity. Additionally, the position of the best moth is considered as the base vector to change the moths’ positions with respect to the current best moth position.
- The proposed MTV-MFO algorithm concurrently executes three trial vector producers on the dedicated portion of the population based on the TVP’s improved rate. Experimental results demonstrate that the MTV-MFO performs better than the canonical MFO and other state-of-the-art nature-inspired algorithms.
2. Related Work
3. Moth Flame Optimization (MFO) Algorithm
4. Multi-Trial Vector-Based Moth-Flame Optimization (MTV-MFO) Algorithm
Algorithm 1. Moth-flame trial vector producer (MFO-TVP). | |
Input: MMFO-TVP | |
Output: CMFO-TVP | |
1: | Procedure MFO-TVP |
2: | For i = 1 to NMFO-TVP |
3: | |
4: | |
5: | End |
6: | Return produced vectors in CMFO-TVP |
7: | End procedure |
Algorithm 2. Flag-guided trial vector producer (F-TVP). | |
Input: MF-TVP | |
Output: CF-TVP | |
1: | Procedure F-TVP |
2: | For i = 1 to NF-TVP |
3: | |
4: | |
5: | End |
6: | Return produced vectors in CF-TVP |
7: | End procedure |
Algorithm 3. Contingent trial vector producer (C-TVP). | |
Input: MC-TVP, M, XInfSolution, XInfCandidate | |
Output: CC-TVP | |
1: | Procedure C-TVP |
2: | |
3: | For i = 1 to NC-TVP |
4: | ) |
5: | End |
6: | Return produced vectors in CC-TVP |
7: | End procedure |
Algorithm 4. Multi-trial Vector-based Moth-Flame Optimization (MTV-MFO) Algorithm. | |
Input: N, Dim, MaxIter, nIter | |
Output: The global optimum (Fbest) | |
1: | Begin |
2: | iter = 1, Rewarded-TVP = MFO-TVP. |
3: | Randomly distribute N moths in the search space. |
4: | Evaluating fitness f(Mi) and set the Fbest. |
5: | While iter ≤ MaxIter |
6: | If mod (iter, nIter) == 0 |
7: | Determining ImpRateMFO-TVP, ImpRateF-TVP, and ImpRateC-TVP using Equation 5. |
8: | Calculating NMFO-TVP, NF-TVP, and NC-TVP using Equation 6. |
9: | End if |
10: | Distributing M into MMFO-TVP, MF-TVP, MC-TVP based on reward distributing policy. |
11: | Do for each TVP |
12: | For i = 1 to Nsub-pop |
13: | Multi-trial vector producing. |
14: | If f(Ci) < f(Mi) |
15: | Updating Mi by Ci and counting the improved moth. |
16: | End if |
17: | Archiving. |
18: | End for |
19: | End do |
20: | Updating Fbest. |
21: | iter = iter + 1. |
22: | End while |
23: | Return the global optimum (Fbest). |
24: | End |
5. Experimental Evaluation and Results
5.1. Benchmark Test Functions and Experimental Environment
5.2. Experimental Setup
5.3. Exploration and Exploitation Evaluation
5.4. Evaluation of Local Optima Avoidance
5.5. Convergence Evaluation
6. Statistical Analysis
6.1. Friedman Test
6.2. Student’s t-Test
6.3. Box Plot Analysis
7. Conclusions and Future Works
- -
- The proposed F-TVP and C-TVP enhance exploitation and exploitation.
- -
- Cooperation of the proposed F-TVP and C-TVP with the canonical MFO-TVP enhances the balance between exploration and exploitation, which enables the MTV-MFO algorithm to escape from the local optima.
- -
- The results obtained from different experiments on diverse test functions with various characteristics and statistical tests verify the performance of the MTV-MFO algorithm in comparison to other, comparative algorithms.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A
Function | Name and Formulation | Fi* = Fi(x*) |
---|---|---|
Func 1 | Shifted and Rotated Bent Cigar Function | 100 |
Func 3 | Shifted and Rotated Zakharov Function | 300 |
Func 4 | Shifted and Rotated Rosenbrock’s Function | 400 |
Func 5 | Shifted and Rotated Rastrigin’s Function | 500 |
Func 6 | Shifted and Rotated Expanded Scaffer’s F6 Function | 600 |
Func 7 | Shifted and Rotated Lunacek Bi_Rastrigin Function , , for i = 1,2,…,D | 700 |
Func 8 | Shifted and Rotated Non-Continuous Rastrigin’s Function for i = 1,2,…, D , i = 1,2,…,D. , for i=1,…,D | 800 |
Func 9 | Shifted and Rotated Levy Function | 900 |
Func 10 | Shifted and Rotated Schwefel’s Function | 1000 |
Func 11 | Hybrid Function 1 (N = 3) | 1100 |
Func 12 | Hybrid Function 2 (N = 3) | 1200 |
Func 13 | Hybrid Function 3 (N = 3) | 1300 |
Func 14 | Hybrid Function 4 (N = 4) | 1400 |
Func 15 | Hybrid Function 5 (N = 4) | 1500 |
Func 16 | Hybrid Function 6 (N = 4) | 1600 |
Func 17 | Hybrid Function 6 (N = 5) | 1700 |
Func 18 | Hybrid Function 6 (N = 5) | 1800 |
Func 19 | Hybrid Function 6 (N = 5) | 1900 |
Func 20 | Hybrid Function 6 (N = 6) | 2000 |
Func 21 | Composition Function 1 (N = 3) ’ | 2100 |
Func 22 | Composition Function 2 (N = 3) ’ | 2200 |
Func 23 | Composition Function 3 (N = 4) ’ | 2300 |
Func 24 | Composition Function 4 (N = 4) ’ | 2400 |
Func 25 | Composition Function 5 (N = 5) ’ | 2500 |
Func 26 | Composition Function 6 (N = 5) ’ | 2600 |
Func 27 | Composition Function 7 (N = 6) ’ | 2700 |
Func 28 | Composition Function 8 (N = 6) ’ | 2800 |
Func 29 | Composition Function 9 (N = 3) ’ | 2900 |
Func 30 | Composition Function 10 (N = 3) ’ | 3000 |
Appendix B
Func | Dim | Metric | KH (2012) | GWO (2014) | MFO (2015) | WOA (2016) | SSA (2017) | BOA (2019) | HGSO (2019) | AOA (2020) | MTV-MFO |
---|---|---|---|---|---|---|---|---|---|---|---|
Func 1 | 10 | Avg | 4.81 × 102 | 2.69 × 106 | 3.51 × 106 | 2.37 × 105 | 3.17 × 103 | 9.77 × 109 | 5.64 × 108 | 3.64 × 107 | 0 |
SD | 5.15 × 102 | 7.21 × 106 | 1.57 × 107 | 4.36 × 105 | 2.96 × 103 | 2.39 × 109 | 2.52 × 108 | 1.23 × 107 | 0 | ||
Min | 3.00 × 101 | 5.00 × 103 | 3.15 × 101 | 1.36 × 104 | 4.58 × 100 | 3.62 × 109 | 2.39 × 108 | 1.64 × 107 | 0 | ||
30 | Avg | 1.59 × 104 | 8.15 × 108 | 6.85 × 109 | 3.01 × 106 | 4.86 × 103 | 5.62 × 1010 | 1.52 × 1010 | 4.79 × 107 | 1.33 × 102 | |
SD | 1.44 × 104 | 6.24 × 108 | 5.86 × 109 | 2.24 × 106 | 5.76 × 103 | 5.04 × 109 | 3.24 × 109 | 2.37 × 107 | 1.43 × 102 | ||
Min | 2.86 × 103 | 1.60 × 108 | 5.49 × 103 | 7.79 × 105 | 5.58 × 101 | 4.75 × 1010 | 1.07 × 1010 | 1.72 × 107 | 3.53 × 10−2 | ||
50 | Avg | 2.31 × 105 | 4.74 × 109 | 3.64 × 1010 | 1.02 × 107 | 6.71 × 103 | 1.07 × 1011 | 3.95 × 1010 | 5.69 × 108 | 2.06 × 103 | |
SD | 1.70 × 105 | 2.11 × 109 | 1.10 × 1010 | 1.06 × 107 | 8.58 × 103 | 5.19 × 109 | 8.59 × 109 | 3.09 × 108 | 1.52 × 103 | ||
Min | 6.31 × 104 | 1.19 × 109 | 1.87 × 1010 | 2.86 × 106 | 9.38 × 100 | 9.43 × 1010 | 2.64 × 1010 | 2.29 × 108 | 8.40 × 100 | ||
Func 3 | 10 | Avg | 9.01 × 102 | 5.33 × 102 | 3.41 × 103 | 1.68 × 102 | 1.17 × 10−9 | 1.35 × 104 | 7.31 × 102 | 1.81 × 103 | 0 |
SD | 1.13 × 103 | 8.25 × 102 | 5.53 × 103 | 1.52 × 102 | 4.43 × 1010 | 2.86 × 103 | 3.07 × 102 | 1.02 × 103 | 0 | ||
Min | 2.85 × 101 | 2.52 × 101 | 0 | 3.79 × 100 | 3.37 × 1010 | 8.42 × 103 | 3.40 × 102 | 3.19 × 102 | 0 | ||
30 | Avg | 4.53 × 104 | 2.62 × 104 | 8.80 × 104 | 1.54 × 105 | 3.61 × 10−8 | 8.30 × 104 | 3.84 × 104 | 4.15 × 104 | 0 | |
SD | 1.41 × 104 | 7.06 × 103 | 4.64 × 104 | 7.27 × 104 | 1.10 × 10−8 | 8.16 × 103 | 7.17 × 103 | 1.01 × 104 | 0 | ||
Min | 2.66 × 104 | 9.68 × 103 | 1.18 × 104 | 4.94 × 104 | 2.49 × 10−8 | 6.44 × 104 | 2.11 × 104 | 2.15 × 104 | 0 | ||
50 | Avg | 1.15 × 105 | 6.76 × 104 | 1.89 × 105 | 6.98 × 104 | 1.96 × 10−7 | 2.35 × 105 | 1.39 × 105 | 1.01 × 105 | 0 | |
