Multi-Swarm Algorithm for Extreme Learning Machine Optimization
Abstract
:1. Introduction
2. Background
2.1. Extreme Learning Machine
2.2. Swarm Intelligence
2.3. ELM Tuning by Swarm Intelligence Meta-Heuristics
3. Proposed Hybrid Meta-Heuristics
3.1. Original Algorithms
3.1.1. The Original ABC Algorithm
3.1.2. The Original Firefly Algorithm
3.1.3. The Original SCA Method
3.2. Proposed Multi-Swarm Meta-Heuristics Algorithm
3.2.1. Motivation and Preliminaries
3.2.2. Overview of MS-AFS
- Chaotic and quasi-reflection-based learning (QRL) population initialization in order to establish boosting of the search by redirecting solutions towards more favorable parts of the domain;
- Efficient learning mechanism between swarms with the goal of combining weakness and strengths of different approaches more efficiently.
Algorithm 1 Pseudo-code for chaotic and QRL population initialization |
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Algorithm 2 Search process of s1—ABC algorithm |
Algorithm 3 Search process of s2—LLH between FA and SCA |
Algorithm 4 High-level MS-AFS pseudo-code |
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3.2.3. Computational Complexity, MS-AFS Solutions’ Encoding for ELM Tuning and Flow-Chart
4. Experiments
4.1. Datasets
4.2. Metrics
4.3. Experimental Results and Comparative Analysis with Other Cutting-Edge Meta-Heuristics
Statistical Tests
4.4. Hybridization by Pairs
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Dataset | Samples | Training Data | Testing Data | Attributes | Classes |
---|---|---|---|---|---|
Diabetes | 768 | 538 | 230 | 8 | 2 |
Disease | 270 | 189 | 81 | 13 | 2 |
Iris | 150 | 105 | 45 | 4 | 3 |
Wine | 178 | 125 | 53 | 13 | 3 |
Wine Quality | 1599 | 1120 | 479 | 11 | 6 |
Satellite | 6400 | 5400 | 1000 | 36 | 6 |
Shuttle | 58,000 | 50,750 | 7250 | 9 | 7 |
Diabetes | Disease | Iris | Wine | Wine Quality | Satellite | Shuttle | ||
---|---|---|---|---|---|---|---|---|
ELM | best (%) | 73.59 | 87.99 | 80 | 98.15 | 60 | 77.24 | 84.12 |
worst (%) | 61.90 | 79.87 | 66.67 | 83.33 | 54.37 | 68.48 | 10.39 | |
mean (%) | 71.22 | 84.67 | 72.18 | 92.52 | 57 | 73.68 | 55.44 | |
std | 2.5628 | 1.9972 | 3.9811 | 3.7214 | 1.2527 | 2.3860 | 24.6222 | |
ELM-IWO | best (%) | 80.95 | 89.94 | 100.00 | 100.00 | 62.92 | 82.04 | 93.13 |
worst (%) | 80.09 | 88.96 | 100.00 | 100.00 | 62.29 | 81.59 | 91.14 | |
mean (%) | 80.52 | 89.61 | 100.00 | 100.00 | 62.76 | 81.79 | 92.20 | |
std | 0.0061 | 0.0046 | 0.0000 | 0.0000 | 0.0031 | 0.0023 | 0.0100 | |
ELM-WOA | best (%) | 80.52 | 89.61 | 100.00 | 98.15 | 62.92 | 81.59 | 92.90 |
worst (%) | 79.22 | 87.01 | 100.00 | 96.30 | 61.67 | 80.34 | 88.43 | |
mean (%) | 79.87 | 88.72 | 100.00 | 97.69 | 62.29 | 80.94 | 90.93 | |
std | 0.0092 | 0.0123 | 0.0000 | 0.0093 | 0.0051 | 0.0067 | 0.0228 | |
ELM-HHO | best (%) | 79.65 | 89.29 | 100.00 | 100.00 | 62.71 | 82.09 | 93.85 |
worst (%) | 79.22 | 87.34 | 100.00 | 94.44 | 61.25 | 80.89 | 88.08 | |
mean (%) | 79.44 | 88.56 | 100.00 | 98.15 | 61.82 | 81.44 | 91.24 | |
