Applications of the Chaotic Quantum Genetic Algorithm with Support Vector Regression in Load Forecasting
Abstract
:1. Introduction
2. The Proposed SVRCQGA Model
2.1. Brief Description of the SVR Model
2.2. Chaotic Quantum Genetic Algorithm (CQGA)
2.2.1. Introduction of QGA
2.2.2. Quantum Computing Concepts
2.2.3. Implementation Steps of CQGA
3. Experimental Examples
3.1. Data Sets of Experimental Examples
3.1.1. Regional Electricity Load Data in Taiwan: Example 1
3.1.2. Annual Electricity Load Data in Taiwan: Example 2
3.1.3. 2014 Global Energy Forecasting Competition (GEFCOM 2014) Electricity Load Data: Example 3
3.2. Parameters Setting & Forecasting Results and Analysis
3.2.1. Setting the CQGA Parameters
3.2.2. Forecasting Accuracy Indexes
3.2.3. Forecasting Performance Superiority Tests
3.2.4. Results and Analysis: Example 1
3.2.5. Results and Analysis: Example 2
3.2.6. Results and Analysis: Example 3
4. Conclusions
Author Contributions
Conflicts of Interest
References
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Examples | Data Type | Data Length | Data Size | Data Characteristics |
---|---|---|---|---|
Example 1 | Regional and annual | From 1981 to 2000 | 4 regions and 20 years | Increment with fluctuation caused by some accidental event (921 earthquake) |
Example 2 | Annual | From 1945 to 2003 | 59 years | Increment with the continuous economic development in Taiwan |
Example 3 | Hourly | From 1 December 2011 to 1 January 2012 | 744 h | Cyclic fluctuation |
Regions | SVRCQGA Parameters | MAPE of Testing (%) | ||
σ | C | ε | ||
Northern | 4.0000 | 0.6500 | 1.0760 | |
Central | 6.0000 | 0.3500 | 1.2130 | |
Southern | 8.0000 | 0.4800 | 1.1650 | |
Eastern | 12.0000 | 0.2800 | 1.5180 | |
Regions | SVRQGA Parameters | MAPE of Testing (%) | ||
σ | C | ε | ||
Northern | 3.0000 | 0.3400 | 1.3150 | |
Central | 10.0000 | 0.4800 | 1.6830 | |
Southern | 6.0000 | 0.3500 | 1.3640 | |
Eastern | 4.0000 | 0.6800 | 1.9680 |
Indexes | SVRCQGA | SVRQGA | SVRCQTS | SVRQTS | SVRCQPSO | SVRQPSO |
---|---|---|---|---|---|---|
Northern region | ||||||
MAPE (%) | 1.0760 | 1.3150 | 1.0870 | 1.3260 | 1.1070 | 1.3370 |
RMSE | 131.48 | 159.26 | 132.79 | 159.43 | 142.62 | 160.28 |
MAE | 130.00 | 157.50 | 141.00 | 158.50 | 132.25 | 159.00 |
Central region | ||||||
MAPE (%) | 1.2130 | 1.6830 | 1.2650 | 1.6870 | 1.2840 | 1.6890 |
RMSE | 64.46 | 90.18 | 67.69 | 90.67 | 67.70 | 89.87 |
MAE | 64.00 | 89.25 | 67.00 | 89.75 | 67.50 | 89.25 |
Southern region | ||||||
MAPE (%) | 1.1650 | 1.3640 | 1.1720 | 1.3670 | 1.1840 | 1.3590 |
RMSE | 75.44 | 87.82 | 75.57 | 88.84 | 76.03 | 88.05 |
MAE | 74.75 | 87.50 | 75.25 | 88.00 | 75.75 | 87.25 |
Eastern region | ||||||
MAPE (%) | 1.5180 | 1.9680 | 1.5430 | 1.9720 | 1.5940 | 1.9830 |
RMSE | 6.12 | 7.86 | 6.38 | 7.95 | 6.30 | 7.79 |
MAE | 6.00 | 7.75 | 6.00 | 7.75 | 6.25 | 7.75 |
Compared Models | Wilcoxon Signed-Rank Test α = 0.05; Wilcoxon W Statistic = 0 | Friedman Test α = 0.05 |
---|---|---|
Northern region | H0: e1 = e2 = e3 = e4 = e5 = e6 F = 12.46; p = 0.028 (reject H0) | |
SVRCQGA vs. SVRQPSO | W = 0 * | |
SVRCQGA vs. SVRCQPSO | W = 0 * | |
SVRCQGA vs. SVRQTS | W = 0 * | |
SVRCQGA vs. SVRCQTS | W = 1 | |
SVRCQGA vs. SVRQGA | W = 0 * | |
Central region | H0: e1 = e2 = e3 = e4 = e5 = e6 F = 13.43; p = 0.021 (reject H0) | |
SVRCQGA vs. SVRQPSO | W = 0 * | |
SVRCQGA vs. SVRCQPSO | W = 0 * | |
SVRCQGA vs. SVRQTS | W = 0 * | |