SD | 2.23 × 104 | 1.55 × 104 | 9.49 × 104 | 2.77 × 104 | 5.46 × 10−8 | 5.73 × 104 | 8.39 × 103 | 1.10 × 104 | 0 | ||
Min | 8.23 × 104 | 4.21 × 104 | 1.44 × 104 | 3.65 × 104 | 1.28 × 10−7 | 1.78 × 105 | 1.26 × 105 | 8.24 × 104 | 0 | ||
Rank | 10 | (w/l/t) | 0/2/0 | 0/2/0 | 0/2/0 | 0/2/0 | 0/2/0 | 0/2/0 | 0/2/0 | 0/2/0 | 2/0/0 |
30 | (w/l/t) | 0/2/0 | 0/2/0 | 0/2/0 | 0/2/0 | 0/2/0 | 0/2/0 | 0/2/0 | 0/2/0 | 2/0/0 | |
50 | (w/l/t) | 0/2/0 | 0/2/0 | 0/2/0 | 0/2/0 | 0/2/0 | 0/2/0 | 0/2/0 | 0/2/0 | 2/0/0 |
Func | Dim | Metric | KH (2012) | GWO (2014) | MFO (2015) | WOA (2016) | SSA (2017) | BOA (2019) | HGSO (2019) | AOA (2020) | MTV-MFO |
---|---|---|---|---|---|---|---|---|---|---|---|
Func 4 | 10 | Avg | 5.91 × 100 | 7.85 × 100 | 5.48 × 100 | 4.01 × 101 | 3.97 × 100 | 1.24 × 103 | 4.65 × 101 | 1.80 × 101 | 0 |
SD | 2.42 × 100 | 2.76 × 100 | 2.67 × 100 | 4.52 × 101 | 1.55 × 100 | 3.21 × 102 | 1.28 × 101 | 1.42 × 101 | 0 | ||
Min | 1.18 × 10−1 | 6.17 × 100 | 1.15 × 100 | 3.05 × 100 | 8.81 × 10−3 | 6.26 × 102 | 2.33 × 101 | 7.86 × 100 | 0 | ||
30 | Avg | 9.87 × 101 | 1.59 × 102 | 5.10 × 102 | 1.58 × 102 | 8.71 × 101 | 2.12 × 104 | 1.63 × 103 | 1.28 × 102 | 7.42 × 10−1 | |
SD | 2.03 × 101 | 4.16 × 101 | 4.00 × 102 | 3.94 × 101 | 1.71 × 101 | 3.62 × 103 | 4.48 × 102 | 2.01 × 101 | 1.41 × 100 | ||
Min | 6.83 × 101 | 9.85 × 101 | 9.92 × 101 | 1.13 × 102 | 3.70 × 101 | 1.15 × 104 | 1.06 × 103 | 1.02 × 102 | 1.70 × 10−3 | ||
50 | Avg | 1.54 × 102 | 4.42 × 102 | 2.78 × 103 | 2.82 × 102 | 1.41 × 102 | 4.16 × 104 | 7.71 × 103 | 3.48 × 102 | 6.16 × 101 | |
SD | 5.06 × 101 | 1.86 × 102 | 2.48 × 103 | 6.46 × 101 | 5.08 × 101 | 5.30 × 103 | 1.78 × 103 | 7.15 × 101 | 3.82 × 101 | ||
Min | 7.32 × 101 | 2.08 × 102 | 4.46 × 102 | 2.10 × 102 | 3.25 × 101 | 3.24 × 104 | 4.51 × 103 | 2.00 × 102 | 5.74 × 10−2 | ||
Func 5 | 10 | Avg | 2.69 × 101 | 1.14 × 101 | 2.20 × 101 | 4.44 × 101 | 1.85 × 101 | 1.18 × 102 | 4.97 × 101 | 3.35 × 101 | 8.95 × 100 |
SD | 7.13 × 100 | 4.41 × 100 | 5.47 × 100 | 2.26 × 101 | 9.29 × 100 | 1.35 × 101 | 5.38 × 100 | 6.49 × 100 | 2.96 × 100 | ||
Min | 1.59 × 101 | 4.08 × 100 | 8.95 × 100 | 1.50 × 101 | 7.96 × 100 | 9.06 × 101 | 3.64 × 101 | 1.93 × 101 | 3.98 × 100 | ||
30 | Avg | 1.37 × 102 | 9.53 × 101 | 1.88 × 102 | 2.64 × 102 | 1.27 × 102 | 5.86 × 102 | 3.06 × 102 | 2.11 × 102 | 6.13 × 101 | |
SD | 3.14 × 101 | 2.03 × 101 | 3.29 × 101 | 5.56 × 101 | 2.96 × 101 | 4.66 × 101 | 1.71 × 101 | 1.45 × 101 | 1.51 × 101 | ||
Min | 9.06 × 101 | 5.58 × 101 | 1.31 × 102 | 1.79 × 102 | 7.76 × 101 | 5.05 × 102 | 2.56 × 102 | 1.90 × 102 | 3.08 × 101 | ||
50 | Avg | 2.56 × 102 | 1.81 × 102 | 4.43 × 102 | 4.13 × 102 | 3.04 × 102 | 9.51 × 102 | 5.45 × 102 | 3.68 × 102 | 1.47 × 102 | |
SD | 3.11 × 101 | 3.45 × 101 | 8.55 × 101 | 8.06 × 101 | 6.46 × 101 | 5.18 × 101 | 2.80 × 101 | 7.74 × 101 | 2.08 × 101 | ||
Min | 2.09 × 102 | 1.21 × 102 | 3.29 × 102 | 2.73 × 102 | 2.06 × 102 | 8.18 × 102 | 4.80 × 102 | 2.11 × 102 | 9.25 × 101 | ||
Func 6 | 10 | Avg | 5.40 × 100 | 1.19 × 100 | 4.21 × 10−1 | 3.15 × 101 | 6.38 × 100 | 6.51 × 101 | 2.43 × 101 | 9.41 × 10−1 | 0 |
SD | 6.81 × 100 | 1.52 × 100 | 7.00 × 10−1 | 1.28 × 101 | 7.55 × 100 | 1.38 × 101 | 4.30 × 100 | 4.36 × 10−1 | 0 | ||
Min | 3.86 × 10−5 | 2.51 × 10−2 | 0 | 1.28 × 101 | 2.72 × 10−2 | 4.37 × 101 | 1.60 × 101 | 2.70 × 10−1 | 0 | ||
30 | Avg | 3.55 × 101 | 5.24 × 100 | 2.82 × 101 | 6.93 × 101 | 3.12 × 101 | 1.17 × 102 | 6.48 × 101 | 8.75 × 100 | 1.34 × 10−1 | |
SD | 9.06 × 100 | 2.81 × 100 | 1.44 × 101 | 9.73 × 100 | 1.32 × 101 | 1.24 × 101 | 6.35 × 100 | 2.63 × 100 | 1.07 × 10−1 | ||
Min | 1.95 × 101 | 8.70 × 10−1 | 7.63 × 100 | 5.02 × 101 | 9.19 × 100 | 8.83 × 101 | 4.73 × 101 | 5.06 × 100 | 1.49 × 10−2 | ||
50 | Avg | 5.13 × 101 | 1.10 × 101 | 4.76 × 101 | 7.54 × 101 | 4.34 × 101 | 1.32 × 102 | 8.24 × 101 | 2.06 × 101 | 4.70 × 100 | |
SD | 6.46 × 100 | 3.96 × 100 | 6.44 × 100 | 9.30 × 100 | 9.48 × 100 | 7.76 × 100 | 4.74 × 100 | 4.14 × 100 | 2.41 × 100 | ||
Min | 3.74 × 101 | 5.12 × 100 | 3.66 × 101 | 6.58 × 101 | 2.40 × 101 | 1.18 × 102 | 7.14 × 101 | 1.46 × 101 | 6.24 × 10−1 | ||
Func 7 | 10 | Avg | 2.10 × 101 | 2.52 × 101 | 3.58 × 101 | 7.61 × 101 | 3.46 × 101 | 3.21 × 102 | 6.63 × 101 | 3.77 × 101 | 1.80 × 101 |
SD | 5.34 × 100 | 8.53 × 100 | 1.17 × 101 | 3.26 × 101 | 1.25 × 101 | 6.53 × 101 | 7.30 × 100 | 5.29 × 100 | 4.04 × 100 | ||
Min | 1.26 × 101 | 1.46 × 101 | 1.48 × 101 | 2.71 × 101 | 2.00 × 101 | 1.82 × 102 | 4.52 × 101 | 2.99 × 101 | 7.78 × 100 | ||
30 | Avg | 1.33 × 102 | 1.53 × 102 | 3.27 × 102 | 5.04 × 102 | 1.64 × 102 | 1.15 × 103 | 4.01 × 102 | 2.44 × 102 | 1.16 × 102 | |
SD | 2.64 × 101 | 4.96 × 101 | 1.22 × 102 | 1.01 × 102 | 3.09 × 101 | 1.17 × 102 | 3.32 × 101 | 1.37 × 101 | 1.30 × 101 | ||
Min | 8.34 × 101 | 9.08 × 101 | 1.56 × 102 | 3.35 × 102 | 1.11 × 102 | 9.01 × 102 | 3.24 × 102 | 2.15 × 102 | 9.23 × 101 | ||
50 | Avg | 3.62 × 102 | 3.38 × 102 | 9.72 × 102 | 1.01 × 103 | 3.36 × 102 | 1.86 × 103 | 8.29 × 102 | 5.15 × 102 | 2.82 × 102 | |
SD | 5.66 × 101 | 8.31 × 101 | 3.07 × 102 | 1.01 × 102 | 9.21 × 101 | 1.28 × 102 | 6.43 × 101 | 3.84 × 101 | 3.84 × 101 | ||
Min | 2.74 × 102 | 2.07 × 102 | 4.02 × 102 | 7.66 × 102 | 2.18 × 102 | 1.66 × 103 | 7.17 × 102 | 4.31 × 102 | 1.93 × 102 | ||
Func 8 | 10 | Avg | 1.63 × 101 | 1.04 × 101 | 2.48 × 101 | 4.05 × 101 | 1.73 × 101 | 1.04 × 102 | 3.21 × 101 | 2.34 × 101 | 1.02 × 101 |
SD | 6.96 × 100 | 3.67 × 100 | 1.12 × 101 | 1.58 × 101 | 9.37 × 100 | 1.32 × 101 | 3.30 × 100 | 5.24 × 100 | 3.41 × 100 | ||
Min | 7.96 × 100 | 5.97 × 100 | 4.97 × 100 | 2.09 × 101 | 4.97 × 100 | 7.63 × 101 | 2.67 × 101 | 1.36 × 101 | 1.99 × 100 | ||
30 | Avg | 1.09 × 102 | 7.73 × 101 | 1.67 × 102 | 2.16 × 102 | 1.19 × 102 | 4.82 × 102 | 2.53 × 102 | 1.89 × 102 | 7.27 × 101 | |
SD | 1.69 × 101 | 2.83 × 101 | 3.83 × 101 | 5.54 × 101 | 2.72 × 101 | 3.62 × 101 | 1.36 × 101 | 1.55 × 101 | 1.07 × 101 | ||
Min | 7.36 × 101 | 4.22 × 101 | 9.11 × 101 | 1.28 × 102 | 8.36 × 101 | 4.22 × 102 | 2.27 × 102 | 1.57 × 102 | 5.07 × 101 | ||
50 | Avg | 2.84 × 102 | 2.02 × 102 | 3.97 × 102 | 4.11 × 102 | 2.89 × 102 | 9.91 × 102 | 5.71 × 102 | 3.59 × 102 | 1.28 × 102 | |
SD | 4.77 × 101 | 3.18 × 101 | 7.78 × 101 | 7.29 × 101 | 8.11 × 101 | 5.42 × 101 | 2.75 × 101 | 9.00 × 101 | 2.10 × 101 | ||
Min | 2.09 × 102 | 1.36 × 102 | 2.69 × 102 | 2.93 × 102 | 1.93 × 102 | 8.76 × 102 | 5.03 × 102 | 2.18 × 102 | 8.16 × 101 | ||
Func 9 | 10 | Avg | 8.52 × 100 | 6.17 × 100 | 3.79 × 101 | 4.52 × 102 | 4.79 × 100 | 2.54 × 103 | 9.80 × 101 | 3.81 × 100 | 0 |
SD | 2.28 × 101 | 1.58 × 101 | 1.53 × 102 | 3.37 × 102 | 1.80 × 101 | 6.69 × 102 | 2.43 × 101 | 2.71 × 100 | 0 | ||
Min | 3.35 × 10−5 | 4.93 × 10−2 | 0 | 4.81 × 101 | 1.36 × 1010 | 1.13 × 103 | 4.46 × 101 | 1.02 × 100 | 0 | ||
30 | Avg | 2.31 × 103 | 5.29 × 102 | 4.68 × 103 | 6.42 × 103 | 2.23 × 103 | 2.69 × 104 | 4.98 × 103 | 9.96 × 102 | 1.50 × 102 | |
SD | 6.62 × 102 | 3.60 × 102 | 1.55 × 103 | 2.04 × 103 | 1.24 × 103 | 4.98 × 103 | 9.90 × 102 | 3.18 × 102 | 9.61 × 101 | ||