std | 0.0031 | 0.0093 | 0.0000 | 0.0262 | 0.0071 | 0.0062 | 0.0292 | |
ELM-BA | best (%) | 80.52 | 88.31 | 100.00 | 100.00 | 63.75 | 81.44 | 90.98 |
worst (%) | 80.09 | 87.66 | 100.00 | 100.00 | 61.67 | 80.64 | 89.86 | |
mean (%) | 80.30 | 88.07 | 100.00 | 100.00 | 62.66 | 81.09 | 90.39 | |
std | 0.0031 | 0.0031 | 0.0000 | 0.0000 | 0.0086 | 0.0039 | 0.0056 | |
ELM-SCA | best (%) | 81.39 | 89.94 | 100.00 | 100.00 | 63.13 | 81.89 | 92.97 |
worst (%) | 80.95 | 88.31 | 100.00 | 100.00 | 61.67 | 81.49 | 89.75 | |
mean (%) | 81.17 | 89.12 | 100.00 | 100.00 | 62.50 | 81.72 | 91.83 | |
std | 0.0031 | 0.0077 | 0.0000 | 0.0000 | 0.0066 | 0.0017 | 0.018 | |
ELM-FA | best (%) | 80.95 | 89.61 | 100.00 | 98.15 | 62.50 | 81.24 | 91.97 |
worst (%) | 80.95 | 87.66 | 100.00 | 96.30 | 61.46 | 80.54 | 89.95 | |
mean (%) | 80.95 | 88.72 | 100.00 | 97.22 | 61.98 | 80.90 | 91.11 | |
std | 0.0000 | 0.0081 | 0.0000 | 0.0107 | 0.0043 | 0.0032 | 0.0104 | |
ELM-ABC | best (%) | 81.39 | 90.58 | 100.00 | 100.00 | 62.50 | 81.99 | 92.28 |
worst (%) | 80.09 | 88.64 | 100.00 | 100.00 | 60.21 | 81.29 | 88.82 | |
mean (%) | 80.74 | 89.37 | 100.00 | 100.00 | 61.72 | 81.73 | 90.65 | |
std | 0.0092 | 0.0093 | 0.0000 | 0.0000 | 0.0104 | 0.0032 | 0.0174 | |
ELM-MS-AFS | best (%) | 86.15 | 92.53 | 100.00 | 100.00 | 66.25 | 84.59 | 98.67 |
worst (%) | 83.12 | 90.91 | 100.00 | 100.00 | 65.63 | 82.99 | 97.71 | |
mean (%) | 84.63 | 91.80 | 100.00 | 100.00 | 65.99 | 83.67 | 98.21 | |
std | 0.0214 | 0.0072 | 0.0000 | 0.0000 | 0.0026 | 0.0076 | 0.0048 |
Diabetes | Disease | Iris | Wine | Wine Quality | Satellite | Shuttle | ||
---|---|---|---|---|---|---|---|---|
ELM | best (%) | 69.69 | 89.93 | 71.11 | 94.44 | 58.96 | 80.09 | 90.00 |
worst (%) | 55.84 | 83.12 | 40 | 81.48 | 52.29 | 74.59 | 3.04 | |
mean (%) | 64.85 | 86.52 | 54.4 | 89.48 | 55.87 | 78.11 | 42.43 | |
std | 3.9713 | 1.4753 | 7.9534 | 3.9447 | 1.9326 | 1.2749 | 32.6834 | |
ELM-IWO | best (%) | 77.49 | 89.94 | 100.00 | 100.00 | 62.92 | 83.59 | 94.64 |
worst (%) | 77.49 | 88.96 | 100.00 | 100.00 | 61.67 | 83.34 | 88.22 | |
mean (%) | 77.49 | 89.45 | 100.00 | 100.00 | 62.24 | 83.47 | 91.42 | |
std | 0.0107 | 0.0042 | 0.0000 | 0.0000 | 0.0057 | 0.0018 | 0.0321 | |
ELM-WOA | best (%) | 79.22 | 88.96 | 100.00 | 100.00 | 62.29 | 83.34 | 94.45 |
worst (%) | 77.49 | 88.31 | 100.00 | 98.15 | 61.88 | 82.64 | 91.52 | |
mean (%) | 78.35 | 88.64 | 100.00 | 99.07 | 62.08 | 82.99 | 92.67 | |
std | 0.0122 | 0.0027 | 0.0000 | 0.0107 | 0.0017 | 0.0050 | 0.0156 | |
ELM-HHO | best (%) | 79.22 | 90.26 | 100.00 | 100.00 | 63.54 | 83.34 | 93.43 |
worst (%) | 77.92 | 87.99 | 100.00 | 98.15 | 62.08 | 83.34 | 89.32 | |
mean (%) | 78.57 | 89.29 | 100.00 | 99.07 | 63.07 | 83.34 | 91.90 | |
std | 0.0092 | 0.0103 | 0.0000 | 0.0107 | 0.0069 | 0.0000 | 0.0224 | |
ELM-BA | best (%) | 79.65 | 88.96 | 100.00 | 100.00 | 63.54 | 83.39 | 90.61 |
worst (%) | 78.35 | 88.31 | 97.78 | 98.15 | 62.29 | 82.84 | 87.46 | |
mean (%) | 79.00 | 88.56 | 97.78 | 99.54 | 62.76 | 83.12 | 88.79 | |
