https://github.com/krproject-tech/fp_nsgaii
NSGA-II with Floating point representation.
https://github.com/krproject-tech/fp_nsgaii
genetic-algorithm matlab multi-objective-optimization optimization
Last synced: 7 months ago
JSON representation
NSGA-II with Floating point representation.
- Host: GitHub
- URL: https://github.com/krproject-tech/fp_nsgaii
- Owner: KRproject-tech
- License: mit
- Created: 2022-09-29T04:31:28.000Z (almost 3 years ago)
- Default Branch: main
- Last Pushed: 2024-09-16T11:07:06.000Z (10 months ago)
- Last Synced: 2024-09-16T19:07:19.301Z (10 months ago)
- Topics: genetic-algorithm, matlab, multi-objective-optimization, optimization
- Language: MATLAB
- Homepage:
- Size: 36.1 MB
- Stars: 1
- Watchers: 1
- Forks: 1
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
README
#
FP_NSGAII
**Communication**
**Language**
__Multi-objective optimization analysis by Non-dominated Sorting Genetic Algorithm (NSGA-II) [^1] with Floating Point representation [^2][^4] (MATLAB R2007b - ).__
__This code is validated with MATLAB R2007b or later versions. However, the PlatEMO library (https://github.com/BIMK/PlatEMO), which can operate MATLAB 2018a or later versions, is more convenient and performs faster.__
## Directory
└─NSGA_2_ver3
├─Bench_mark
│ └─進化計算パラメータ
│ └─html
├─cores
│ └─functions
│ └─NSGA_2_functions
└─save
└─fig
## Usage
__[Step 1] Start GUI form__
Open the “GUI.fig” from MATLAB.
__[Step 2] Pre-setting__
Edit the code for evaluation functions in "./cores/functions/NSGA_2_functions/evaluation_func.m".
````
function f_vec = evaluation_func(pop_vec)
%% 評価関数 (pop_vecの行が個体番号，列が個体パラメータ)
x_vec = pop_vec;
%% SCH問題：パレート解 -> x in [0,2]
% f_vec = [x_vec(:,1).^2 ...
% (x_vec(:,1) - 2).^2 ];
%% FON問題：パレート解 -> x1 = x2 = x3 in [-1/√3,1/√3]
% f_k = @(k, x_vec)( 1 - exp( -sum( (x_vec + (-1).^k/sqrt(3)).^2 , 2) ) );
% f_vec = [f_k(1, x_vec) ...
% f_k(2, x_vec)];
%% テスト問題2
a = 49;b = 4; c = 0.5;
f_1 = @(x_vec)( 0.5*(x_vec(:,1).^2 + x_vec(:,2).^2) + sin(x_vec(:,1).^2 + x_vec(:,2).^2) );
f_2 = @(x_vec)( -exp( -a*(cos( b*(x_vec(:,1) + x_vec(:,2)) ) - ((x_vec(:,1) - x_vec(:,2))) ).^2 - c*(x_vec(:,1) + x_vec(:,2) + 1).^2 ));
f_3 = @(x_vec)( 1./(x_vec(:,1).^2 + x_vec(:,2).^2 + 1) - 1.1*exp(-(x_vec(:,1).^2 + x_vec(:,2).^2)) );
f_vec = [f_1(x_vec) ...
f_2(x_vec) ...
f_3(x_vec)];
%% MOP3
% f_1 = @(x_vec)( 0.5*(x_vec(:,1).^2 + x_vec(:,2).^2) + sin(x_vec(:,1).^2 + x_vec(:,2).^2) );
% f_2 = @(x_vec)( ( 3*x_vec(:,1) - 2*x_vec(:,2) + 4 ).^2/8 + ( x_vec(:,1) - x_vec(:,2) + 1 ).^2/27 + 15 );
% f_3 = @(x_vec)( 1./(x_vec(:,1).^2 + x_vec(:,2).^2 + 1) - 1.1*exp(-(x_vec(:,1).^2 + x_vec(:,2).^2)) );
%
% f_vec = [f_1(x_vec) ...
% f_2(x_vec) ...
% f_3(x_vec)];
%% テスト問題 (最適解：部分球面)
% g_func = @(x3)( sin(x3) + 1 );
% f_1 = @(x_vec)( (1 + g_func(x_vec(:,3))).*( abs(cos(x_vec(:,1)).*cos(x_vec(:,2)) ) + 1e-3) );
% f_2 = @(x_vec)( (1 + g_func(x_vec(:,3))).*( abs(cos(x_vec(:,1)).*sin(x_vec(:,2)) ) + 1e-3) );
% f_3 = @(x_vec)( (1 + g_func(x_vec(:,3))).*(abs(sin(x_vec(:,1)) ) + 1e-3) );
%
% f_vec = [f_1(x_vec) ...
% f_2(x_vec) ...
% f_3(x_vec)];
````
Next, push the "Parameters" button and edit parameters, or edit the code for parameters in "./save/param_setting.m".
````
%% parameter for NSGA-2
%----------------------- 解析パラメータ ------------------------------------
GENERATION = 200; %% GENERATION[-]
TOURNAMENT_RATE = 0.5; %% TOURNAMENT_RATE[-]
CROSSOVER_RATE = 1.0; %% CROSSOVER_RATE[-]
MUTATION_RATE = 0.4; %% 突然変異個体選択率[-]
MUTATION_RATE_1 = 0.8; %% 突然変異率[-]
%----------------------- 個体パラメータ ------------------------------------
MAX_POP_NUM = 500; %% the number of Populations[-]
POP_LGT = 3; %% Length of variable[-]
% Initial value of populations [-]
pop_weight = 0.1*ones(1,POP_LGT);
% Mutation change width
pop_mutation_width = 10*pop_weight;
````
__[Step 3] Start optimization__
Push the “exe” button or execute the code in "./cores/exe.m", and wait until the finish of the analysis.