Min | 9.31 × 102 | 8.54 × 101 | 2.82 × 103 | 2.72 × 103 | 4.25 × 101 | 1.65 × 104 | 3.17 × 103 | 5.03 × 102 | 9.80 × 100 | ||
50 | Avg | 9.41 × 103 | 4.49 × 103 | 1.47 × 104 | 2.01 × 104 | 1.01 × 104 | 7.99 × 104 | 2.61 × 104 | 1.02 × 104 | 1.26 × 103 | |
SD | 1.36 × 103 | 3.26 × 103 | 3.08 × 103 | 6.78 × 103 | 2.22 × 103 | 5.95 × 103 | 2.02 × 103 | 1.93 × 103 | 4.98 × 102 | ||
Min | 7.64 × 103 | 1.51 × 103 | 7.99 × 103 | 1.24 × 104 | 6.49 × 103 | 6.85 × 104 | 2.05 × 104 | 7.01 × 103 | 4.15 × 102 | ||
Func 10 | 10 | Avg | 9.94 × 102 | 5.21 × 102 | 7.37 × 102 | 9.41 × 102 | 9.15 × 102 | 2.24 × 103 | 1.36 × 103 | 1.05 × 103 | 4.06 × 102 |
SD | 2.88 × 102 | 3.13 × 102 | 2.73 × 102 | 2.47 × 102 | 2.60 × 102 | 2.16 × 102 | 1.82 × 102 | 2.51 × 102 | 1.28 × 102 | ||
Min | 4.56 × 102 | 4.14 × 101 | 3.14 × 102 | 4.81 × 102 | 2.99 × 102 | 1.73 × 103 | 8.50 × 102 | 5.36 × 102 | 1.34 × 102 | ||
30 | Avg | 4.06 × 103 | 3.25 × 103 | 4.23 × 103 | 5.18 × 103 | 3.60 × 103 | 8.93 × 103 | 5.72 × 103 | 6.60 × 103 | 3.08 × 103 | |
SD | 4.36 × 102 | 9.30 × 102 | 7.04 × 102 | 7.27 × 102 | 5.51 × 102 | 3.18 × 102 | 3.44 × 102 | 4.75 × 102 | 5.31 × 102 | ||
Min | 3.37 × 103 | 1.77 × 103 | 2.98 × 103 | 3.83 × 103 | 2.75 × 103 | 8.24 × 103 | 5.10 × 103 | 5.61 × 103 | 1.97 × 103 | ||
50 | Avg | 6.65 × 103 | 5.45 × 103 | 7.32 × 103 | 8.87 × 103 | 6.47 × 103 | 1.56 × 104 | 1.17 × 104 | 1.32 × 104 | 5.36 × 103 | |
SD | 8.55 × 102 | 7.81 × 102 | 1.09 × 103 | 1.13 × 103 | 1.03 × 103 | 4.33 × 102 | 6.84 × 102 | 4.13 × 102 | 4.48 × 102 | ||
Min | 5.33 × 103 | 3.91 × 103 | 4.94 × 103 | 7.22 × 103 | 4.81 × 103 | 1.49 × 104 | 1.08 × 104 | 1.26 × 104 | 4.92 × 103 | ||
Rank | 10 | (w/l/t) | 0/7/0 | 0/7/0 | 0/7/0 | 0/7/0 | 0/7/0 | 0/7/0 | 0/7/0 | 0/7/0 | 7/0/0 |
30 | (w/l/t) | 0/7/0 | 0/7/0 | 0/7/0 | 0/7/0 | 0/7/0 | 0/7/0 | 0/7/0 | 0/7/0 | 7/0/0 | |
50 | (w/l/t) | 0/7/0 | 0/7/0 | 0/7/0 | 0/7/0 | 0/7/0 | 0/7/0 | 0/7/0 | 0/7/0 | 7/0/0 |
Func | Dim | Metric | KH (2012) | GWO (2014) | MFO (2015) | WOA (2016) | SSA (2017) | BOA (2019) | HGSO (2019) | AOA (2020) | MTV-MFO |
---|---|---|---|---|---|---|---|---|---|---|---|
Func 11 | 10 | Avg | 4.09 × 101 | 1.97 × 101 | 4.13 × 101 | 8.50 × 101 | 9.43 × 101 | 1.70 × 103 | 1.30 × 102 | 2.11 × 102 | 4.30 × 100 |
SD | 2.30 × 101 | 9.59 × 100 | 4.78 × 101 | 5.71 × 101 | 7.99 × 101 | 1.34 × 103 | 4.43 × 101 | 1.05 × 102 | 1.79 × 100 | ||
Min | 2.67 × 100 | 6.26 × 100 | 3.48 × 100 | 3.02 × 101 | 1.36 × 101 | 2.55 × 102 | 6.00 × 101 | 7.94 × 101 | 9.95 × 10−1 | ||
30 | Avg | 4.02 × 102 | 2.30 × 102 | 1.92 × 103 | 3.52 × 102 | 1.66 × 102 | 7.00 × 103 | 1.44 × 103 | 8.34 × 102 | 9.20 × 101 | |
SD | 1.84 × 102 | 4.87 × 101 | 1.97 × 103 | 9.76 × 101 | 4.74 × 101 | 1.94 × 103 | 5.84 × 102 | 3.08 × 102 | 2.32 × 101 | ||
Min | 1.56 × 102 | 1.40 × 102 | 2.22 × 102 | 1.96 × 102 | 9.11 × 101 | 3.95 × 103 | 5.80 × 102 | 4.50 × 102 | 5.77 × 101 | ||
50 | Avg | 3.56 × 103 | 1.34 × 103 | 7.81 × 103 | 4.69 × 102 | 2.77 × 102 | 2.45 × 104 | 4.89 × 103 | 9.76 × 103 | 1.59 × 102 | |
SD | 1.69 × 103 | 1.09 × 103 | 9.73 × 103 | 1.04 × 102 | 7.45 × 101 | 2.95 × 103 | 1.25 × 103 | 1.63 × 103 | 3.40 × 101 | ||
Min | 1.29 × 103 | 3.63 × 102 | 5.38 × 102 | 3.31 × 102 | 1.46 × 102 | 1.70 × 104 | 2.51 × 103 | 6.82 × 103 | 1.11 × 102 | ||
Func 12 | 10 | Avg | 1.10 × 106 | 4.87 × 105 | 2.82 × 105 | 4.21 × 106 | 1.03 × 106 | 4.12 × 108 | 6.48 × 106 | 2.07 × 106 | 1.91 × 102 |
SD | 9.36 × 105 | 7.19 × 105 | 1.17 × 106 | 5.96 × 106 | 1.66 × 106 | 1.88 × 108 | 2.96 × 106 | 1.32 × 106 | 8.94 × 101 | ||
Min | 7.29 × 104 | 2.04 × 104 | 1.13 × 103 | 4.17 × 104 | 1.95 × 104 | 3.51 × 107 | 9.12 × 105 | 3.40 × 105 | 1.14 × 101 | ||
30 | Avg | 2.83 × 106 | 3.40 × 107 | 1.38 × 108 | 3.69 × 107 | 2.26 × 106 | 1.55 × 1010 | 1.27 × 109 | 3.07 × 106 | 2.99 × 103 | |
SD | 1.77 × 106 | 3.93 × 107 | 2.37 × 108 | 2.80 × 107 | 2.55 × 106 | 2.67 × 109 | 5.32 × 108 | 1.32 × 106 | 1.23 × 103 | ||
Min | 3.07 × 105 | 7.71 × 105 | 4.42 × 105 | 1.17 × 107 | 2.23 × 105 | 1.04 × 1010 | 5.61 × 108 | 1.57 × 106 | 9.78 × 102 | ||
50 | Avg | 1.06 × 107 | 4.62 × 108 | 2.75 × 109 | 1.85 × 108 | 1.87 × 107 | 8.30 × 1010 | 1.57 × 1010 | 2.38 × 107 | 5.00 × 104 | |
SD | 9.25 × 106 | 6.18 × 108 | 3.33 × 109 | 9.28 × 107 | 1.17 × 107 | 9.33 × 109 | 3.89 × 109 | 1.05 × 107 | 1.96 × 104 | ||
Min | 1.93 × 106 | 2.77 × 107 | 7.25 × 107 | 4.84 × 107 | 4.33 × 106 | 6.93 × 1010 | 8.50 × 109 | 7.26 × 106 | 1.44 × 104 | ||
Func 13 | 10 | Avg | 9.77 × 103 | 7.93 × 103 | 1.09 × 104 | 1.52 × 104 | 1.21 × 104 | 4.79 × 106 | 1.67 × 104 | 1.06 × 104 | 6.65 × 100 |
SD | 6.47 × 103 | 6.70 × 103 | 1.27 × 104 | 1.04 × 104 | 1.10 × 104 | 5.68 × 106 | 8.32 × 103 | 2.46 × 103 | 2.91 × 100 | ||
Min | 2.47 × 103 | 7.16 × 102 | 1.38 × 102 | 3.50 × 103 | 1.01 × 103 | 1.64 × 105 | 4.36 × 103 | 6.38 × 103 | 9.95 × 10−1 | ||
30 | Avg | 3.74 × 104 | 1.01 × 107 | 5.38 × 105 | 1.21 × 105 | 1.19 × 105 | 1.38 × 1010 | 4.36 × 108 | 3.65 × 104 | 9.99 × 102 | |
SD | 1.80 × 104 | 3.02 × 107 | 1.36 × 106 | 6.24 × 104 | 7.87 × 104 | 3.45 × 109 | 1.37 × 108 | 2.77 × 104 | 4.50 × 102 | ||
Min | 1.49 × 104 | 2.54 × 104 | 1.58 × 104 | 3.64 × 104 | 2.93 × 104 | 4.94 × 109 | 2.27 × 108 | 2.51 × 103 | 1.07 × 102 | ||
50 | Avg | 4.80 × 104 | 7.92 × 107 | 5.58 × 108 | 1.54 × 105 | 1.15 × 105 | 5.04 × 1010 | 2.36 × 109 | 1.40 × 104 | 3.54 × 103 | |
SD | 2.29 × 104 | 1.02 × 108 | 1.32 × 109 | 7.49 × 104 | 6.10 × 104 | 1.05 × 1010 | 9.74 × 108 | 7.73 × 103 | 2.58 × 103 | ||
Min | 2.22 × 104 | 5.08 × 104 | 8.46 × 104 | 4.18 × 104 | 3.36 × 104 | 3.16 × 1010 | 9.55 × 108 | 5.51 × 103 | 1.48 × 102 | ||
Func 14 | 10 | Avg | 8.02 × 102 | 9.30 × 102 | 5.82 × 102 | 3.38 × 102 | 8.59 × 101 | 4.17 × 103 | 5.39 × 102 | 2.00 × 102 | 1.88 × 101 |
SD | 1.42 × 103 | 1.53 × 103 | 6.04 × 102 | 6.49 × 102 | 2.75 × 101 | 4.71 × 103 | 5.42 × 102 | 2.27 × 102 | 9.20 × 100 | ||
Min | 6.46 × 101 | 5.75 × 101 | 5.62 × 101 | 4.93 × 101 | 4.16 × 101 | 1.69 × 102 | 1.15 × 102 | 4.05 × 101 | 1.99 × 100 | ||
30 | Avg | 3.45 × 105 | 1.09 × 105 | 8.86 × 104 | 9.55 × 105 | 5.67 × 103 | 4.99 × 106 | 4.46 × 105 | 5.25 × 105 | 1.22 × 102 | |
SD | 4.58 × 105 | 2.06 × 105 | 1.13 × 105 | 1.52 × 106 | 4.59 × 103 | 2.61 × 106 | 2.21 × 105 | 3.23 × 105 | 2.96 × 101 | ||
Min | 1.47 × 104 | 1.37 × 103 | 9.32 × 103 | 3.39 × 104 | 5.03 × 102 | 1.55 × 106 | 4.05 × 104 | 3.91 × 104 | 6.42 × 101 | ||
50 | Avg | 3.55 × 105 | 4.55 × 105 | 7.81 × 105 | 5.52 × 105 | 5.29 × 104 | 1.53 × 108 | 3.40 × 106 | 4.72 × 106 | 2.77 × 102 | |
SD | 3.41 × 105 | 7.11 × 105 | 1.28 × 106 | 4.01 × 105 | 3.87 × 104 | 8.75 × 107 | 1.28 × 106 | 8.69 × 105 | 4.31 × 101 | ||
Min | 2.14 × 104 | 2.08 × 104 | 2.06 × 103 | 1.44 × 105 | 1.24 × 104 | 2.83 × 107 | 1.69 × 106 | 3.08 × 106 | 1.89 × 102 | ||
Func 15 | 10 | Avg | 2.97 × 103 | 1.34 × 103 | 1.74 × 103 | 2.36 × 103 | 5.23 × 102 | 1.89 × 104 | 2.33 × 103 | 7.88 × 102 | 2.92 × 100 |
SD | 3.48 × 103 | 1.52 × 103 | 1.79 × 103 | 2.78 × 103 | 5.39 × 102 | 1.20 × 104 | 1.23 × 103 | 7.55 × 102 | 1.69 × 100 | ||
Min | 2.54 × 102 | 4.24 × 101 | 1.12 × 102 | 1.29 × 102 | 4.22 × 101 | 6.99 × 103 | 2.37 × 102 | 2.18 × 102 | 1.04 × 100 | ||