std | 0.0092 | 0.0031 | 0.0000 | 0.0093 | 0.0060 | 0.0039 | 0.0163 | |
ELM-SCA | best (%) | 79.22 | 89.61 | 100.00 | 100.00 | 62.92 | 83.84 | 90.83 |
worst (%) | 77.49 | 88.64 | 100.00 | 98.15 | 61.25 | 83.54 | 89.46 | |
mean (%) | 78.35 | 89.29 | 100.00 | 99.54 | 62.19 | 83.69 | 90.10 | |
std | 0.0122 | 0.0046 | 0.0000 | 0.0093 | 0.0086 | 0.0021 | 0.0069 | |
ELM-FA | best (%) | 78.79 | 89.61 | 100.00 | 100.00 | 63.33 | 82.64 | 91.59 |
worst (%) | 77.49 | 88.64 | 100.00 | 100.00 | 62.08 | 82.54 | 85.79 | |
mean (%) | 78.14 | 89.29 | 100.00 | 100.00 | 62.45 | 82.59 | 88.67 | |
std | 0.0092 | 0.0046 | 0.0000 | 0.0000 | 0.0060 | 0.0007 | 0.0290 | |
ELM-ABC | best (%) | 79.22 | 89.94 | 100.00 | 100.00 | 62.71 | 83.54 | 96.77 |
worst (%) | 79.22 | 89.29 | 100.00 | 100.00 | 62.29 | 83.34 | 87.72 | |
mean (%) | 79.22 | 89.61 | 100.00 | 100.00 | 62.55 | 83.44 | 91.83 | |
std | 0.0000 | 0.0027 | 0.0000 | 0.0000 | 0.0002 | 0.0014 | 0.0458 | |
ELM-MS-AFS | best (%) | 82.68 | 94.16 | 100.00 | 100.00 | 68.13 | 86.89 | 97.68 |
worst (%) | 80.52 | 91.88 | 100.00 | 100.00 | 66.88 | 85.89 | 84.74 | |
mean (%) | 81.60 | 92.86 | 100.00 | 100.00 | 67.60 | 86.39 | 91.62 | |
std | 0.0153 | 0.0103 | 0.0000 | 0.0000 | 0.0052 | 0.0071 | 0.0651 |
Diabetes | Disease | Iris | Wine | Wine Quality | Satellite | Shuttle | ||
---|---|---|---|---|---|---|---|---|
ELM | best (%) | 70.56 | 92.53 | 75.55 | 90.74 | 61.04 | 80.64 | 80.42 |
worst (%) | 61.04 | 83.44 | 57.78 | 40.74 | 46.04 | 77.59 | 4.70 | |
mean (%) | 65.56 | 87.83 | 67.29 | 71.48 | 53.79 | 79.43 | 44.12 | |
std | 2.2178 | 2.1791 | 4.5550 | 10.5018 | 3.1374 | 0.7149 | 29.1458 | |
ELM-IWO | best (%) | 80.09 | 94.48 | 97.78 | 100.00 | 62.92 | 85.39 | 91.84 |
worst (%) | 79.65 | 92.86 | 97.78 | 100.00 | 61.25 | 84.84 | 89.19 | |
mean (%) | 79.87 | 93.34 | 97.78 | 100.00 | 62.24 | 85.12 | 90.29 | |
std | 0.0030 | 0.0077 | 0.0000 | 0.0000 | 0.0071 | 0.0039 | 0.0138 | |
ELM-WOA | best (%) | 79.65 | 93.51 | 97.78 | 100.00 | 62.71 | 84.84 | 92.49 |
worst (%) | 79.22 | 92.53 | 97.78 | 100.00 | 60.21 | 83.94 | 89.05 | |
mean (%) | 79.44 | 93.18 | 97.78 | 100.00 | 61.61 | 84.39 | 90.27 | |
std | 0.0031 | 0.0046 | 0.0000 | 0.0000 | 0.0112 | 0.0064 | 0.0193 | |
ELM-HHO | best (%) | 80.52 | 93.51 | 100.00 | 100.00 | 64.17 | 84.34 | 93.00 |
worst (%) | 77.22 | 92.53 | 97.78 | 100.00 | 61.25 | 84.04 | 84.74 | |
mean (%) | 79.87 | 92.86 | 98.33 | 100.00 | 61.60 | 84.19 | 87.72 | |
std | 0.0092 | 0.0046 | 0.0111 | 0.0000 | 0.0121 | 0.0021 | 0.0458 | |
ELM-BA | best (%) | 79.22 | 94.48 | 97.78 | 100.00 | 62.08 | 85.39 | 91.63 |
worst (%) | 78.35 | 88.31 | 97.78 | 100.00 | 61.67 | 82.84 | 88.12 | |
mean (%) | 79.00 | 88.56 | 97.78 | 100.00 | 62.66 | 83.12 | 90.29 | |
std | 0.0092 | 0.0031 | 0.0000 | 0.0000 | 0.0086 | 0.0039 | 0.0189 | |
ELM-SCA | best (%) | 79.65 | 93.51 | 97.78 | 100.00 | 63.33 | 85.49 | 89.29 |
worst (%) | 79.65 | 92.53 | 97.78 | 100.00 | 61.88 | 84.59 | 85.52 | |
mean (%) | 79.65 | 93.02 | 97.78 | 100.00 | 62.34 | 85.04 | 86.87 | |
