Genetic Algorithm Approach to Design of Multi-Layer Perceptron for Combined Cycle Power Plant Electrical Power Output Estimation
"> Figure 1
<p>Schematic diagram of the analyzed CCPP.</p> "> Figure 2
<p>Graphical representation of the cross-validation procedure (<math display="inline"><semantics> <msub> <mi>F</mi> <mn>1</mn> </msub> </semantics></math> - Fold 1; <math display="inline"><semantics> <msub> <mi>F</mi> <mn>2</mn> </msub> </semantics></math> - Fold 2; <math display="inline"><semantics> <msub> <mi>F</mi> <mn>3</mn> </msub> </semantics></math> - Fold 3; <math display="inline"><semantics> <msub> <mi>F</mi> <mn>4</mn> </msub> </semantics></math> - Fold 4; <math display="inline"><semantics> <msub> <mi>F</mi> <mn>5</mn> </msub> </semantics></math> - Fold 5).</p> "> Figure 3
<p>Graphical representation of the mutation procedure on the example with <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math> (<math display="inline"><semantics> <msub> <mi>K</mi> <mn>1</mn> </msub> </semantics></math> - parent chromosome, <math display="inline"><semantics> <msub> <mi>K</mi> <mn>3</mn> </msub> </semantics></math> - child chromosome, <span class="html-italic">G</span> - gene).</p> "> Figure 4
<p>Graphical representation of used random selection tree (<b>a</b>) and used crossover methods (<b>b</b>–<b>d</b>) (<math display="inline"><semantics> <msub> <mi>K</mi> <mn>1</mn> </msub> </semantics></math> - first parent chromosome, <math display="inline"><semantics> <msub> <mi>K</mi> <mn>2</mn> </msub> </semantics></math> - second parent chromosome, <math display="inline"><semantics> <msub> <mi>K</mi> <mn>4</mn> </msub> </semantics></math> - first child chromosome, <math display="inline"><semantics> <msub> <mi>K</mi> <mn>5</mn> </msub> </semantics></math> - second child chromosome, <span class="html-italic">G</span> - gene).</p> "> Figure 5
<p>Bland-Altman plots for all five MLP configurations designed with GA implementation with <math display="inline"><semantics> <mover> <mrow> <mi>M</mi> <mi>R</mi> <mi>E</mi> </mrow> <mo>¯</mo> </mover> </semantics></math> as a fitness function.</p> "> Figure 6
<p>Bland-Altman plots for all five MLP configurations designed with GA implementation with <math display="inline"><semantics> <mover> <mrow> <mi>M</mi> <mi>S</mi> <mi>E</mi> </mrow> <mo>¯</mo> </mover> </semantics></math> as a fitness function.</p> "> Figure 7
<p>Bias and associated confidence interval for each MLP configuration (<math display="inline"><semantics> <msub> <mi>R</mi> <mn>1</mn> </msub> </semantics></math> - MLP with one hidden layer and <math display="inline"><semantics> <mover> <mrow> <mi>M</mi> <mi>R</mi> <mi>E</mi> </mrow> <mo>¯</mo> </mover> </semantics></math> as a fitness function, <math display="inline"><semantics> <msub> <mi>R</mi> <mn>2</mn> </msub> </semantics></math> - MLP with two hidden layers and <math display="inline"><semantics> <mover> <mrow> <mi>M</mi> <mi>R</mi> <mi>E</mi> </mrow> <mo>¯</mo> </mover> </semantics></math> as a fitness function, <math display="inline"><semantics> <msub> <mi>R</mi> <mn>4</mn> </msub> </semantics></math> - MLP with four hidden layers and <math display="inline"><semantics> <mover> <mrow> <mi>M</mi> <mi>R</mi> <mi>E</mi> </mrow> <mo>¯</mo> </mover> </semantics></math> as a fitness function, <math display="inline"><semantics> <msub> <mi>R</mi> <mn>5</mn> </msub> </semantics></math> - MLP with five hidden layers and <math display="inline"><semantics> <mover> <mrow> <mi>M</mi> <mi>R</mi> <mi>E</mi> </mrow> <mo>¯</mo> </mover> </semantics></math> as a fitness function, <math display="inline"><semantics> <msub> <mi>S</mi> <mn>1</mn> </msub> </semantics></math> - MLP with one hidden layer and <math display="inline"><semantics> <mover> <mrow> <mi>M</mi> <mi>S</mi> <mi>E</mi> </mrow> <mo>¯</mo> </mover> </semantics></math> as a fitness function, <math display="inline"><semantics> <msub> <mi>S</mi> <mn>3</mn> </msub> </semantics></math> - MLP with three hidden layers and <math display="inline"><semantics> <mover> <mrow> <mi>M</mi> <mi>S</mi> <mi>E</mi> </mrow> <mo>¯</mo> </mover> </semantics></math> as a fitness function).</p> "> Figure 8