30 | Avg | 1.64 × 104 | 1.34 × 105 | 3.98 × 104 | 8.84 × 104 | 4.55 × 104 | 1.10 × 109 | 3.28 × 106 | 5.90 × 102 | 1.33 × 102 | |
SD | 6.40 × 103 | 4.53 × 105 | 4.35 × 104 | 4.71 × 104 | 2.85 × 104 | 3.63 × 108 | 1.64 × 106 | 3.60 × 102 | 5.11 × 101 | ||
Min | 7.88 × 103 | 6.09 × 103 | 9.05 × 102 | 5.19 × 103 | 9.34 × 103 | 6.06 × 108 | 6.91 × 105 | 2.01 × 102 | 1.61 × 101 | ||
50 | Avg | 2.12 × 104 | 4.81 × 106 | 3.17 × 107 | 7.74 × 104 | 4.50 × 104 | 9.58 × 109 | 2.31 × 108 | 1.72 × 104 | 5.82 × 102 | |
SD | 7.14 × 103 | 8.72 × 106 | 9.46 × 107 | 6.32 × 104 | 3.02 × 104 | 2.47 × 109 | 5.50 × 107 | 4.31 × 103 | 2.68 × 102 | ||
Min | 1.10 × 104 | 2.78 × 104 | 3.70 × 104 | 1.59 × 104 | 1.27 × 104 | 5.52 × 109 | 1.18 × 108 | 9.09 × 103 | 2.30 × 102 | ||
Func 16 | 10 | Avg | 3.18 × 102 | 8.05 × 101 | 1.03 × 102 | 1.77 × 102 | 9.00 × 101 | 7.36 × 102 | 2.13 × 102 | 1.19 × 102 | 6.62 × 10−1 |
SD | 1.22 × 102 | 7.56 × 101 | 8.98 × 101 | 1.29 × 102 | 9.35 × 101 | 1.78 × 102 | 6.25 × 101 | 7.38 × 101 | 4.12 × 10−1 | ||
Min | 2.24 × 101 | 4.11 × 100 | 4.53 × 100 | 1.69 × 101 | 2.80 × 100 | 3.22 × 102 | 4.79 × 101 | 3.69 × 101 | 2.57 × 10−2 | ||
30 | Avg | 1.16 × 103 | 6.53 × 102 | 1.46 × 103 | 1.89 × 103 | 9.85 × 102 | 4.94 × 103 | 2.10 × 103 | 1.60 × 103 | 7.64 × 102 | |
SD | 2.81 × 102 | 2.82 × 102 | 3.89 × 102 | 4.90 × 102 | 2.35 × 102 | 7.24 × 102 | 1.35 × 102 | 2.00 × 102 | 1.40 × 102 | ||
Min | 8.12 × 102 | 1.83 × 102 | 3.65 × 102 | 1.01 × 103 | 4.62 × 102 | 3.71 × 103 | 1.81 × 103 | 1.20 × 103 | 5.43 × 102 | ||
50 | Avg | 1.74 × 103 | 1.30 × 103 | 2.55 × 103 | 3.06 × 103 | 1.58 × 103 | 9.84 × 103 | 2.97 × 103 | 1.69 × 103 | 1.16 × 103 | |
SD | 3.13 × 102 | 3.05 × 102 | 5.22 × 102 | 7.24 × 102 | 4.20 × 102 | 1.37 × 103 | 4.24 × 102 | 7.00 × 102 | 2.23 × 102 | ||
Min | 1.12 × 103 | 8.21 × 102 | 1.47 × 103 | 1.71 × 103 | 8.63 × 102 | 7.14 × 103 | 1.90 × 103 | 5.47 × 102 | 1.10 × 103 | ||
Func 17 | 10 | Avg | 5.71 × 101 | 5.38 × 101 | 4.53 × 101 | 9.74 × 101 | 5.52 × 101 | 3.34 × 102 | 7.30 × 101 | 6.59 × 101 | 9.82 × 100 |
SD | 1.60 × 101 | 3.07 × 101 | 1.67 × 101 | 6.20 × 101 | 1.63 × 101 | 1.09 × 102 | 7.04 × 100 | 1.12 × 101 | 7.42 × 100 | ||
Min | 1.74 × 101 | 2.44 × 101 | 2.20 × 101 | 4.11 × 101 | 2.37 × 101 | 1.29 × 102 | 5.76 × 101 | 3.99 × 101 | 1.31 × 100 | ||
30 | Avg | 4.62 × 102 | 2.53 × 102 | 7.26 × 102 | 7.29 × 102 | 3.50 × 102 | 3.86 × 103 | 8.08 × 102 | 4.27 × 102 | 1.96 × 102 | |
SD | 2.13 × 102 | 1.33 × 102 | 2.78 × 102 | 2.17 × 102 | 1.67 × 102 | 1.73 × 103 | 1.29 × 102 | 1.05 × 102 | 9.83 × 101 | ||
Min | 9.94 × 101 | 6.81 × 101 | 1.16 × 102 | 3.83 × 102 | 1.23 × 102 | 1.94 × 103 | 5.23 × 102 | 2.74 × 102 | 3.82 × 101 | ||
50 | Avg | 1.64 × 103 | 9.90 × 102 | 2.08 × 103 | 2.35 × 103 | 1.40 × 103 | 1.71 × 104 | 2.11 × 103 | 1.67 × 103 | 1.02 × 103 | |
SD | 2.82 × 102 | 2.55 × 102 | 3.89 × 102 | 3.43 × 102 | 2.33 × 102 | 8.10 × 103 | 2.29 × 102 | 2.01 × 102 | 2.39 × 102 | ||
Min | 9.95 × 102 | 4.41 × 102 | 1.50 × 103 | 1.63 × 103 | 1.05 × 103 | 7.15 × 103 | 1.54 × 103 | 1.35 × 103 | 3.60 × 102 | ||
Func 18 | 10 | Avg | 9.37 × 103 | 2.38 × 104 | 1.74 × 104 | 9.12 × 103 | 2.14 × 104 | 6.45 × 107 | 2.07 × 105 | 4.02 × 103 | 1.79 × 101 |
SD | 7.83 × 103 | 1.65 × 104 | 1.75 × 104 | 8.10 × 103 | 1.47 × 104 | 7.19 × 107 | 1.61 × 105 | 2.81 × 103 | 7.55 × 100 | ||
Min | 4.41 × 102 | 1.05 × 103 | 1.55 × 103 | 9.68 × 102 | 2.17 × 103 | 8.98 × 105 | 7.91 × 103 | 4.14 × 102 | 1.40 × 100 | ||
30 | Avg | 3.94 × 105 | 6.73 × 105 | 1.55 × 106 | 1.93 × 106 | 1.57 × 105 | 1.05 × 108 | 2.23 × 106 | 1.11 × 106 | 3.06 × 102 | |
SD | 4.45 × 105 | 8.50 × 105 | 2.30 × 106 | 2.12 × 106 | 1.55 × 105 | 7.39 × 107 | 1.40 × 106 | 3.49 × 105 | 1.24 × 102 | ||
Min | 2.94 × 104 | 3.79 × 104 | 5.76 × 104 | 1.10 × 105 | 4.88 × 104 | 1.54 × 107 | 8.23 × 105 | 5.48 × 105 | 9.16 × 101 | ||
50 | Avg | 2.62 × 106 | 3.06 × 106 | 4.38 × 106 | 4.93 × 106 | 4.16 × 105 | 2.50 × 108 | 9.12 × 106 | 2.89 × 106 | 5.23 × 103 | |
SD | 1.58 × 106 | 4.06 × 106 | 5.78 × 106 | 5.17 × 106 | 2.14 × 105 | 9.00 × 107 | 2.60 × 106 | 6.07 × 105 | 2.97 × 103 | ||
Min | 6.76 × 105 | 1.64 × 105 | 1.78 × 105 | 6.09 × 105 | 1.66 × 105 | 4.32 × 107 | 4.74 × 106 | 1.62 × 106 | 1.16 × 103 | ||
Func 19 | 10 | Avg | 1.25 × 103 | 4.16 × 103 | 7.45 × 103 | 1.27 × 104 | 8.09 × 102 | 1.07 × 105 | 4.18 × 103 | 1.34 × 103 | 3.30 × 100 |
SD | 2.09 × 103 | 5.58 × 103 | 1.13 × 104 | 1.16 × 104 | 1.68 × 103 | 1.16 × 105 | 3.54 × 103 | 7.88 × 102 | 1.17 × 100 | ||
Min | 5.03 × 101 | 2.31 × 101 | 1.07 × 102 | 6.90 × 101 | 1.42 × 101 | 8.63 × 103 | 2.16 × 102 | 3.51 × 102 | 8.15 × 10−1 | ||
30 | Avg | 1.20 × 105 | 3.54 × 105 | 1.29 × 105 | 2.65 × 106 | 3.98 × 105 | 1.05 × 109 | 9.34 × 106 | 3.38 × 103 | 8.86 × 101 | |
SD | 1.28 × 105 | 4.69 × 105 | 1.79 × 105 | 2.77 × 106 | 2.51 × 105 | 4.92 × 108 | 3.32 × 106 | 1.25 × 103 | 2.79 × 101 | ||
Min | 5.38 × 103 | 4.48 × 103 | 1.56 × 103 | 2.58 × 105 | 1.45 × 104 | 4.34 × 107 | 3.00 × 106 | 1.33 × 103 | 5.03 × 101 | ||
50 | Avg | 1.66 × 105 | 3.21 × 106 | 3.62 × 106 | 2.31 × 106 | 6.52 × 105 | 4.74 × 109 | 1.67 × 108 | 1.90 × 104 | 5.01 × 102 | |
SD | 1.18 × 105 | 7.31 × 106 | 3.67 × 106 | 2.07 × 106 | 3.52 × 105 | 1.38 × 109 | 6.29 × 107 | 3.01 × 103 | 2.60 × 102 | ||
Min | 1.99 × 104 | 3.79 × 104 | 1.30 × 104 | 2.67 × 104 | 4.39 × 104 | 1.87 × 109 | 5.75 × 107 | 1.39 × 104 | 1.97 × 102 | ||
Func 20 | 10 | Avg | 1.37 × 102 | 7.69 × 101 | 5.86 × 101 | 1.32 × 102 | 7.33 × 101 | 2.75 × 102 | 1.15 × 102 | 5.49 × 101 | 3.44 × 100 |
SD | 7.09 × 101 | 6.15 × 101 | 4.86 × 101 | 5.77 × 101 | 4.72 × 101 | 8.17 × 101 | 3.57 × 101 | 1.53 × 101 | 4.84 × 100 | ||
Min | 4.87 × 101 | 2.30 × 101 | 6.24 × 10−1 | 6.06 × 101 | 2.58 × 101 | 1.13 × 102 | 5.67 × 101 | 3.32 × 101 | 0 | ||
30 | Avg | 5.76 × 102 | 4.19 × 102 | 5.90 × 102 | 6.72 × 102 | 4.84 × 102 | 1.41 × 103 | 5.91 × 102 | 5.40 × 102 | 1.97 × 102 | |
SD | 2.17 × 102 | 1.32 × 102 | 2.41 × 102 | 1.82 × 102 | 1.40 × 102 | 1.54 × 102 | 6.82 × 101 | 1.02 × 102 | 1.13 × 102 | ||
Min | 2.88 × 102 | 2.39 × 102 | 8.86 × 101 | 3.88 × 102 | 2.86 × 102 | 1.03 × 103 | 4.80 × 102 | 3.57 × 102 | 3.02 × 101 | ||
50 | Avg | 1.33 × 103 | 7.59 × 102 | 1.46 × 103 | 1.68 × 103 | 1.00 × 103 | 2.88 × 103 | 1.40 × 103 | 1.44 × 103 | 7.13 × 102 | |
SD | 3.25 × 102 | 2.09 × 102 | 3.58 × 102 | 2.58 × 102 | 2.79 × 102 | 3.78 × 102 | 2.14 × 102 | 1.69 × 102 | 1.81 × 102 | ||
Min | 4.85 × 102 | 4.58 × 102 | 5.58 × 102 | 1.34 × 103 | 3.65 × 102 | 1.87 × 103 | 1.02 × 103 | 9.59 × 102 | 6.28 × 102 | ||
Rank | 10 | (w/l/t) | 0/10/0 | 0/10/0 | 0/10/0 | 0/10/0 | 0/10/0 | 0/10/0 | 0/10/0 | 0/10/0 | 10/0/0 |
30 | (w/l/t) | 0/10/0 | 1/9/0 | 0/10/0 | 0/10/0 | 0/10/0 | 0/10/0 | 0/10/0 | 0/10/0 | 9/1/0 | |
50 | (w/l/t) | 0/10/0 | 1/9/0 | 0/10/0 | 0/10/0 | 0/10/0 | 0/10/0 | 0/10/0 | 0/10/0 | 9/1/0 |
Func | Dim | Metric | KH (2012) | GWO (2014) | MFO (2015) | WOA (2016) | SSA (2017) | BOA (2019) | HGSO (2019) | AOA (2020) | MTV-MFO |
---|---|---|---|---|---|---|---|---|---|---|---|