std | 0.0000 | 0.0042 | 0.0000 | 0.0000 | 0.0069 | 0.0063 | 0.0210 | |
ELM-FA | best (%) | 80.95 | 94.16 | 100.00 | 100.00 | 61.88 | 84.44 | 92.39 |
worst (%) | 79.65 | 92.86 | 97.78 | 100.00 | 60.42 | 82.54 | 90.99 | |
mean (%) | 80.30 | 93.59 | 98.33 | 100.00 | 61.09 | 82.59 | 91.70 | |
std | 0.0092 | 0.0067 | 0.0111 | 0.0000 | 0.0069 | 0.0007 | 0.0070 | |
ELM-ABC | best (%) | 79.65 | 92.86 | 97.78 | 100.00 | 62.29 | 84.64 | 96.47 |
worst (%) | 78.35 | 89.29 | 97.78 | 100.00 | 61.04 | 83.34 | 89.68 | |
mean (%) | 79.00 | 89.61 | 97.78 | 100.00 | 61.56 | 83.44 | 92.61 | |
std | 0.0092 | 0.0026 | 0.0000 | 0.0000 | 0.0055 | 0.0014 | 0.0349 | |
ELM-MS-AFS | best (%) | 84.42 | 96.75 | 97.78 | 100.00 | 68.33 | 88.19 | 97.62 |
worst (%) | 82.68 | 95.13 | 97.78 | 100.00 | 66.25 | 87.74 | 93.13 | |
mean (%) | 83.55 | 95.70 | 97.78 | 100.00 | 67.40 | 87.97 | 94.70 | |
std | 0.0122 | 0.0072 | 0.0000 | 0.0000 | 0.0100 | 0.0072 | 0.0253 |
Diabetes | Disease | Iris | Wine | Wine Quality | Satellite | Shuttle | ||
---|---|---|---|---|---|---|---|---|
ELM-IWO | accuracy (%) | 80.95 | 89.94 | 100.00 | 100.00 | 62.92 | 82.04 | 93.13 |
precision | 0.789 | 0.900 | 1.000 | 1.000 | 0.294 | 0.806 | 0.391 | |
recall | 0.754 | 0.899 | 1.000 | 1.000 | 0.287 | 0.765 | 0.338 | |
f1-score | 0.767 | 0.899 | 1.000 | 1.000 | 0.286 | 0.769 | 0.358 | |
ELM-WOA | accuracy (%) | 80.52 | 89.61 | 100.00 | 98.15 | 62.92 | 81.59 | 92.90 |
precision | 0.784 | 0.898 | 1.000 | 0.978 | 0.344 | 0.708 | 0.335 | |
recall | 0.747 | 0.895 | 1.000 | 0.984 | 0.267 | 0.744 | 0.313 | |
f1-score | 0.760 | 0.896 | 1.000 | 0.980 | 0.267 | 0.719 | 0.312 | |
ELM-HHO | accuracy (%) | 79.65 | 89.29 | 100.00 | 100.00 | 62.71 | 82.09 | 93.85 |
precision | 0.777 | 0.894 | 1.000 | 1.000 | 0.303 | 0.827 | 0.397 | |
recall | 0.730 | 0.892 | 1.000 | 1.000 | 0.274 | 0.755 | 0.382 | |
f1-score | 0.745 | 0.893 | 1.0 | 1.000 | 0.274 | 0.735 | 0.387 | |
ELM-BA | accuracy (%) | 80.52 | 88.31 | 100.00 | 100.00 | 63.75 | 81.44 | 90.98 |
precision | 0.800 | 0.887 | 1.000 | 1.000 | 0.318 | 0.866 | 0.244 | |
recall | 0.729 | 0.882 | 1.000 | 1.000 | 0.272 | 0.744 | 0.351 | |
f1-score | 0.748 | 0.883 | 1.000 | 1.000 | 0.271 | 0.718 | 0.271 | |
ELM-SCA | accuracy (%) | 81.39 | 89.94 | 100.00 | 100.00 | 63.13 | 81.89 | 92.97 |
precision | 0.818 | 0.900 | 1.000 | 1.000 | 0.310 | 0.868 | 0.342 | |
recall | 0.735 | 0.899 | 1.000 | 1.000 | 0.270 | 0.752 | 0.381 | |
f1-score | 0.757 | 0.899 | 1.000 | 1.000 | 0.270 | 0.724 | 0.352 | |
ELM-FA | accuracy (%) | 80.95 | 89.61 | 100.00 | 98.15 | 62.50 | 81.24 | 91.97 |
precision | 0.797 | 0.899 | 1.0 | 0.985 | 0.313 | 0.699 | 0.407 | |
recall | 0.743 | 0.895 | 1.000 | 0.982 | 0.272 | 0.748 | 0.356 | |
f1-score | 0.760 | 0.896 | 1.000 | 0.983 | 0.275 | 0.718 | 0.372 | |
ELM-ABC | accuracy (%) | 81.39 | 90.58 | 100.00 | 100.00 | 62.50 | 81.99 | 92.28 |
precision | 0.805 | 0.906 | 1.000 | 1.000 | 0.372 | 0.205 | 0.347 | |
recall | 0.746 | 0.906 | 1.000 | 1.000 | 0.285 | 0.167 | 0.343 | |