__[Step 4] Restart optimization (if solutions do not converge at [Step 3])__
Execute the code in "./cores/exe_func_restart.m".
__[Step 5] Plot results__
Push the “plot” button.
__[Step 6] View plotted results__
Results (figures and movie) plotted by [Step 4] are in "./save" directory.
## Optimal results
Optimal solutions are in `h_pop_vec{end}(pop_rank{1},:)`.
Pareto-front is plotted by `plot3(f_vec(pop_rank{1},1),f_vec(pop_rank{1},2),f_vec(pop_rank{1},3),'ro')`
## Gallery
__MOP3__ bench problem [^3]
$$
\min_{x \in \mathbb{R}^2} f_1, f_2, f_3,
$$
where,
$$
\left.
\begin{eqnarray}
&& f_1(x_1,x_2) = 0.5(x_1^2 + x_2^2) + \sin(x_1^2 + x_2^2) \\
&& f_2(x_1,x_2) = \frac{1}{8}(3 x_1^2 - 2 x_2^2 + 4)^2 + \frac{1}{27}(x_1^2 - x_2^2 + 1)^2 + 15 \\
&& f_3(x_1,x_2) = \frac{1}{x_1^2 + x_2^2 + 1} - 1.1 \exp( -x_1^2 - x_2^2 )
\end{eqnarray}
\right).
$$
__ZDT3__ bench problem [^5]
$$
\min_{x \in \mathbb{R}^N} f_1, f_2,
$$
where, $x_i := 2^{-1} \left(\frac{2}{\pi} \tan^{-1}{ x^*_i} + 1\right), i \in \\{1, \ldots, N \\}, N=30$ and,
$$
\left.
\begin{eqnarray}
&& f_1(x_i) = x_1 \\
&& f_2(x_i) = g(x_i) h( f_1(x_i), g(x_i)) \\
&& g(x_i) := 1 + \frac{9}{N-1} \sum_{k=2}^N x_k \\
&& h(f_1, g) := 1 - \sqrt{ \frac{f_1}{g} } - \frac{f_1}{g} \sin{ 10 \pi f_1 } \\
\end{eqnarray}
\right).
$$
The red solid line includes the analytical solution of the Pareto front for the ZDT3 problem,
$$
\left.
\begin{eqnarray}
&& x_i = 0, i \in \\{2, \ldots, N \\} \\
&& x_1 \in [0, 1] \\
\end{eqnarray}
\right).
$$
Namely,
$$
\left.
\begin{eqnarray}
&& g(x_i) = 1 \\
&& f_2(x_i) = g(x_i) \cdot h( f_1(x_i), g(x_i)) = 1 \cdot h( f_1(x_i), 1) = 1 - \sqrt{ f_1 } - f_1 \sin{ 10 \pi f_1 } \\
\end{eqnarray}
\right).
$$
__DTLZ7__ bench problem [^6]
$$
\min_{x \in \mathbb{R}^N} f_1, f_2, f_3,
$$
where, $x_i := 2^{-1} \left(\frac{2}{\pi} \tan^{-1}{ x^*_i} + 1\right), i \in \\{1, \ldots, N \\}, N=20$ and,
$$
\left.
\begin{eqnarray}
&& f_1(x_i) = x_1 \\
&& f_2(x_i) = x_2 \\
&& f_3(x_i) = (1 + g(x_i)) h( f_1(x_i), f_2(x_i), g(x_i)) \\
&& g(x_i) := 1 + \frac{9}{N} \sum_{k=2}^N x_k \\
&& h(f_1, f_2, g) := 3 - \sum_{k=1}^{2} \frac{f_k}{1 + g} (1 + \sin{ 3 \pi f_k }) \\
\end{eqnarray}
\right).
$$
### References
[^1]: K. Deb, A. Pratap, S. Agarwal, T. Meyarivan, A fast and elitist multiobjective genetic algorithm: NSGA-II, IEEE Transactions on Evolutionary Computation 6 (2) (2002) 182–197. doi:10.1109/4235.996017.
[^2]: C. Su, A genetic algorithm approach employing floating point representation for economic dispatch of electric power, in: The International Congress on Modelling and Simulation 1997, Vol. 204, 1997, pp. 1444–1449.
[^3]: Veldhuizen, D.A.V. and Lamont, G.B., Multiobjective evolutionary algorithm test suites, Proceedings of the 1999 ACM symposium on Applied computing, February 1999.
[^4]: Reducing the Power Consumption of a Shape Memory Alloy Wire Actuator Drive by Numerical Analysis and Experiment, IEEE/ASME Transactions on Mechatronics, Vol. 23, No. 4 (2018).
https://doi.org/10.1109/TMECH.2018.2836352
[^5]: Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C., and Fonseca, da V., Performance assessment of multiobjective optimizers: an analysis and review, IEEE Transactions on Evolutionary Computation, Vol. 7, No. 2, pp. 117–132 (2003).
[^6]: K. Deb et al, Scalable Test Problems for Evolutionary Multi-Objective Optimization, TIK-Technical Report No. 112, 2001.