Func 21 | 10 | Avg | 1.28 × 102 | 1.96 × 102 | 1.89 × 102 | 2.35 × 102 | 1.31 × 102 | 2.85 × 102 | 1.52 × 102 | 1.54 × 102 | 1.33 × 102 |
SD | 4.69 × 101 | 4.12 × 101 | 6.00 × 101 | 4.85 × 101 | 5.09 × 101 | 4.92 × 101 | 3.81 × 101 | 3.05 × 101 | 5.20 × 101 | ||
Min | 1.01 × 102 | 1.01 × 102 | 1.00 × 102 | 1.05 × 102 | 1.00 × 102 | 1.54 × 102 | 1.12 × 102 | 1.12 × 102 | 1.00 × 102 | ||
30 | Avg | 3.12 × 102 | 2.81 × 102 | 3.73 × 102 | 4.52 × 102 | 3.16 × 102 | 7.18 × 102 | 4.67 × 102 | 3.88 × 102 | 2.65 × 102 | |
SD | 2.18 × 101 | 1.64 × 101 | 3.93 × 101 | 7.32 × 101 | 2.95 × 101 | 5.18 × 101 | 2.50 × 101 | 1.53 × 101 | 1.78 × 101 | ||
Min | 2.69 × 102 | 2.61 × 102 | 2.89 × 102 | 3.38 × 102 | 2.61 × 102 | 6.41 × 102 | 3.98 × 102 | 3.36 × 102 | 2.35 × 102 | ||
50 | Avg | 4.39 × 102 | 3.75 × 102 | 6.27 × 102 | 7.47 × 102 | 4.30 × 102 | 1.27 × 103 | 8.20 × 102 | 4.60 × 102 | 3.25 × 102 | |
SD | 3.34 × 101 | 3.03 × 101 | 5.49 × 101 | 9.57 × 101 | 4.76 × 101 | 6.05 × 101 | 3.33 × 101 | 9.51 × 101 | 2.02 × 101 | ||
Min | 3.66 × 102 | 3.24 × 102 | 5.11 × 102 | 6.04 × 102 | 3.65 × 102 | 1.12 × 103 | 7.44 × 102 | 3.22 × 102 | 2.75 × 102 | ||
Func 22 | 10 | Avg | 9.44 × 101 | 1.06 × 102 | 9.73 × 101 | 1.34 × 102 | 8.82 × 101 | 1.08 × 103 | 1.83 × 102 | 1.35 × 102 | 9.03 × 101 |
SD | 2.30 × 101 | 7.39 × 100 | 2.68 × 101 | 1.01 × 102 | 3.27 × 101 | 2.63 × 102 | 3.56 × 101 | 2.95 × 101 | 2.68 × 101 | ||
Min | 2.03 × 101 | 1.01 × 102 | 3.43 × 101 | 3.16 × 101 | 2.24 × 10−5 | 5.84 × 102 | 9.47 × 101 | 1.08 × 102 | 2.44 × 101 | ||
30 | Avg | 1.00 × 102 | 2.05 × 103 | 2.82 × 103 | 3.64 × 103 | 1.49 × 103 | 8.62 × 103 | 1.72 × 103 | 5.79 × 103 | 1.01 × 102 | |
SD | 5.08 × 10−1 | 1.55 × 103 | 1.91 × 103 | 2.37 × 103 | 2.00 × 103 | 7.63 × 102 | 3.65 × 102 | 1.12 × 103 | 1.15 × 100 | ||
Min | 1.00 × 102 | 2.43 × 102 | 2.16 × 102 | 1.12 × 102 | 1.00 × 102 | 7.01 × 103 | 9.08 × 102 | 2.95 × 103 | 1.00 × 102 | ||
50 | Avg | 8.21 × 103 | 6.15 × 103 | 8.23 × 103 | 9.35 × 103 | 7.05 × 103 | 1.60 × 104 | 9.30 × 103 | 1.34 × 104 | 6.07 × 103 | |
SD | 9.28 × 102 | 7.59 × 102 | 7.07 × 102 | 1.25 × 103 | 1.58 × 103 | 5.51 × 102 | 2.48 × 103 | 7.32 × 102 | 5.91 × 102 | ||
Min | 6.04 × 103 | 4.79 × 103 | 7.29 × 103 | 6.69 × 103 | 5.10 × 103 | 1.51 × 104 | 5.41 × 103 | 1.15 × 104 | 4.51 × 103 | ||
Func 23 | 10 | Avg | 3.33 × 102 | 3.13 × 102 | 3.24 × 102 | 3.42 × 102 | 3.18 × 102 | 4.79 × 102 | 3.68 × 102 | 3.36 × 102 | 3.09 × 102 |
SD | 1.04 × 101 | 8.44 × 100 | 7.97 × 100 | 1.37 × 101 | 8.66 × 100 | 4.84 × 101 | 1.05 × 101 | 5.64 × 100 | 2.12 × 100 | ||
Min | 3.12 × 102 | 3.04 × 102 | 3.12 × 102 | 3.19 × 102 | 3.04 × 102 | 3.98 × 102 | 3.47 × 102 | 3.26 × 102 | 3.05 × 102 | ||
30 | Avg | 5.90 × 102 | 4.31 × 102 | 5.01 × 102 | 7.02 × 102 | 4.53 × 102 | 1.37 × 103 | 7.85 × 102 | 5.73 × 102 | 4.19 × 102 | |
SD | 5.56 × 101 | 3.57 × 101 | 3.29 × 101 | 6.65 × 101 | 3.26 × 101 | 1.56 × 102 | 4.75 × 101 | 3.13 × 101 | 1.50 × 101 | ||
Min | 4.87 × 102 | 3.94 × 102 | 4.38 × 102 | 5.70 × 102 | 3.97 × 102 | 1.05 × 103 | 6.96 × 102 | 4.79 × 102 | 3.87 × 102 | ||
50 | Avg | 1.06 × 103 | 6.10 × 102 | 8.18 × 102 | 1.30 × 103 | 6.56 × 102 | 2.63 × 103 | 1.35 × 103 | 7.81 × 102 | 5.78 × 102 | |
SD | 1.02 × 102 | 3.56 × 101 | 5.94 × 101 | 1.53 × 102 | 5.69 × 101 | 1.58 × 102 | 1.27 × 102 | 1.07 × 102 | 2.24 × 101 | ||
Min | 8.62 × 102 | 5.39 × 102 | 7.29 × 102 | 1.04 × 103 | 5.43 × 102 | 2.36 × 103 | 1.07 × 103 | 6.43 × 102 | 5.30 × 102 | ||
Func 24 | 10 | Avg | 2.61 × 102 | 3.44 × 102 | 3.61 × 102 | 3.57 × 102 | 3.10 × 102 | 5.09 × 102 | 1.65 × 102 | 2.94 × 102 | 2.91 × 102 |
SD | 1.22 × 102 | 9.49 × 100 | 1.01 × 101 | 9.78 × 101 | 9.11 × 101 | 4.69 × 101 | 5.18 × 101 | 7.80 × 101 | 9.80 × 101 | ||
Min | 1.00 × 102 | 3.32 × 102 | 3.43 × 102 | 5.49 × 101 | 1.00 × 102 | 4.19 × 102 | 1.32 × 102 | 1.70 × 102 | 1.00 × 102 | ||
30 | Avg | 6.99 × 102 | 5.34 × 102 | 5.72 × 102 | 7.69 × 102 | 5.12 × 102 | 1.59 × 103 | 8.66 × 102 | 6.22 × 102 | 4.81 × 102 | |
SD | 7.24 × 101 | 6.84 × 101 | 2.46 × 101 | 9.04 × 101 | 2.59 × 101 | 1.96 × 102 | 6.21 × 101 | 4.43 × 101 | 1.23 × 101 | ||
Min | 5.79 × 102 | 4.64 × 102 | 5.35 × 102 | 6.06 × 102 | 4.63 × 102 | 1.21 × 103 | 7.66 × 102 | 5.23 × 102 | 4.55 × 102 | ||
50 | Avg | 1.23 × 103 | 6.90 × 102 | 8.06 × 102 | 1.27 × 103 | 7.09 × 102 | 2.87 × 103 | 1.53 × 103 | 1.02 × 103 | 6.49 × 102 | |
SD | 1.45 × 102 | 8.60 × 101 | 4.80 × 101 | 1.51 × 102 | 5.37 × 101 | 2.84 × 102 | 1.18 × 102 | 5.64 × 101 | 2.59 × 101 | ||
Min | 1.04 × 103 | 6.07 × 102 | 7.36 × 102 | 1.03 × 103 | 6.16 × 102 | 2.12 × 103 | 1.26 × 103 | 8.81 × 102 | 5.87 × 102 | ||
Func 25 | 10 | Avg | 4.29 × 102 | 4.34 × 102 | 4.39 × 102 | 4.45 × 102 | 4.22 × 102 | 1.09 × 103 | 4.50 × 102 | 4.52 × 102 | 4.03 × 102 |
SD | 2.26 × 101 | 2.08 × 101 | 2.50 × 101 | 2.01 × 101 | 2.38 × 101 | 1.50 × 102 | 1.14 × 101 | 2.67 × 100 | 1.39 × 101 | ||
Min | 3.98 × 102 | 3.98 × 102 | 3.98 × 102 | 3.99 × 102 | 3.98 × 102 | 7.41 × 102 | 4.24 × 102 | 4.46 × 102 | 3.98 × 102 | ||
30 | Avg | 4.20 × 102 | 4.49 × 102 | 7.07 × 102 | 4.46 × 102 | 4.06 × 102 | 3.56 × 103 | 8.20 × 102 | 5.02 × 102 | 3.87 × 102 | |
SD | 2.08 × 101 | 2.59 × 101 | 2.90 × 102 | 2.70 × 101 | 2.20 × 101 | 5.12 × 102 | 6.48 × 101 | 1.46 × 101 | 1.37 × 100 | ||
Min | 3.89 × 102 | 4.06 × 102 | 3.89 × 102 | 3.94 × 102 | 3.83 × 102 | 2.79 × 103 | 7.08 × 102 | 4.63 × 102 | 3.83 × 102 | ||
50 | Avg | 5.91 × 102 | 8.83 × 102 | 2.16 × 103 | 6.22 × 102 | 5.25 × 102 | 1.46 × 104 | 3.94 × 103 | 8.21 × 102 | 5.06 × 102 | |
SD | 2.42 × 101 | 1.88 × 102 | 1.38 × 103 | 4.54 × 101 | 3.86 × 101 | 1.42 × 103 | 5.48 × 102 | 5.54 × 101 | 3.79 × 101 | ||
Min | 5.36 × 102 | 7.03 × 102 | 5.52 × 102 | 5.26 × 102 | 4.60 × 102 | 1.19 × 104 | 2.80 × 103 | 7.56 × 102 | 4.59 × 102 | ||
Func 26 | 10 | Avg | 4.13 × 102 | 3.24 × 102 | 3.73 × 102 | 7.44 × 102 | 2.95 × 102 | 1.63 × 103 | 5.54 × 102 | 5.66 × 102 | 3.00 × 102 |
SD | 2.84 × 102 | 5.97 × 101 | 4.49 × 101 | 4.51 × 102 | 7.38 × 101 | 3.64 × 102 | 6.25 × 101 | 1.14 × 102 | 0 | ||
Min | 4.90 × 10−3 | 3.00 × 102 | 3.00 × 102 | 2.03 × 102 | 3.37 × 10−4 | 8.94 × 102 | 4.48 × 102 | 3.24 × 102 | 3.00 × 102 | ||
30 | Avg | 3.28 × 103 | 1.77 × 103 | 2.81 × 103 | 4.95 × 103 | 1.58 × 103 | 1.04 × 104 | 4.44 × 103 | 3.62 × 103 | 1.91 × 103 | |
SD | 1.39 × 103 | 2.25 × 102 | 4.01 × 102 | 1.15 × 103 | 1.08 × 103 | 9.77 × 102 | 3.72 × 102 | 5.22 × 102 | 2.31 × 102 | ||
Min | 2.00 × 102 | 1.45 × 103 | 2.22 × 103 | 1.63 × 103 | 2.00 × 102 | 8.13 × 103 | 3.73 × 103 | 2.83 × 103 | 1.44 × 103 | ||
50 | Avg | 7.40 × 103 | 3.27 × 103 | 5.34 × 103 | 1.09 × 104 | 2.08 × 103 | 1.61 × 104 | 8.64 × 103 | 6.53 × 103 | 2.95 × 103 | |
SD | 8.69 × 102 | 5.35 × 102 | 5.75 × 102 | 1.51 × 103 | 1.88 × 103 | 7.06 × 102 | 1.11 × 103 | 9.53 × 102 | 3.20 × 102 | ||
Min | 5.58 × 103 | 2.71 × 103 | 4.61 × 103 | 7.89 × 103 | 3.00 × 102 | 1.47 × 104 | 7.24 × 103 | 4.23 × 103 | 2.36 × 103 | ||
Func 27 | 10 | Avg | 4.27 × 102 | 3.95 × 102 | 3.93 × 102 | 4.24 × 102 | 3.95 × 102 | 5.72 × 102 | 4.22 × 102 | 4.15 × 102 | 3.92 × 102 |