f1-score | 0.764 | 0.906 | 1.000 | 1.000 | 0.297 | 0.065 | 0.345 | |
ELM-MS-AFS | accuracy (%) | 86.15 | 92.53 | 100.00 | 100.00 | 66.25 | 84.59 | 98.67 |
precision | 0.857 | 0.926 | 1.000 | 1.000 | 0.527 | 0.841 | 0.564 | |
recall | 0.814 | 0.925 | 1.000 | 1.000 | 0.370 | 0.793 | 0.436 | |
f1-score | 0.830 | 0.925 | 1.000 | 1.000 | 0.402 | 0.792 | 0.448 |
Diabetes | Disease | Iris | Wine | Wine Quality | Satellite | Shuttle | ||
---|---|---|---|---|---|---|---|---|
ELM-IWO | accuracy (%) | 77.49 | 89.94 | 100.00 | 100.00 | 62.92 | 83.59 | 94.64 |
precision | 0.747 | 0.899 | 1.000 | 1.000 | 0.285 | 0.826 | 0.538 | |
recall | 0.750 | 0.900 | 1.000 | 1.000 | 0.296 | 0.778 | 0.422 | |
f1-score | 0.748 | 0.899 | 1.000 | 1.000 | 0.290 | 0.747 | 0.427 | |
ELM-WOA | accuracy (%) | 79.22 | 88.96 | 100.00 | 100.00 | 62.29 | 83.34 | 94.45 |
precision | 0.768 | 0.890 | 1.000 | 1.000 | 0.277 | 0.885 | 0.377 | |
recall | 0.756 | 0.889 | 1.000 | 1.000 | 0.253 | 0.770 | 0.384 | |
f1-score | 0.761 | 0.889 | 1.000 | 1.000 | 0.239 | 0.749 | 0.380 | |
ELM-HHO | accuracy (%) | 79.22 | 90.26 | 100.00 | 100.00 | 63.54 | 83.34 | 93.43 |
precision | 0.769 | 0.902 | 1.000 | 1.000 | 0.277 | 0.850 | 0.366 | |
recall | 0.753 | 0.902 | 1.000 | 1.000 | 0.271 | 0.771 | 0.374 | |
f1-score | 0.760 | 0.902 | 1.000 | 1.000 | 0.265 | 0.749 | 0.370 | |
ELM-BA | accuracy (%) | 79.65 | 88.96 | 100.00 | 100.00 | 63.54 | 83.39 | 90.61 |
precision | 0.773 | 0.890 | 1.000 | 1.000 | 0.304 | 0.846 | 0.231 | |
recall | 0.760 | 0.889 | 1.000 | 1.000 | 0.297 | 0.772 | 0.260 | |
f1-score | 0.766 | 0.889 | 1.000 | 1.000 | 0.296 | 0.748 | 0.244 | |
ELM-SCA | accuracy (%) | 79.22 | 89.61 | 100.00 | 100.00 | 62.92 | 83.84 | 90.83 |
precision | 0.767 | 0.896 | 1.000 | 1.000 | 0.285 | 0.831 | 0.400 | |
recall | 0.763 | 0.896 | 1.000 | 1.000 | 0.296 | 0.787 | 0.325 | |
f1-score | 0.765 | 0.896 | 1.000 | 1.000 | 0.290 | 0.781 | 0.353 | |
ELM-FA | accuracy (%) | 78.79 | 89.61 | 100.00 | 100.00 | 63.33 | 82.64 | 91.59 |
precision | 0.768 | 0.898 | 1.000 | 1.000 | 0.320 | 0.794 | 0.353 | |
recall | 0.737 | 0.895 | 1.000 | 1.000 | 0.282 | 0.759 | 0.311 | |
f1-score | 0.748 | 0.896 | 1.000 | 1.000 | 0.284 | 0.742 | 0.308 | |
ELM-ABC | accuracy (%) | 79.22 | 89.94 | 100.00 | 100.00 | 62.71 | 83.54 | 96.77 |
precision | 0.770 | 0.900 | 1.000 | 1.000 | 0.263 | 0.815 | 0.410 | |
recall | 0.750 | 0.898 | 1.000 | 1.000 | 0.257 | 0.778 | 0.410 | |
f1-score | 0.758 | 0.899 | 1.000 | 1.000 | 0.246 | 0.756 | 0.410 | |
ELM-MS-AFS | accuracy (%) | 82.68 | 94.16 | 100.00 | 100.00 | 68.13 | 86.89 | 97.68 |
precision | 0.805 | 0.942 | 1.000 | 1.000 | 0.550 | 0.866 | 0.412 | |
recall | 0.805 | 0.942 | 1.000 | 1.000 | 0.357 | 0.829 | 0.420 | |
f1-score | 0.805 | 0.942 | 1.000 | 1.000 | 0.386 | 0.835 | 0.416 |
Diabetes | Disease | Iris | Wine | Wine Quality | Satellite | Shuttle | ||
---|---|---|---|---|---|---|---|---|
ELM-IWO | accuracy (%) | 80.09 | 94.48 | 97.78 | 100.00 | 62.92 | 85.39 | 91.84 |
