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Minimize problem using PSO
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I want to find a minimum value of y(and the corresponding value of L and x), for various values of L and x. How to do this using Particle Swarm Optimization ?
The equation is:
Y= (20+500*L)/x^(1.2+(3*L))
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Accepted Answer
Sam Chak
on 15 Jun 2022
Edited: Sam Chak
on 17 Jun 2022
Hi @Reji G
It seems that the function does not have any global minima.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1033715/image.png)
[X, L] = meshgrid(1:3/40:4, 0.1:0.3/40:0.4);
Y = (20 + 500*L)./X.^(1.2 + 3*L);
surf(X, L, Y)
xlabel('x'); ylabel('L'); zlabel('y');
view(45, 30)
% Using PSO to minimize the function with the specified bound constraints
f = @(x) (20 + 500*x(2))./x(1).^(1.2 + 3*x(2));
nvars = 2;
lb = [1 0.1]; % lower bounds
ub = [4 0.4]; % upper bounds
[x, fval] = particleswarm(f, nvars, lb, ub)
4 Comments
Sam Chak
on 17 Jun 2022
Hi Reji,
1. The final objective function value of swarm particles is displayed as fval which indicates the function value at best solution found so far.
2. This is how to perform the maximization:
% Using PSO to maximize the function with the specified bound constraints
f = @(x) (20 + 500*x(2))./x(1).^(1.2 + 3*x(2));
fmax = @(x) -f(x);
nvars = 2;
lb = [1 0.1]; % lower bounds
ub = [4 0.4]; % upper bounds
[x, fval] = particleswarm(fmax, nvars, lb, ub)
fmaxValue = -fval % can verify the result with the graphical representation
3. Although the algorithm performs the search within the bound constraints, it does NOT search the entire space as in
to
(as in your scenario). It is possible list/store the position and the objective function value of each swarm particle in each iteration through calling the OutputFcn, something like this:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1036255/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1036260/image.png)
options = optimoptions(@particleswarm, 'OutputFcn', @pswoutfun)
[x, fval] = particleswarm(fmax, nvars, lb, ub, options)
where you have write the code for the pswoutfun.m file. But it can be a little tedious to write the code here. You can find some templates in
edit pswplotbestf
edit psoutputfile
For more info, please check:
If you find this tutorial on using particleswarm() is helpful, consider accepting ✔ and voting 👍 the Answer. Thanks, @Reji G!
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