SD | 2.64 × 101 | 4.00 × 100 | 2.30 × 100 | 3.57 × 101 | 1.55 × 101 | 5.52 × 101 | 1.26 × 101 | 1.89 × 101 | 2.20 × 100 | ||
Min | 3.95 × 102 | 3.90 × 102 | 3.90 × 102 | 3.94 × 102 | 3.89 × 102 | 4.69 × 102 | 4.06 × 102 | 3.96 × 102 | 3.89 × 102 | ||
30 | Avg | 7.05 × 102 | 5.30 × 102 | 5.37 × 102 | 6.40 × 102 | 5.33 × 102 | 2.12 × 103 | 5.00 × 102 | 5.00 × 102 | 5.13 × 102 | |
SD | 8.40 × 101 | 1.32 × 101 | 2.02 × 101 | 7.23 × 101 | 1.21 × 101 | 3.77 × 102 | 8.23 × 10−5 | 1.72 × 10−4 | 1.00 × 101 | ||
Min | 5.75 × 102 | 5.09 × 102 | 5.10 × 102 | 5.40 × 102 | 5.12 × 102 | 1.49 × 103 | 5.00 × 102 | 5.00 × 102 | 4.89 × 102 | ||
50 | Avg | 1.70 × 103 | 7.93 × 102 | 8.26 × 102 | 1.40 × 103 | 6.94 × 102 | 5.14 × 103 | 5.00 × 102 | 5.00 × 102 | 7.15 × 102 | |
SD | 2.96 × 102 | 7.05 × 101 | 1.05 × 102 | 2.37 × 102 | 7.10 × 101 | 5.76 × 102 | 1.60 × 10−4 | 2.29 × 10−4 | 5.11 × 101 | ||
Min | 1.30 × 103 | 6.32 × 102 | 6.46 × 102 | 9.83 × 102 | 5.84 × 102 | 4.02 × 103 | 5.00 × 102 | 5.00 × 102 | 6.18 × 102 | ||
Func 28 | 10 | Avg | 4.60 × 102 | 5.37 × 102 | 5.06 × 102 | 4.79 × 102 | 4.91 × 102 | 9.94 × 102 | 4.77 × 102 | 4.94 × 102 | 3.00 × 102 |
SD | 1.43 × 102 | 9.79 × 101 | 9.75 × 101 | 1.08 × 102 | 1.62 × 102 | 1.47 × 102 | 5.30 × 101 | 7.03 × 100 | 0 | ||
Min | 3.00 × 102 | 3.68 × 102 | 3.69 × 102 | 3.01 × 102 | 3.00 × 102 | 7.45 × 102 | 3.99 × 102 | 4.82 × 102 | 3.00 × 102 | ||
30 | Avg | 4.47 × 102 | 5.38 × 102 | 1.30 × 103 | 4.94 × 102 | 4.09 × 102 | 5.32 × 103 | 9.19 × 102 | 5.00 × 102 | 3.15 × 102 | |
SD | 2.66 × 101 | 6.17 × 101 | 7.91 × 102 | 2.63 × 101 | 3.35 × 101 | 7.82 × 102 | 4.56 × 102 | 1.94 × 10−4 | 3.78 × 101 | ||
Min | 3.95 × 102 | 4.65 × 102 | 5.70 × 102 | 4.38 × 102 | 3.10 × 102 | 3.25 × 103 | 5.00 × 102 | 5.00 × 102 | 3.00 × 102 | ||
50 | Avg | 5.40 × 102 | 1.15 × 103 | 4.94 × 103 | 6.38 × 102 | 4.89 × 102 | 1.17 × 104 | 3.46 × 103 | 1.20 × 103 | 4.77 × 102 | |
SD | 3.87 × 101 | 3.54 × 102 | 1.43 × 103 | 6.42 × 101 | 2.05 × 101 | 1.38 × 103 | 1.60 × 103 | 4.34 × 102 | 1.85 × 101 | ||
Min | 4.81 × 102 | 6.53 × 102 | 7.90 × 102 | 5.70 × 102 | 4.61 × 102 | 7.14 × 103 | 5.00 × 102 | 5.00 × 102 | 4.53 × 102 | ||
Func 29 | 10 | Avg | 3.26 × 102 | 2.72 × 102 | 2.96 × 102 | 4.23 × 102 | 2.69 × 102 | 6.86 × 102 | 3.44 × 102 | 3.34 × 102 | 2.51 × 102 |
SD | 5.02 × 101 | 1.74 × 101 | 5.04 × 101 | 7.65 × 101 | 3.01 × 101 | 1.30 × 102 | 2.14 × 101 | 2.03 × 101 | 1.25 × 101 | ||
Min | 2.64 × 102 | 2.50 × 102 | 2.37 × 102 | 3.16 × 102 | 2.40 × 102 | 3.94 × 102 | 2.99 × 102 | 2.92 × 102 | 2.31 × 102 | ||
30 | Avg | 1.28 × 103 | 7.57 × 102 | 1.11 × 103 | 1.88 × 103 | 1.09 × 103 | 6.13 × 103 | 1.37 × 103 | 7.43 × 102 | 7.52 × 102 | |
SD | 2.81 × 102 | 1.40 × 102 | 2.65 × 102 | 2.93 × 102 | 1.76 × 102 | 2.51 × 103 | 2.62 × 102 | 1.88 × 102 | 1.24 × 102 | ||
Min | 6.77 × 102 | 5.61 × 102 | 7.23 × 102 | 1.35 × 103 | 7.77 × 102 | 2.69 × 103 | 1.02 × 103 | 4.45 × 102 | 5.31 × 102 | ||
50 | Avg | 2.40 × 103 | 1.33 × 103 | 2.20 × 103 | 4.02 × 103 | 1.80 × 103 | 1.30 × 105 | 3.84 × 103 | 1.26 × 103 | 1.13 × 103 | |
SD | 5.31 × 102 | 2.91 × 102 | 2.89 × 102 | 7.43 × 102 | 2.33 × 102 | 8.23 × 104 | 1.10 × 103 | 4.41 × 102 | 2.16 × 102 | ||
Min | 1.62 × 103 | 7.63 × 102 | 1.69 × 103 | 2.35 × 103 | 1.30 × 103 | 3.08 × 104 | 2.22 × 103 | 6.05 × 102 | 6.21 × 102 | ||
Func 30 | 10 | Avg | 1.04 × 106 | 7.62 × 105 | 2.95 × 105 | 6.44 × 105 | 1.64 × 105 | 3.99 × 107 | 5.53 × 104 | 1.31 × 105 | 5.04 × 102 |
SD | 1.64 × 106 | 1.06 × 106 | 3.66 × 105 | 6.32 × 105 | 4.66 × 105 | 3.03 × 107 | 1.10 × 105 | 2.21 × 105 | 8.47 × 101 | ||
Min | 1.40 × 104 | 4.39 × 103 | 1.46 × 103 | 1.81 × 104 | 3.87 × 103 | 1.60 × 106 | 2.92 × 102 | 2.85 × 102 | 3.95 × 102 | ||
30 | Avg | 1.91 × 106 | 6.01 × 106 | 9.35 × 105 | 9.31 × 106 | 1.47 × 106 | 1.62 × 109 | 7.45 × 107 | 3.13 × 103 | 4.09 × 103 | |
SD | 1.49 × 106 | 7.61 × 106 | 1.76 × 106 | 6.55 × 106 | 1.06 × 106 | 8.17 × 108 | 1.98 × 107 | 1.86 × 103 | 1.15 × 103 | ||
Min | 1.72 × 105 | 3.18 × 105 | 1.28 × 104 | 1.05 × 106 | 4.04 × 105 | 5.62 × 108 | 4.06 × 107 | 2.99 × 102 | 2.44 × 103 | ||
50 | Avg | 4.48 × 107 | 6.99 × 107 | 6.59 × 107 | 9.07 × 107 | 2.71 × 107 | 8.72 × 109 | 5.84 × 108 | 6.34 × 103 | 7.58 × 105 | |
SD | 2.13 × 107 | 1.99 × 107 | 1.33 × 108 | 3.26 × 107 | 5.80 × 106 | 2.12 × 109 | 1.37 × 108 | 2.70 × 103 | 1.07 × 105 | ||
Min | 1.87 × 107 | 3.55 × 107 | 4.99 × 106 | 3.51 × 107 | 1.94 × 107 | 5.31 × 109 | 3.74 × 108 | 1.86 × 103 | 6.18 × 105 | ||
Rank | 10 | (w/l/t) | 1/9/0 | 0/10/0 | 0/10/0 | 0/10/0 | 2/8/0 | 0/10/0 | 1/9/0 | 0/10/0 | 6/4/0 |
30 | (w/l/t) | 1/9/0 | 0/10/0 | 0/10/0 | 0/10/0 | 1/9/0 | 0/10/0 | 0/9/1 | 2/7/1 | 5/4/1 | |
50 | (w/l/t) | 0/10/0 | 0/10/0 | 0/10/0 | 0/10/0 | 1/9/0 | 0/10/0 | 0/9/1 | 1/8/1 | 7/3/0 |
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Parameter | Description |
---|---|
M, F | The moths and flames’ position matrixes |
ImpRateMFO-TVP, ImpRateF-TVP, ImpRateC-TVP | The improved rate of MFO-TVP, F-TVP, and C-TVP |
NMFO-TVP, NF-TVP, NC-TVP | The portion size of MFO-TVP, F-TVP, and C-TVP |
MMFO-TVP, MF-TVP, MC-TVP | The sub-population of each TVP |
XInfSolution, XInfCandidate | The archive of inferior and candidate solutions |
XAll | The union population of XInfSolution, XInfCandidate, and M |
Algorithms | Parameters Values |
---|---|
KH | Vf = 0.02, Dmax = 0.005, Nmax = 0.01 |
GWO, WOA | a = [2 0] |
SSA | c2,c3 = random numbers in [0, 1] |
BOA | p = 0.8, a = [0.1 0.3], c = 0.01 |
HGSO | Cluster number = 5, M1 = 0.1, M2 = 0.2, α =β = K = 1, l1 = 0.005, l2 = 100, l3 = 0.01 β |
AOA | u = 0.9, l = 0.1, C1 = 2, C2 = 6, C3 = 1, C4 = 2 |
MTV-MFO | nIter = 20 |
Dim | Metric | KH (2012) | GWO (2014) | MFO (2015) | WOA (2016) | SSA (2017) | BOA (2019) | HGSO (2019) | AOA (2020) | MTV-MFO | |
---|---|---|---|---|---|---|---|---|---|---|---|
Overall results | 10 | (w/l/t) | 0/2/0 | 0/2/0 | 0/2/0 | 0/2/0 | 0/2/0 | 0/2/0 | 0/2/0 | 0/2/0 | 2/0/0 |
30 | (w/l/t) | 0/2/0 | 0/2/0 | 0/2/0 | 0/2/0 | 0/2/0 | 0/2/0 | 0/2/0 | 0/2/0 | 2/0/0 | |
50 | (w/l/t) | 0/2/0 | 0/2/0 | 0/2/0 | 0/2/0 | 0/2/0 | 0/2/0 | 0/2/0 | 0/2/0 | 2/0/0 |
Dim | Metric | KH (2012) | GWO (2014) | MFO (2015) | WOA (2016) | SSA (2017) | BOA (2019) | HGSO (2019) | AOA (2020) | MTV-MFO | |
---|---|---|---|---|---|---|---|---|---|---|---|
Overall results | 10 | (w/l/t) | 0/7/0 | 0/7/0 | 0/7/0 | 0/7/0 | 0/7/0 | 0/7/0 | 0/7/0 | 0/7/0 | 7/0/0 |
30 | (w/l/t) | 0/7/0 | 0/7/0 | 0/7/0 | 0/7/0 | 0/7/0 | 0/7/0 | 0/7/0 | 0/7/0 | 7/0/0 | |
50 | (w/l/t) | 0/7/0 | 0/7/0 | 0/7/0 | 0/7/0 | 0/7/0 | 0/7/0 | 0/7/0 | 0/7/0 | 7/0/0 |
Dim | Metric | KH (2012) | GWO (2014) | MFO (2015) | WOA (2016) | SSA (2017) | BOA (2019) | HGSO (2019) | AOA (2020) | MTV-MFO | |
---|---|---|---|---|---|---|---|---|---|---|---|
Overall results | 10 | (w/l/t) | 0/10/0 | 0/10/0 | 0/10/0 | 0/10/0 | 0/10/0 | 0/10/0 | 0/10/0 | 0/10/0 | 10/0/0 |
30 | (w/l/t) | 0/10/0 | 1/9/0 | 0/10/0 | 0/10/0 | 0/10/0 | 0/10/0 | 0/10/0 | 0/10/0 | 9/1/0 | |
50 | (w/l/t) | 0/10/0 | 1/9/0 | 0/10/0 | 0/10/0 | 0/10/0 | 0/10/0 | 0/10/0 | 0/10/0 | 9/1/0 |