precision | 0.789 | 0.945 | 0.978 | 1.000 | 0.335 | 0.850 | 0.404 | |
recall | 0.772 | 0.945 | 0.980 | 1.000 | 0.290 | 0.808 | 0.357 | |
f1-score | 0.779 | 0.945 | 0.978 | 1.000 | 0.294 | 0.814 | 0.371 | |
ELM-WOA | accuracy (%) | 79.65 | 93.51 | 97.78 | 100.00 | 62.71 | 84.84 | 92.49 |
precision | 0.780 | 0.935 | 0.978 | 1.000 | 0.627 | 0.838 | 0.239 | |
recall | 0.781 | 0.935 | 0.980 | 1.000 | 0.627 | 0.792 | 0.273 | |
f1-score | 0.781 | 0.935 | 0.978 | 1.000 | 0.627 | 0.780 | 0.254 | |
ELM-HHO | accuracy (%) | 80.52 | 93.51 | 100.00 | 100.00 | 64.17 | 84.34 | 93.00 |
precision | 0.790 | 0.935 | 1.000 | 1.000 | 0.315 | 0.889 | 0.409 | |
recall | 0.788 | 0.935 | 1.000 | 1.000 | 0.289 | 0.782 | 0.367 | |
f1-score | 0.789 | 0.935 | 1.000 | 1.000 | 0.290 | 0.751 | 0.380 | |
ELM-BA | accuracy (%) | 79.22 | 94.48 | 97.78 | 100.00 | 62.08 | 85.39 | 91.63 |
precision | 0.776 | 0.945 | 0.978 | 1.000 | 0.325 | 0.840 | 0.370 | |
recall | 0.786 | 0.944 | 0.980 | 1.000 | 0.288 | 0.818 | 0.317 | |
f1-score | 0.780 | 0.945 | 0.978 | 1.000 | 0.291 | 0.823 | 0.312 | |
ELM-SCA | accuracy (%) | 79.65 | 93.51 | 97.78 | 100.00 | 63.33 | 85.49 | 89.29 |
precision | 0.780 | 0.935 | 0.978 | 1.000 | 0.356 | 0.841 | 0.321 | |
recall | 0.779 | 0.935 | 0.980 | 1.000 | 0.305 | 0.822 | 0.316 | |
f1-score | 0.780 | 0.935 | 0.978 | 1.000 | 0.313 | 0.826 | 0.309 | |
ELM-FA | accuracy (%) | 80.95 | 94.16 | 100.00 | 100.00 | 61.88 | 84.44 | 92.39 |
precision | 0.796 | 0.941 | 1.000 | 1.000 | 0.319 | 0.833 | 0.412 | |
recall | 0.786 | 0.942 | 1.000 | 1.000 | 0.268 | 0.788 | 0.360 | |
f1-score | 0.791 | 0.941 | 1.000 | 1.000 | 0.267 | 0.784 | 0.375 | |
ELM-ABC | accuracy (%) | 79.65 | 92.86 | 95.56 | 100.00 | 62.29 | 84.64 | 96.47 |
precision | 0.796 | 0.930 | 0.958 | 1.000 | 0.330 | 0.830 | 0.402 | |
recall | 0.753 | 0.929 | 0.956 | 1.000 | 0.284 | 0.798 | 0.384 | |
f1-score | 0.765 | 0.928 | 0.955 | 1.000 | 0.288 | 0.799 | 0.391 | |
ELM-MS-AFS | accuracy (%) | 84.42 | 96.75 | 97.78 | 100.00 | 68.33 | 88.19 | 97.62 |
precision | 0.844 | 0.967 | 0.978 | 1.000 | 0.345 | 0.878 | 0.445 | |
recall | 0.814 | 0.968 | 0.980 | 1.000 | 0.321 | 0.853 | 0.490 | |
f1-score | 0.825 | 0.967 | 0.978 | 1.000 | 0.325 | 0.860 | 0.461 |
Dataset | ELM-ABC | ELM-FA | ELM-SCA | ELM-BA | ELM-HHO | ELM-WOA | ELM-IWO | ELM-MS-AFS |
---|---|---|---|---|---|---|---|---|
Diabetes | 45 | 12 | 45 | 53 | 26 | 45 | 34 | 2 |
Disease | 51 | 21 | 38 | 10.5 | 38 | 38 | 10.5 | 6 |
Iris | 30.5 | 30.5 | 30.5 | 30.5 | 7 | 30.5 | 30.5 | 9 |
Wine | 16.5 | 16.5 | 16.5 | 16.5 | 16.5 | 16.5 | 16.5 | 16.5 |
Wine Quality | 49 | 55 | 27 | 52 | 8 | 42 | 35 | 1 |
Satellite | 43 | 47 | 22 | 24.5 | 48 | 40 | 24.5 | 4 |
Shuttle | 5 | 41 | 56 | 54 | 23 | 36 | 50 | 3 |
Average | 34.28 | 31.86 | 33.57 | 34.43 | 23.78 | 35.43 | 28.71 | 5.93 |
Rank | 6 | 4 | 5 | 7 | 2 | 8 | 3 | 1 |
Comparison | p-Value | Rank | 0.05/() | 0.1/() |
---|---|---|---|---|
MS-AFS vs. ABC | 0 | 0.007143 | 0.014286 | |
MS-AFS vs. BA | 1 | 0.008333 | 0.016667 | |
