FP_NSGAII

Communication

Language

Multi-objective optimization analysis by Non-dominated Sorting Genetic Algorithm (NSGA-II) ¹ with Floating Point representation ²³ (MATLAB R2007b - ).

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".

Next, push the "Parameters" button and edit parameters, or edit the code for parameters in "./save/param_setting.m".

[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 ⁴

$$ \min_{x \in \mathbb{R}^2} f_1, f_2, f_3, $$

where,

$$ \left. \begin{eqnarray} && f_1(x_1,x_2) = 0.5(x_1^2 + x_2^2) + \sin(x_1^2 + x_2^2) \\ && f_2(x_1,x_2) = \frac{1}{8}(3 x_1^2 - 2 x_2^2 + 4)^2 + \frac{1}{27}(x_1^2 - x_2^2 + 1)^2 + 15 \\ && f_3(x_1,x_2) = \frac{1}{x_1^2 + x_2^2 + 1} - 1.1 \exp( -x_1^2 - x_2^2 ) \end{eqnarray} \right). $$

References

Footnotes

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. 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 ↩

4. Veldhuizen, D.A.V. and Lamont, G.B., Multiobjective evolutionary algorithm test suites, Proceedings of the 1999 ACM symposium on Applied computing, February 1999. ↩