Dim | Metric | KH (2012) | GWO (2014) | MFO (2015) | WOA 2016) | SSA (2017) | BOA (2019) | HGSO (2019) | AOA (2020) | MTV-MFO | |
---|---|---|---|---|---|---|---|---|---|---|---|
Overall results | 10 | (w/l/t) | 1/9/0 | 0/10/0 | 0/10/0 | 0/10/0 | 2/8/0 | 0/10/0 | 1/9/0 | 0/10/0 | 6/4/0 |
30 | (w/l/t) | 1/9/0 | 0/10/0 | 0/10/0 | 0/10/0 | 1/9/0 | 0/10/0 | 0/9/1 | 2/7/1 | 5/4/1 | |
50 | (w/l/t) | 0/10/0 | 0/10/0 | 0/10/0 | 0/10/0 | 1/9/0 | 0/10/0 | 0/9/1 | 1/8/1 | 7/3/0 |
KH | GWO | MFO | WOA | SSA | BOA | HGSO | AOA | MTV-MFO | |
---|---|---|---|---|---|---|---|---|---|
Dim = 10 | 1/28/0 | 0/29/0 | 0/29/0 | 0/29/0 | 2/27/0 | 0/29/0 | 1/28/0 | 0/29/0 | 25/4/0 |
Dim = 30 | 1/28/0 | 1/28/0 | 0/29/0 | 0/29/0 | 1/28/0 | 0/29/0 | 0/28/1 | 2/26/3 | 23/5/1 |
Dim = 50 | 0/29/0 | 1/28/0 | 0/29/0 | 0/29/0 | 1/28/0 | 0/29/0 | 0/28/1 | 1/27/1 | 25/4/0 |
Total (w/l/t) | 2/85/0 | 2/85/0 | 0/87/0 | 0/87/0 | 4/83/0 | 0/87/0 | 1/84/2 | 3/82/4 | 73/13/1 |
OE | 2.29% | 2.29% | 0% | 0% | 4.59% | 0% | 3.44% | 5.74% | 85.05% |
Algorithm | Dim | F1 | F3 | F4 | F5 | F6 | F7 | F8 | F9 | F10 | F11 | F12 | F13 | F14 | F15 | F16 | F17 |
KH | 10 | 2.35 | 5.60 | 4.00 | 5.00 | 4.95 | 2.10 | 3.50 | 3.45 | 5.00 | 3.85 | 5.10 | 4.90 | 5.40 | 6.35 | 8.00 | 4.55 |
30 | 2.85 | 5.85 | 2.80 | 3.70 | 5.40 | 2.45 | 3.15 | 4.80 | 4.00 | 4.45 | 3.40 | 2.90 | 5.95 | 3.60 | 3.95 | 4.15 | |
50 | 3.00 | 5.35 | 3.25 | 3.90 | 5.65 | 3.20 | 4.60 | 4.55 | 4.50 | 5.50 | 2.45 | 3.25 | 4.50 | 2.90 | 4.20 | 5.55 | |
GWO | 10 | 5.10 | 4.75 | 4.75 | 2.05 | 3.70 | 3.05 | 2.10 | 4.45 | 2.35 | 2.65 | 3.65 | 3.90 | 4.60 | 4.35 | 3.50 | 3.90 |
30 | 6.10 | 3.55 | 5.15 | 2.25 | 2.25 | 2.90 | 1.65 | 2.15 | 2.25 | 3.10 | 5.60 | 5.45 | 4.10 | 4.90 | 1.75 | 2.25 | |
50 | 6.00 | 3.40 | 5.70 | 2.25 | 1.95 | 2.80 | 2.60 | 2.50 | 2.25 | 4.10 | 6.15 | 5.85 | 4.40 | 5.80 | 2.10 | 2.35 | |
MFO | 10 | 3.90 | 5.03 | 3.65 | 4.05 | 2.50 | 4.55 | 5.25 | 3.38 | 3.55 | 3.60 | 2.30 | 4.60 | 6.25 | 4.95 | 3.95 | 3.55 |
30 | 6.85 | 7.20 | 6.70 | 5.10 | 4.75 | 5.75 | 5.35 | 6.50 | 4.40 | 7.00 | 5.55 | 4.65 | 4.40 | 4.65 | 5.05 | 6.35 | |
50 | 7.45 | 7.35 | 7.00 | 6.75 | 4.75 | 7.90 | 6.35 | 6.60 | 5.00 | 6.40 | 6.75 | 6.55 | 4.50 | 6.15 | 6.65 | 7.20 | |
WOA | 10 | 5.65 | 4.00 | 5.75 | 6.50 | 8.25 | 7.65 | 7.65 | 8.55 | 5.10 | 5.60 | 5.80 | 5.85 | 5.25 | 5.90 | 5.65 | 6.50 |
30 | 4.10 | 8.45 | 5.60 | 7.15 | 8.20 | 7.80 | 6.60 | 7.75 | 5.75 | 4.50 | 6.05 | 5.55 | 6.70 | 6.40 | 6.55 | 6.55 | |
50 | 4.00 | 6.55 | 3.05 | 3.80 | 7.20 | 5.20 | 3.20 | 3.20 | 2.10 | 2.60 | 4.35 | 4.80 | 4.55 | 5.50 | 4.85 | 1.45 | |
SSA | 10 | 3.05 | 2.40 | 2.70 | 3.50 | 5.10 | 4.65 | 3.60 | 3.35 | 5.15 | 5.40 | 4.70 | 5.00 | 3.45 | 3.55 | 3.95 | 4.50 |
30 | 2.20 | 2.00 | 2.55 | 3.25 | 4.85 | 3.45 | 3.75 | 4.30 | 3.10 | 2.20 | 2.95 | 5.25 | 2.25 | 5.45 | 3.30 | 3.30 | |
50 | 1.60 | 2.00 | 2.70 | 4.60 | 4.65 | 2.75 | 4.40 | 5.15 | 4.25 | 2.25 | 3.50 | 4.65 | 2.40 | 4.25 | 3.45 | 4.25 | |
BOA | 10 | 9.00 | 8.90 | 9.00 | 8.85 | 8.20 | 8.50 | 8.65 | 8.15 | 8.55 | 8.00 | 8.65 | 8.10 | 8.20 | 8.55 | 7.50 | 8.30 |
30 | 9.00 | 6.90 | 9.00 | 8.90 | 8.15 | 8.90 | 8.90 | 8.60 | 8.95 | 8.55 | 9.00 | 9.00 | 5.95 | 8.95 | 9.00 | 9.00 | |
50 | 9.00 | 8.05 | 9.00 | 8.95 | 8.50 | 8.55 | 9.00 | 8.95 | 8.70 | 8.85 | 9.00 | 9.00 | 8.60 | 9.00 | 9.00 | 9.00 | |
HGSO | 10 | 8.00 | 6.00 | 7.65 | 7.70 | 7.35 | 7.65 | 6.95 | 7.15 | 7.75 | 6.70 | 7.65 | 6.45 | 6.60 | 6.45 | 6.75 | 6.80 |
30 | 7.80 | 4.80 | 7.90 | 7.75 | 7.60 | 6.95 | 7.70 | 6.70 | 6.70 | 7.70 | 8.00 | 8.00 | 7.25 | 8.05 | 7.60 | 7.10 | |
50 | 7.55 | 6.60 | 7.95 | 7.85 | 8.25 | 7.40 | 7.95 | 8.05 | 7.05 | 6.35 | 8.00 | 7.90 | 7.10 | 7.95 | 7.65 | 7.30 | |
AOA | 10 | 6.95 | 7.30 | 6.50 | 5.95 | 3.80 | 5.00 | 4.90 | 5.25 | 5.85 | 8.15 | 6.15 | 5.20 | 4.25 | 3.90 | 4.70 | 5.85 |
30 | 5.10 | 5.25 | 4.30 | 5.85 | 2.80 | 5.25 | 6.20 | 3.05 | 7.95 | 6.40 | 3.45 | 3.20 | 7.40 | 2.00 | 5.90 | 4.40 | |
50 | 5.00 | 4.70 | 5.25 | 5.70 | 2.95 | 5.55 | 5.80 | 5.00 | 8.25 | 7.75 | 3.80 | 2.00 | 7.95 | 2.45 | 3.90 | 5.40 | |
MTV-MFO | 10 | 1.00 | 1.02 | 1.00 | 1.40 | 1.15 | 1.85 | 2.40 | 1.27 | 1.70 | 1.05 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.05 |
30 | 1.00 | 1.00 | 1.00 | 1.05 | 1.00 | 1.55 | 1.70 | 1.15 | 1.90 | 1.10 | 1.00 | 1.00 | 1.00 | 1.00 | 1.90 | 1.90 | |
50 | 1.40 | 1.00 | 1.10 | 1.20 | 1.10 | 1.65 | 1.10 | 1.00 | 2.90 | 1.20 | 1.00 | 1.00 | 1.00 | 1.00 | 3.20 | 2.50 | |
Algorithm | Dim | F18 | F19 | F20 | F21 | F22 | F23 | F24 | F25 | F26 | F27 | F28 | F29 | F30 | Avg. Rank | Overall Rank | |
KH | 10 | 4.15 | 4.30 | 6.85 | 3.65 | 2.50 | 5.30 | 4.30 | 3.25 | 4.20 | 7.25 | 4.60 | 5.45 | 6.45 | 4.70 | 5 | |
30 | 3.70 | 4.10 | 5.15 | 4.15 | 2.25 | 5.60 | 6.25 | 3.20 | 5.30 | 7.90 | 3.00 | 5.65 | 4.65 | 4.29 | 4 | ||
50 | 5.00 | 3.25 | 5.80 | 4.35 | 5.80 | 7.00 | 7.15 | 4.00 | 7.00 | 8.00 | 4.10 | 6.25 | 5.60 | 4.82 | 5 | ||
GWO | 10 | 5.95 | 4.20 | 4.55 | 6.15 | 4.15 | 2.05 | 5.45 | 3.85 | 4.10 | 3.35 | 6.40 | 2.80 | 5.85 | 4.06 | 3 | |
30 | 4.60 | 4.60 | 3.15 | 2.80 | 5.40 | 1.75 | 2.75 | 4.65 | 1.90 | 4.80 | 5.55 | 2.25 | 5.60 | 3.63 | 3 | ||
50 | 5.00 | 5.25 | 2.40 | 2.60 | 3.10 | 2.25 | 2.40 | 5.65 | 2.45 | 6.15 | 5.80 | 2.55 | 6.70 | 3.88 | 4 | ||
MFO | 10 | 5.00 | 5.90 | 3.65 | 6.28 | 3.60 | 3.95 | 7.50 | 5.10 | 4.10 | 2.45 | 5.65 | 4.05 | 5.20 | 4.40 | 4 | |
30 | 5.35 | 4.10 | 5.70 | 6.10 | 6.35 | 3.75 | 3.95 | 6.60 | 4.20 | 5.05 | 7.75 | 4.80 | 3.60 | 5.43 | 6 | ||
50 | 5.10 | 5.70 | 6.35 | 7.20 | 6.00 | 5.50 | 4.45 | 6.80 | 4.60 | 6.05 | 7.75 | 6.00 | 4.15 | 6.17 | 7 | ||
WOA | 10 | 4.10 | 7.30 | 7.10 | 8.20 | 6.25 | 6.50 | 7.75 | 6.25 | 7.10 | 6.45 | 5.05 | 8.35 | 6.70 | 6.44 | 7 | |
30 | 6.30 | 7.00 | 6.50 | 7.95 | 6.90 | 7.05 | 6.80 | 4.10 | 7.20 | 7.10 | 4.90 | 7.90 | 6.65 | 6.55 | 7 | ||
50 | 4.25 | 5.95 | 1.90 | 4.50 | 1.20 | 3.85 | 3.65 | 1.05 | 4.45 | 3.65 | 2.60 | 5.00 | 3.45 | 3.86 | 3 | ||
SSA | 10 | 5.70 | 3.40 | 4.60 | 3.70 | 3.60 | 3.35 | 5.40 | 3.50 | 2.90 | 2.35 | 4.65 | 2.70 | 4.40 | 3.94 | 2 | |
30 | 2.65 | 5.35 | 4.05 | 4.10 | 3.50 | 2.90 | 2.45 | 2.15 | 2.30 | 4.85 | 2.15 | 4.80 | 4.50 | 3.44 | 2 | ||
50 | 2.35 | 4.75 | 3.65 | 4.05 | 4.20 | 3.25 | 2.95 | 2.75 | 2.00 | 4.30 | 2.40 | 4.40 | 5.10 | 3.55 | 2 | ||
BOA | 10 | 7.80 | 7.65 | 6.85 | 3.55 | 7.50 | 7.95 | 2.55 | 9.00 | 6.15 | 7.25 | 7.55 | 7.70 | 8.25 | 7.75 | 9 | |
30 | 7.50 | 8.95 | 8.40 | 2.25 | 4.65 | 8.60 | 9.00 | 9.00 | 8.95 | 8.95 | 9.00 | 9.00 | 9.00 | 8.28 | 9 | ||
50 | 8.85 | 8.95 | 8.95 | 8.00 | 6.65 | 8.85 | 9.00 | 9.00 | 9.00 | 9.00 | 9.00 | 9.00 | 9.00 | 8.77 | 9 | ||
HGSO | 10 | 8.10 | 6.10 | 6.60 | 5.45 | 8.35 | 8.75 | 2.25 | 6.05 | 7.50 | 7.15 | 4.65 | 6.30 | 3.45 | 6.70 | 8 | |
30 | 7.75 | 7.85 | 5.90 | 8.60 | 5.80 | 8.15 | 7.70 | 7.75 | 7.10 | 1.80 | 6.60 | 6.20 | 8.00 | 7.13 | 8 | ||
50 | 7.75 | 8.05 | 6.30 | 8.60 | 6.15 | 8.15 | 7.85 | 7.90 | 7.65 | 1.65 | 6.35 | 7.85 | 8.00 | 7.35 | 8 | ||
AOA | 10 | 3.20 | 5.15 | 3.75 | 5.50 | 6.95 | 5.65 | 5.85 | 6.50 | 7.65 | 6.50 | 5.45 | 6.05 | 3.25 | 5.56 | 6 | |
30 | 6.15 | 2.05 | 4.90 | 6.80 | 8.60 | 5.50 | 4.80 | 6.15 | 5.55 | 1.30 | 4.95 | 2.15 | 1.50 | 4.79 | 5 | ||