SVRCQGA vs. SVRCQTS | W = 1 | |
SVRCQGA vs. SVRQGA | W = 0 * | |
Southern region | H0: e1 = e2 = e3 = e4 = e5 = e6 F = 15.57; p = 0.013 (reject H0) | |
SVRCQGA vs. SVRQPSO | W = 0 * | |
SVRCQGA vs. SVRCQPSO | W = 0 * | |
SVRCQGA vs. SVRQTS | W = 0 * | |
SVRCQGA vs. SVRCQTS | W = 1 | |
SVRCQGA vs. SVRQGA | W = 0 * | |
Eastern region | H0: e1 = e2 = e3 = e4 = e5 = e6 F = 11.34; p = 0.035 (reject H0) | |
SVRCQGA vs. SVRQPSO | W = 0 * | |
SVRCQGA vs. SVRCQPSO | W = 0 * | |
SVRCQGA vs. SVRQTS | W = 0 * | |
SVRCQGA vs. SVRCQTS | W = 1 | |
SVRCQGA vs. SVRQGA | W = 0 * |
Optimization Algorithms | Parameters | MAPE of Testing (%) | ||
---|---|---|---|---|
σ | C | ε | ||
QPSO algorithm [27] | 12.0000 | 0.380 | 1.3460 | |
CQPSO algorithm [27] | 10.0000 | 0.560 | 1.1850 | |
QTS algorithm [28] | 5.0000 | 0.630 | 1.3210 | |
CQTS algorithm [28] | 6.0000 | 0.340 | 1.1540 | |
QGA algorithm | 9.0000 | 0.480 | 1.3180 | |
CQGA algorithm | 12.0000 | 0.650 | 1.1160 |
Years | SVRCQGA | SVRQGA | SVRCQTS | SVRQTS | SVRCQPSO | SVRQPSO |
---|---|---|---|---|---|---|
MAPE (%) | 1.1160 | 1.3180 | 1.1540 | 1.3210 | 1.1850 | 1.3460 |
RMSE | 1502.66 | 1774.62 | 1631.48 | 1778.74 | 1618.34 | 1812.51 |
MAE | 1466.33 | 1731.78 | 1554.89 | 1735.78 | 1575.67 | 1768.78 |
Compared Models | Wilcoxon Signed-Rank Test α = 0.05; Wilcoxon W Statistic = 8 | Friedman Test α = 0.05 |
---|---|---|
SVRCQGA vs. SVRQPSO | W = 4 * | H0: e1 = e2 = e3 = e4 = e5 = e6 F = 13.35; p = 0.022 (reject H0) |
SVRCQGA vs. SVRCQPSO | W = 2 * | |
SVRCQGA vs. SVRQTS | W = 4 * | |
SVRCQGA vs. SVRCQTS | W = 4 * | |
SVRCQGA vs. SVRQGA | W = 4 * |
Optimization Algorithms | Parameters | MAPE of Testing (%) | ||
---|---|---|---|---|
σ | C | ε | ||
QPSO algorithm [27] | 9.000 | 42.000 | 0.1800 | 1.9600 |
CQPSO algorithm [27] | 19.000 | 35.000 | 0.8200 | 1.2900 |
QTS algorithm [28] | 25.000 | 67.000 | 0.0900 | 1.8900 |
CQTS algorithm [28] | 12.000 | 26.000 | 0.3200 | 1.3200 |
QGA algorithm | 5.000 | 79.000 | 0.3800 | 1.7500 |
CQGA algorithm | 6.000 | 54.000 | 0.6200 | 1.1700 |
Indexes | SVRCQGA | SVRQGA | SVRCQTS | SVRQTS | SVRCQPSO | SVRQPSO |
---|---|---|---|---|---|---|
MAPE (%) | 1.1700 | 1.7500 | 1.3200 | 1.8900 | 1.2900 | 1.9600 |
RMSE | 1.4927 | 1.6584 | 1.9909 | 2.8507 | 1.9257 | 2.9358 |
MAE | 1.4522 | 1.6174 | 1.8993 | 2.7181 | 1.8474 | 2.8090 |
Compared Models | Wilcoxon Signed-Rank Test | Friedman Test | |
---|---|---|---|
α = 0.05; Wilcoxon W Statistic = 2328 | p-Value | α = 0.05 | |
SVRCQGA vs. SVRQPSO | W = 1278.0 * | 0.00012 | H0: e1 = e2 = e3 = e4 = e5 = e6 F = 71.266; p = 0.000 (reject H0) |
SVRCQGA vs. SVRCQPSO | W = 1152.5 * | 0.00000 | |
SVRCQGA vs. SVRQTS | W = 1256.0 * | 0.00000 | |
SVRCQGA vs. SVRCQTS | W = 1263.0 * | 0.00010 | |
SVRCQGA vs. SVRQGA | W = 2134.5 * | 0.00720 |
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Lee, C.-W.; Lin, B.-Y. Applications of the Chaotic Quantum Genetic Algorithm with Support Vector Regression in Load Forecasting. Energies 2017, 10, 1832. https://doi.org/10.3390/en10111832
Lee C-W, Lin B-Y. Applications of the Chaotic Quantum Genetic Algorithm with Support Vector Regression in Load Forecasting. Energies. 2017; 10(11):1832. https://doi.org/10.3390/en10111832
Chicago/Turabian StyleLee, Cheng-Wen, and Bing-Yi Lin. 2017. "Applications of the Chaotic Quantum Genetic Algorithm with Support Vector Regression in Load Forecasting" Energies 10, no. 11: 1832. https://doi.org/10.3390/en10111832