Minimize problem using PSO

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Reji G
Reji G 2022-6-15
评论： Sam Chak 2022-6-17

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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Sam Chak
Sam Chak 2022-6-15
编辑：Sam Chak 2022-6-17
Ran in:
Hi @Reji G
It seems that the function does not have any global minima.
[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)
Optimization ended: relative change in the objective value over the last OPTIONS.MaxStallIterations iterations is less than OPTIONS.FunctionTolerance.
x = 1×2
4.0000 0.4000
fval = 7.8973
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Reji G
Reji G 2022-6-17
Hello Sam,
Its working. Thank you. Need a small clarification.
  1. How to know its displaying minimum value?
  2. What changes need to be done in this program to display maximum value?
  3. How to list all the values?(for all x and L combinations. c1 to c15 in case of my image)
Sam Chak
Sam Chak 2022-6-17
Ran in:
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)
Optimization ended: relative change in the objective value over the last OPTIONS.MaxStallIterations iterations is less than OPTIONS.FunctionTolerance.
x = 1×2
1.0000 0.4000
fval = -220
fmaxValue = -fval % can verify the result with the graphical representation
fmaxValue = 220
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:
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:
https://www.mathworks.com/help/gads/particle-swarm-options.html#bued1tk-1
If you find this tutorial on using particleswarm() is helpful, consider accepting ✔ and voting 👍 the Answer. Thanks, @Reji G!

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