MS-AFS vs. FA | 2 | 0.01 | 0.02 | |
MS-AFS vs. WOA | 3 | 0.0125 | 0.025 | |
MS-AFS vs. SCA | 4 | 0.016667 | 0.033333 | |
MS-AFS vs. IWO | 5 | 0.025 | 0.05 | |
MS-AFS vs. HHO | 6 | 0.05 | 0.1 |
Wine Quality | Satellite | Shuttle | NSL-KDD | ||
---|---|---|---|---|---|
Results for ELM with 30 neurons | |||||
ELM-ABC-FA | best (%) | 65.21 | 83.04 | 97.08 | 77.43 |
worst (%) | 63.54 | 82.69 | 92.96 | 73.96 | |
mean (%) | 64.17 | 82.87 | 95.32 | 75.26 | |
std | 0.0091 | 0.0018 | 0.0213 | 0.0189 | |
ELM-ABC-SCA | best (%) | 63.33 | 82.94 | 97.17 | 77.24 |
worst (%) | 62.29 | 82.19 | 84.72 | 72.90 | |
mean (%) | 62.85 | 82.51 | 91.09 | 75.41 | |
std | 0.0052 | 0.0039 | 0.0623 | 0.0225 | |
ELM-FA-SCA | best (%) | 65.21 | 83.14 | 97.88 | 75.60 |
worst (%) | 62.50 | 82.52 | 96.81 | 75.14 | |
mean (%) | 63.61 | 82.91 | 97.40 | 75.45 | |
std | 0.0142 | 0.0032 | 0.0054 | 0.0027 | |
ELM-MS-AFS | best (%) | 66.25 | 84.59 | 98.67 | 79.66 |
worst (%) | 65.63 | 82.99 | 97.71 | 76.59 | |
mean (%) | 65.99 | 83.67 | 98.21 | 77.74 | |
std | 0.0026 | 0.0076 | 0.0048 | 0.0167 | |
Results for ELM with 60 neurons | |||||
ELM-ABC-FA | best (%) | 65.21 | 86.69 | 91.62 | 77.16 |
worst (%) | 60.83 | 84.69 | 85.57 | 74.53 | |
mean (%) | 63.65 | 85.54 | 89.53 | 75.72 | |
std | 0.0194 | 0.0103 | 0.0343 | 0.0133 | |
ELM-ABC-SCA | best (%) | 65.63 | 85.59 | 96.15 | 73.07 |
worst (%) | 62.08 | 84.54 | 92.15 | 71.77 | |
mean (%) | 63.54 | 84.94 | 93.88 | 72.35 | |
std | 0.0160 | 0.0057 | 0.0205 | 0.0066 | |
ELM-FA-SCA | best (%) | 66.04 | 86.34 | 96.51 | 78.88 |
worst (%) | 61.67 | 84.84 | 91.70 | 75.11 | |
mean (%) | 64.22 | 85.83 | 93.97 | 76.84 | |
std | 0.0190 | 0.0085 | 0.0241 | 0.0190 | |
ELM-MS-AFS | best (%) | 68.13 | 86.89 | 97.68 | 80.29 |
worst (%) | 66.88 | 85.89 | 84.74 | 75.55 | |
mean (%) | 67.60 | 86.39 | 91.62 | 78.42 | |
std | 0.0052 | 0.0071 | 0.0651 | 0.0252 | |
Results for ELM with 90 neurons | |||||
ELM-ABC-FA | best (%) | 68.13 | 87.04 | 95.21 | 75.96 |
worst (%) | 63.96 | 85.19 | 90.96 | 73.59 | |
mean (%) | 66.30 | 86.03 | 92.80 | 74.95 | |
std | 0.0173 | 0.0094 | 0.0218 | 0.0122 | |
ELM-ABC-SCA | best (%) | 66.46 | 86.19 | 97.52 | 71.58 |
worst (%) | 64.38 | 85.44 | 90.66 | 69.47 | |
mean (%) | 65.57 | 85.78 | 95.01 | 70.87 | |
std | 0.0087 | 0.0038 | 0.0378 | 0.0122 | |
ELM-FA-SCA | best (%) | 67.71 | 87.34 | 93.17 | 76.16 |
worst (%) | 66.46 | 87.19 | 83.27 | 74.68 | |
mean (%) | 67.03 | 87.26 | 84.73 | 75.62 | |
std | 0.0052 | 0.0008 | 0.0535 | 0.0082 | |
ELM-MS-AFS | best (%) | 68.33 | 88.19 | 97.62 | 79.52 |
worst (%) | 66.25 | 87.74 | 93.13 | 75.34 | |
mean (%) | 67.40 | 87.97 | 94.70 | 77.43 | |
std | 0.0100 | 0.0072 | 0.0253 | 0.0209 |
Wine Quality | Satellite | Shuttle | NSL-KDD | ||
---|---|---|---|---|---|
Results for ELM with 30 neurons | |||||
ELM-ABC-FA | accuracy (%) | 65.21 | 83.04 | 97.08 | 77.43 |
precision (%) | 0.327 | 0.819 | 0.408 | 0.473 | |
recall (%) | 0.326 | 0.764 | 0.420 | 0.483 | |
f1-score | 0.325 | 0.740 | 0.413 | 0.470 | |
