nsga2-matlab

A very fast, almost 90% vectorized implementation of NSGA-II algorithm in MATLAB.

Possibly, it's the fastest in the town.

NOTE: This is the MATLAB/OCTAVE implementation of the original NSGA-II code.

Cloning

git clone https://github.com/chudur-budur/nsga2-matlab
cd nsga2-matlab

Running

GUI:

Open the nsga2-matlab folder in MATLAB/OCTAVE and just run the nsga2.m file, it's the main, simple.

If you want to run it from the CLI (turn off the plotting; do_plot = false; in nsga2.m, before running it):

MATLAB:

matlab -batch "nsga2"                                # R2019a or newer
matlab -nodisplay -nosplash -r "nsga2; exit"         # older versions

-batch exits by itself, and its exit code is non-zero if the script throws an error.

GNU OCTAVE:

octave --no-gui --quiet --eval "nsga2"

In both cases, if you want to save the population and results, set do_save = true; in nsga2.m. They will be saved in MATLAB data format .mat and the plain text format .out in the nsga2-matlab folder.

A number of benchmark multi-objective optimization problems are defined in problemdef folder. Each problem's corresponding standard algorithmic parameters are saved in input_data folder.

E.g. For zdt1, the problem is defined in problemdef/zdt1.m and the algorithm parameters to solve this problem are defined in input_data/zdt1.in, etc.

FAQ

1. What are the values in the files in problemdef mean?

They are parameters for the algorithm to solve a problem:

line 1: population size
line 2: number of generations
line 3: number of objectives
line 4: number of constraints (if no constraints, it's 0)
line 5: number of design variables
line 6+n: lower and upper bound of n design variables, per line
line 6+n+1: probability of crossover
line 6+n+2: probability of mutation
line 6+n+3: eta parameter for simulated binary crossover
line 6+n+4: eta parameter for polynomial mutation

See load_input_data.m for the details.

2. How do I define my own problem and parameter file for it?

Let's say you want to solve this multi-objective optimization problem:

$$ \begin{aligned} \min \quad & f_1(\mathbf{x}) = x_1^2 + x_2^2 \\ \min \quad & f_2(\mathbf{x}) = (x_1 - 1)^2 + 20 (x_2 - 2)^2 \\ \text{subject to} \quad & -5 \le x_i \le 5, \quad i = 1, 2 \end{aligned} $$

Write a function to define the problem in problemdef/example.m:

function [parent_pop] = example(parent_pop)

global nreal ;

x = parent_pop(:,1:nreal);
f1 = (x(:,1) .^ 2.0) + (x(:,2) .^ 2.0);
f2 = ((x(:,1) - 1.0) .^ 2.0) + (20.0 .* ((x(:,2) - 2.0) .^ 2.0));

parent_pop(:, (nreal+1)) = f1;
parent_pop(:, (nreal+2)) = f2;
end

Define the algorithm parameters in input_data/example.in:

100
100
2
0
2
-5 5
-5 5
0.9
0.5
10
10
0
1
1
2

Then refer to the parameter file at the top after the global declarations in nsga2.m:

load_input_data('input_data/example.in');

and then, the function in obj_func:

obj_func = @example;

Now run nsga2.m file to solve it.

WIP

1. Implement CTP functions: ctp1 - ctp8
2. Implement binary problem: zdt5