50 | 5.70 | 2.10 | 6.65 | 4.40 | 8.65 | 4.80 | 6.00 | 5.55 | 6.05 | 1.35 | 5.25 | 2.15 | 1.00 | 4.87 | 6 | ||
MTV-MFO | 10 | 1.00 | 1.00 | 1.05 | 2.52 | 2.10 | 1.50 | 3.95 | 1.50 | 1.30 | 2.25 | 1.00 | 1.60 | 1.45 | 1.45 | 1 | |
30 | 1.00 | 1.00 | 1.25 | 2.25 | 1.55 | 1.70 | 1.30 | 1.40 | 2.50 | 3.25 | 1.10 | 2.25 | 1.50 | 1.46 | 1 | ||
50 | 1.00 | 1.00 | 3.00 | 1.30 | 3.25 | 1.35 | 1.55 | 2.30 | 1.80 | 4.85 | 1.75 | 1.80 | 2.00 | 1.73 | 1 |
Algorithm | Dim | F1 | F3 | F4 | F5 | F6 | F7 | F8 | F9 | F10 | F11 | F12 | F13 | F14 | F15 |
KH | 10 | 4.18 | 3.55 | 10.90 | 9.85 | 3.55 | 1.95 | 3.39 | 1.67 | 8.94 | 7.19 | 5.24 | 6.75 | 2.47 | 3.81 |
30 | 4.91 | 14.40 | 21.20 | 10.10 | 17.40 | 2.93 | 7.40 | 14.00 | 4.94 | 7.82 | 7.16 | 9.09 | 3.37 | 11.40 | |
50 | 6.00 | 23.10 | 6.13 | 14.70 | 28.80 | 5.50 | 14.20 | 24.70 | 5.00 | 8.99 | 5.12 | 8.56 | 4.65 | 12.80 | |
GWO | 10 | 1.67 | 2.89 | 12.70 | 2.31 | 3.50 | 3.09 | −0.17 | 1.74 | 1.46 | 6.96 | 3.03 | 5.29 | 2.66 | 3.93 |
30 | 5.84 | 16.60 | 17.20 | 6.91 | 8.05 | 2.90 | 0.61 | 5.07 | 0.65 | 10.70 | 3.87 | 1.50 | 2.37 | 1.33 | |
50 | 10.10 | 19.60 | 9.64 | 3.79 | 6.07 | 2.83 | 7.47 | 4.51 | −1.85 | 4.86 | 3.34 | 3.48 | 2.86 | 2.47 | |
MFO | 10 | 1.00 | 2.75 | 9.18 | 13.30 | 2.69 | 6.18 | 5.09 | 1.11 | 5.34 | 3.49 | 1.07 | 3.85 | 4.14 | 4.33 |
30 | 5.22 | 8.49 | 5.69 | 18.60 | 8.65 | 7.50 | 11.10 | 13.10 | 5.75 | 4.14 | 2.60 | 1.77 | 3.51 | 4.08 | |
50 | 14.80 | 8.90 | 4.91 | 16.00 | 27.40 | 9.69 | 14.40 | 19.40 | 5.60 | 3.52 | 3.69 | 1.89 | 2.73 | 1.50 | |
WOA | 10 | 2.43 | 4.93 | 3.97 | 6.89 | 11.00 | 8.17 | 7.84 | 5.99 | 9.22 | 6.24 | 3.16 | 6.56 | 2.20 | 3.80 |
30 | 6.00 | 9.50 | 18.00 | 15.40 | 31.70 | 16.70 | 11.30 | 13.50 | 11.20 | 11.30 | 5.89 | 8.59 | 2.81 | 8.39 | |
50 | 6.00 | 9.50 | 7.99 | 9.20 | 27.20 | 8.96 | 6.56 | 10.40 | −3.12 | 8.04 | 5.89 | 8.40 | 2.81 | 8.35 | |
SSA | 10 | 4.80 | 11.80 | 11.50 | 4.15 | 3.78 | 5.66 | 2.83 | 1.19 | 7.29 | 5.06 | 2.79 | 4.95 | 9.82 | 4.32 |
30 | 3.65 | 14.60 | 22.50 | 8.94 | 10.50 | 6.94 | 6.62 | 7.50 | 3.57 | 6.40 | 3.95 | 6.69 | 5.42 | 7.13 | |
50 | 2.33 | 16.00 | 5.14 | 9.72 | 16.90 | 2.25 | 8.81 | 18.50 | 3.12 | 5.38 | 7.13 | 8.16 | 6.08 | 6.59 | |
BOA | 10 | 8.42 | 19.60 | 10.80 | 25.40 | 18.60 | 30.00 | 20.80 | 9.84 | 21.80 | 8.91 | 4.13 | 4.84 | 8.11 | 10.80 |
30 | 18.10 | 25.30 | 24.30 | 44.90 | 42.20 | 52.70 | 60.00 | 33.40 | 32.10 | 18.50 | 14.30 | 7.32 | 10.80 | 3.95 | |
50 | 43.00 | 48.70 | 42.80 | 57.50 | 46.90 | 38.20 | 66.50 | 48.90 | 57.10 | 44.40 | 15.90 | 12.60 | 4.39 | 9.11 | |
HGSO | 10 | 10.00 | 10.60 | 16.30 | 25.60 | 25.20 | 29.90 | 18.20 | 18.00 | 15.70 | 12.80 | 9.78 | 8.97 | 4.31 | 8.46 |
30 | 21.00 | 24.00 | 16.20 | 55.10 | 45.30 | 35.90 | 49.60 | 21.10 | 16.70 | 10.30 | 10.70 | 14.20 | 9.03 | 8.96 | |
50 | 20.60 | 73.90 | 19.00 | 48.30 | 63.00 | 30.10 | 58.40 | 50.90 | 34.30 | 16.80 | 18.00 | 10.80 | 11.90 | 18.80 | |
AOA | 10 | 13.20 | 7.92 | 5.68 | 15.20 | 9.66 | 13.30 | 9.88 | 6.28 | 9.69 | 8.79 | 6.98 | 19.30 | 3.50 | 4.65 |
30 | 9.02 | 18.50 | 28.40 | 34.50 | 14.70 | 27.30 | 36.30 | 11.00 | 18.20 | 10.70 | 10.40 | 5.75 | 7.27 | 5.51 | |
50 | 8.24 | 41.00 | 16.30 | 13.00 | 18.50 | 17.10 | 10.70 | 19.80 | 60.40 | 26.50 | 10.10 | 6.13 | 24.30 | 17.10 | |
Algorithm | Dim | F17 | F18 | F19 | F20 | F21 | F22 | F23 | F24 | F25 | F26 | F27 | F28 | F29 | F30 |
KH | 10 | 10.40 | 5.34 | 2.67 | 8.20 | −0.40 | 0.48 | 10.10 | −0.95 | 4.88 | 1.79 | 5.78 | 5.03 | 6.61 | 2.84 |
30 | 5.15 | 3.96 | 4.20 | 6.92 | 7.95 | −1.17 | 13.50 | 13.40 | 7.12 | 4.33 | 10.40 | 13.60 | 7.25 | 5.73 | |
50 | 8.30 | 7.40 | 6.28 | 5.56 | 14.60 | 8.35 | 19.80 | 16.40 | 8.92 | 22.50 | 14.20 | 7.07 | 10.40 | 9.26 | |
GWO | 10 | 6.19 | 6.47 | 3.33 | 5.24 | 4.15 | 2.47 | 2.00 | 2.36 | 4.49 | 1.83 | 2.76 | 10.80 | 4.34 | 3.20 |
30 | 1.47 | 3.54 | 3.38 | 5.04 | 2.92 | 5.61 | 1.34 | 3.54 | 10.80 | −1.92 | 4.16 | 14.50 | 0.12 | 3.53 | |
50 | −0.31 | 3.36 | 1.96 | −2.42 | 5.97 | −0.61 | 3.75 | 1.90 | 8.98 | 2.52 | 4.45 | 8.43 | 2.38 | 15.60 | |
MFO | 10 | 9.53 | 4.44 | 2.95 | 5.00 | 3.54 | 0.79 | 7.80 | 3.17 | 6.50 | 7.32 | 0.75 | 9.43 | 3.79 | 3.60 |
30 | 8.06 | 3.02 | 3.22 | 8.69 | 11.10 | 6.37 | 10.50 | 17.70 | 4.94 | 9.38 | 5.19 | 5.48 | 5.12 | 2.36 | |
50 | 10.20 | 3.39 | 4.41 | 5.99 | 23.30 | 9.76 | 18.00 | 13.50 | 5.33 | 16.60 | 4.16 | 14.00 | 10.80 | 2.19 | |
WOA | 10 | 6.24 | 5.02 | 4.92 | 9.74 | 6.24 | 1.89 | 11.10 | 2.03 | 8.09 | 4.41 | 4.09 | 7.40 | 9.66 | 4.56 |
30 | 9.87 | 4.06 | 4.28 | 9.37 | 9.88 | 6.69 | 19.60 | 14.20 | 9.97 | 11.00 | 7.83 | 17.40 | 15.40 | 6.35 | |
50 | −3.66 | 4.05 | 4.28 | −3.92 | 6.51 | −4.68 | 8.55 | 5.88 | −6.31 | 7.06 | −3.71 | 2.32 | 8.76 | 5.85 | |
SSA | 10 | 12.00 | 6.51 | 2.14 | 7.06 | −0.20 | −0.27 | 4.66 | 0.70 | 3.63 | −0.33 | 0.71 | 5.27 | 2.98 | 1.57 |
30 | 3.55 | 4.52 | 7.08 | 6.35 | 6.71 | 3.11 | 4.60 | 5.36 | 3.84 | −1.43 | 5.84 | 6.62 | 7.21 | 6.17 | |
50 | 4.64 | 8.57 | 8.29 | 1.00 | 8.51 | 2.16 | 6.04 | 4.00 | 1.64 | −1.92 | −1.17 | 1.73 | 9.66 | 20.30 | |
BOA | 10 | 27.20 | 3.76 | 2.53 | 19.20 | −1.96 | 6.35 | 19.70 | −5.31 | 13.90 | 7.66 | 8.10 | 7.76 | 15.50 | 5.73 |
30 | 5.54 | 3.38 | 5.53 | 18.20 | −0.19 | 10.00 | 22.30 | 18.00 | 22.70 | 21.40 | 15.00 | 40.90 | 8.16 | 6.19 | |
50 | 8.95 | 7.12 | 7.04 | 24.60 | 12.50 | 4.49 | 28.50 | 36.40 | 74.70 | 57.30 | 21.80 | 40.90 | 6.70 | 10.00 | |
HGSO | 10 | 25.60 | 5.74 | 5.27 | 13.30 | 1.22 | 8.37 | 24.20 | −4.28 | 13.20 | 18.20 | 10.80 | 14.90 | 16.30 | 2.23 |
30 | 15.70 | 7.14 | 12.60 | 15.70 | 31.50 | 19.90 | 33.40 | 27.00 | 29.90 | 28.60 | −5.88 | 6.07 | 9.06 | 16.90 | |
50 | 13.00 | 15.70 | 11.90 | 7.20 | 51.00 | 4.80 | 24.90 | 35.50 | 27.20 | 21.10 | −18.80 | 8.33 | 10.80 | 19.00 | |
AOA | 10 | 21.20 | 6.38 | 7.58 | 14.90 | 1.77 | 6.01 | 21.00 | 0.12 | 15.50 | 10.50 | 5.12 | 123.00 | 15.20 | 2.64 |
30 | 8.00 | 14.20 | 11.80 | 10.80 | 23.50 | 22.70 | 18.60 | 13.20 | 35.00 | 14.90 | −5.88 | 21.80 | −0.18 | −1.92 | |
50 | 8.21 | 21.30 | 27.80 | 9.26 | 6.50 | 40.70 | 7.78 | 26.80 | 19.60 | 15.60 | −18.80 | 7.51 | 1.03 | −31.30 |
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Nadimi-Shahraki, M.H.; Taghian, S.; Mirjalili, S.; Ewees, A.A.; Abualigah, L.; Abd Elaziz, M. MTV-MFO: Multi-Trial Vector-Based Moth-Flame Optimization Algorithm. Symmetry 2021, 13, 2388. https://doi.org/10.3390/sym13122388
Nadimi-Shahraki MH, Taghian S, Mirjalili S, Ewees AA, Abualigah L, Abd Elaziz M. MTV-MFO: Multi-Trial Vector-Based Moth-Flame Optimization Algorithm. Symmetry. 2021; 13(12):2388. https://doi.org/10.3390/sym13122388
Chicago/Turabian StyleNadimi-Shahraki, Mohammad H., Shokooh Taghian, Seyedali Mirjalili, Ahmed A. Ewees, Laith Abualigah, and Mohamed Abd Elaziz. 2021. "MTV-MFO: Multi-Trial Vector-Based Moth-Flame Optimization Algorithm" Symmetry 13, no. 12: 2388. https://doi.org/10.3390/sym13122388
APA StyleNadimi-Shahraki, M. H., Taghian, S., Mirjalili, S., Ewees, A. A., Abualigah, L., & Abd Elaziz, M. (2021). MTV-MFO: Multi-Trial Vector-Based Moth-Flame Optimization Algorithm. Symmetry, 13(12), 2388. https://doi.org/10.3390/sym13122388