ELM-ABC-SCA | accuracy (%) | 63.33 | 82.94 | 97.17 | 77.24 |
precision (%) | 0.320 | 0.873 | 0.404 | 0.470 | |
recall (%) | 0.319 | 0.765 | 0.417 | 0.511 | |
f1-score | 0.318 | 0.735 | 0.408 | 0.491 | |
ELM-FA-SCA | accuracy (%) | 65.21 | 83.14 | 97.88 | 75.60 |
precision (%) | 0.328 | 0.882 | 0.413 | 0.453 | |
recall (%) | 0.324 | 0.768 | 0.422 | 0.490 | |
f1-score | 0.324 | 0.739 | 0.417 | 0.468 | |
ELM-MS-AFS | accuracy (%) | 66.25 | 84.59 | 98.67 | 79.66 |
precision (%) | 0.527 | 0.841 | 0.564 | 0.492 | |
recall (%) | 0.370 | 0.793 | 0.436 | 0.518 | |
f1-score | 0.402 | 0.792 | 0.448 | 0.500 | |
Results for ELM with 60 neurons | |||||
ELM-ABC-FA | accuracy (%) | 65.21 | 86.69 | 91.62 | 77.16 |
precision (%) | 0.328 | 0.863 | 0.537 | 0.485 | |
recall (%) | 0.305 | 0.835 | 0.357 | 0.499 | |
f1-score | 0.306 | 0.841 | 0.406 | 0.486 | |
ELM-ABC-SCA | accuracy (%) | 65.63 | 85.59 | 96.15 | 73.07 |
precision (%) | 0.405 | 0.853 | 0.403 | 0.461 | |
recall (%) | 0.305 | 0.808 | 0.414 | 0.477 | |
f1-score | 0.311 | 0.804 | 0.408 | 0.460 | |
ELM-FA-SCA | accuracy (%) | 66.04 | 86.34 | 96.51 | 78.88 |
precision (%) | 0.495 | 0.855 | 0.412 | 0.485 | |
recall (%) | 0.311 | 0.825 | 0.383 | 0.521 | |
f1-score | 0.320 | 0.831 | 0.395 | 0.499 | |
ELM-MS-AFS | accuracy (%) | 68.13 | 86.89 | 97.68 | 80.29 |
precision (%) | 0.550 | 0.866 | 0.412 | 0.486 | |
recall (%) | 0.357 | 0.829 | 0.420 | 0.540 | |
f1-score | 0.386 | 0.835 | 0.416 | 0.511 | |
Results for ELM with 90 neurons | |||||
ELM-ABC-FA | accuracy (%) | 68.13 | 87.04 | 95.21 | 75.96 |
precision (%) | 0.377 | 0.861 | 0.389 | 0.495 | |
recall (%) | 0.342 | 0.834 | 0.370 | 0.498 | |
f1-score | 0.345 | 0.838 | 0.376 | 0.488 | |
ELM-ABC-SCA | accuracy (%) | 66.46 | 86.19 | 97.52 | 71.58 |
precision (%) | 0.370 | 0.879 | 0.411 | 0.475 | |
recall (%) | 0.340 | 0.810 | 0.418 | 0.452 | |
f1-score | 0.347 | 0.807 | 0.414 | 0.449 | |
ELM-FA-SCA | accuracy (%) | 67.71 | 87.34 | 93.17 | 76.16 |
precision (%) | 0.486 | 0.865 | 0.415 | 0.495 | |
recall (%) | 0.486 | 0.839 | 0.367 | 0.495 | |
f1-score | 0.453 | 0.845 | 0.383 | 0.486 | |
ELM-MS-AFS | accuracy (%) | 68.33 | 88.19 | 97.62 | 79.52 |
precision (%) | 0.345 | 0.878 | 0.445 | 0.512 | |
recall (%) | 0.321 | 0.853 | 0.490 | 0.525 | |
f1-score | 0.325 | 0.860 | 0.461 | 0.513 |
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Bacanin, N.; Stoean, C.; Zivkovic, M.; Jovanovic, D.; Antonijevic, M.; Mladenovic, D. Multi-Swarm Algorithm for Extreme Learning Machine Optimization. Sensors 2022, 22, 4204. https://doi.org/10.3390/s22114204
Bacanin N, Stoean C, Zivkovic M, Jovanovic D, Antonijevic M, Mladenovic D. Multi-Swarm Algorithm for Extreme Learning Machine Optimization. Sensors. 2022; 22(11):4204. https://doi.org/10.3390/s22114204
Chicago/Turabian StyleBacanin, Nebojsa, Catalin Stoean, Miodrag Zivkovic, Dijana Jovanovic, Milos Antonijevic, and Djordje Mladenovic. 2022. "Multi-Swarm Algorithm for Extreme Learning Machine Optimization" Sensors 22, no. 11: 4204. https://doi.org/10.3390/s22114204