<p>Comparisson between predicted <math display="inline"><semantics> <msub> <mi>P</mi> <mi>e</mi> </msub> </semantics></math> and real data for three MLPs with the best performance: (<b>a</b>) <math display="inline"><semantics> <msub> <mi>R</mi> <mn>1</mn> </msub> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <msub> <mi>R</mi> <mn>5</mn> </msub> </semantics></math> and (<b>c</b>) <math display="inline"><semantics> <msub> <mi>S</mi> <mn>3</mn> </msub> </semantics></math>.</p> ">
Abstract
:1. Introduction
- to investigate implementation possibility of GA in design of MLP for CCPP electrical power output estimation,
- to compare regression performances of GA - designed MLP with results presented in available literature and
- to determine MLP configuration with optimal performances in regard of regression errors.
2. Materials and Methods
2.1. Dataset Description
2.2. Multilayer Perceptron
- Input layer - layer which represents input data vector,
- Hidden layers - layers between input and output layer and
- Output layer - layer that represents output vector.
2.3. Genetic Algorithm
- Mutation,
- Crossover and
- Parents selection.
2.3.1. Mutation
2.3.2. Crossover
2.3.3. Fitness Function
- and
- .
2.3.4. Population Creation
2.3.5. Parents Selection
2.3.6. New Population Formation
2.3.7. Chromosome Construction
2.4. Bland-Altman Analysis
- Bias,
- Confidence interval upper bound and
- Confidence interval lower bound.
2.5. Root Mean Square Error
3. Results and Discussion
3.1. Results
3.2. Discussion
4. Conclusions and Future Work
- there is a possibility of GA utilization for design of MLP for CCPP electrical power output,
- presented MLP configurations are performing with lower in comparison to regression methods presented in literature and
- the lowest is achieved if MLP configuration with 5 hidden layers of 80,25,65,75 and 80 nodes, respectively, is utilized. Activation functions used in design of aforementioned MLP are: Logistic Sigmoid in the first layer, Tanh in the second layer and ReLU in all other layers. The best results are achieved if MLP is trained by using Adam solver.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Category | Method | RMSE |
---|---|---|
Functions | Simple Linear regression | 5.425 |
Linear Regression | 4.561 | |
Least Median Square | 4.968 | |
Multilayer Perceptron | 5.341 | |
Radial Basis Funcion Neural Network | 7.501 | |
Pace Regression | 4.561 | |
Support Vector Poly Kernel Regression | 4.563 |
Type | Parameter | Range |
---|---|---|
Input | Temperature (T) | 1.81 C–37.11 C |
Input | Ambient Pressure () | mbar– mbar |
Input | Relative Humidity () | %–% |
Input | Exhaust Vacuum (V) | cmHg– cmHg |
Output | Average Hourly Electrical Power Output () | MW– MW |
Parameter | Variations | Range |
---|---|---|
Number of epochs | 50 | |
Number of nodes in the hidden layer | 20 | |
Batch size | 75 |
Parameter | Set |
---|---|
Activation function | , |
Solver | , |
Gene | Gene Representation | Parameter |
---|---|---|
Number of epochs | ||
Number of neurons in the hidden layer | ||
Activation function in the hidden layer | ||
Activation function in the output layer | ||
Batch size | ||
Solver |
Gene | Gene Representation | Parameter |
---|---|---|
Number of epochs | ||
Number of neurons in the first hidden layer | ||
Activation function in the first hidden layer | ||
Number of neurons in the second hidden layer | ||
Activation function in the second hidden layer | ||
Activation function in the output layer | ||
Batch size | ||
Solver |
Configuration | |||||
---|---|---|---|---|---|
Gene | |||||
Number of epochs | 87 | 70 | 99 | 91 | 13 |
Number of neurons in the first hidden layer | 60 | 80 | 65 | 55 | 80 |
Activation function in the first hidden layer | ReLU | ReLU | Sigmoid | ReLU | Sigmoid |
Number of neurons in the second hidden layer | - | 100 | 10 | 55 | 25 |
Activation function in the second hidden layer | - | ReLU | ReLU | Sigmoid | Tanh |
Number of neurons in the third hidden layer | - | - | 60 | 90 | 65 |
Activation function in the third hidden layer | - | - | ReLU | Sigmoid | ReLU |
Number of neurons in the fourth hidden layer | - | - | - | 85 | 75 |
Activation function in the fourth hidden layer | - | - | - | ReLU | ReLU |
Number of neurons in the fifth hidden layer | - | - | - | - | 80 |
Activation function in the fifth hidden layer | - | - | - | - | ReLU |
Activation function in the output layer | ReLU | ReLU | ReLU | ReLU | ReLU |
Batch size | 407 | 1164 | 453 | 223 | 39 |
Solver | Adam | Adam | Adam | SGD | Adam |
Fitness value () | % | % | % | % | % |
Configuration | |||||
---|---|---|---|---|---|
Gene | |||||
Number of epochs | 99 | 55 | 53 | 73 | 55 |
Number of neurons in the first hidden layer | 35 | 40 | 80 | 30 | 50 |
Activation function in the first hidden layer | ReLU | Tanh | Sigmoid | ReLU | ReLU |
Number of neurons in the second hidden layer | - | 100 | 15 | 80 | 15 |
Activation function in the second hidden layer | - | ReLU | ReLU | Sigmoid | Tanh |
Number of neurons in the third hidden layer | - | - | 85 | 80 | 100 |
Activation function in the third hidden layer | - | - | ReLU | Tanh | Tanh |
Number of neurons in the fourth hidden layer | - | - | - | 80 | 35 |
Activation function in the fourth hidden layer | - | - | - | ReLU | ReLU |
Number of neurons in the fifth hidden layer | - | - | - | - | 30 |
Activation function in the fifth hidden layer | - | - | - | - | ReLU |
Activation function in the output layer | ReLU | ReLU | ReLU | ReLU | ReLU |
Batch size | 1278 | 246 | 430 | 820 | 1623 |
Solver | Adam | AdaGrad | P AdaGrad | RMSprop | Adam |
Fitness value () | 28.4081 | 80.7939 | 39.0868 | 216.6123 | 17.6511 |
Category | Method | RMSE |
---|---|---|
Functions | Simple Linear regression | 5.425 |
Linear Regression | 4.561 | |
Least Median Square | 4.968 | |
Multilayer Perceptron | 5.341 | |
Radial Basis Funcion Neural Network | 7.501 | |
Pace Regression | 4.561 | |
Support Vector Poly Kernel Regression | 4.563 | |
MLPs designed with GA | 5.07 | |
4.305 | ||
4.874 |
Configuration | Mean | Minimal | Maximal | Standard Deviation | |
---|---|---|---|---|---|
5-fold cross-validation | 5.37 | 5.01 | 5.85 | 0.29 | |
4.31 | 4.16 | 4.43 | 0.09 | ||
4.64 | 4.53 | 4.93 | 0.15 | ||
10-fold cross-validation | 5.27 | 4.66 | 5.99 | 0.45 | |
4.52 | 4.11 | 5.13 | 0.39 | ||
4.98 | 4.28 | 5.69 | 0.43 |
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Lorencin, I.; Anđelić, N.; Mrzljak, V.; Car, Z. Genetic Algorithm Approach to Design of Multi-Layer Perceptron for Combined Cycle Power Plant Electrical Power Output Estimation. Energies 2019, 12, 4352. https://doi.org/10.3390/en12224352
Lorencin I, Anđelić N, Mrzljak V, Car Z. Genetic Algorithm Approach to Design of Multi-Layer Perceptron for Combined Cycle Power Plant Electrical Power Output Estimation. Energies. 2019; 12(22):4352. https://doi.org/10.3390/en12224352
Chicago/Turabian StyleLorencin, Ivan, Nikola Anđelić, Vedran Mrzljak, and Zlatan Car. 2019. "Genetic Algorithm Approach to Design of Multi-Layer Perceptron for Combined Cycle Power Plant Electrical Power Output Estimation" Energies 12, no. 22: 4352. https://doi.org/10.3390/en12224352