Particle swarm optimisation problem

Hello all,

I am trying to use PSO for solving a system of nonlinear transcendental equations used in SHE PWM.

Following is the code i am using to solve

fun = @(alpha) pwm_equations_multilevel_pso(alpha0,1,2,harmonics)
    nvars = 3;
    lb=[0, 0, 0];ub=[deg2rad(90),deg2rad(90),deg2rad(90)];
    options = optimoptions('particleswarm','SwarmSize',200,'MaxStallIterations',200)    
    options = optimoptions(options,'PlotFcn',@pswplotbestf);
    [x,fval,exitflag,output] = particleswarm(fun,nvars,lb,ub,options)

where 'pwm_equations_multilevel_pso' is simply as follows

        function F_dot = pwm_equations_multilevel_pso(alpha,M,harmonic_cancellation,harmonics)
        
        
        F(1) = cos(harmonics(1)*alpha(1)) + cos(harmonics(1)*alpha(2)) - cos(harmonics(1)*alpha(3));
        F(2) = cos(harmonics(2)*alpha(1)) + cos(harmonics(2)*alpha(2)) - cos(harmonics(2)*alpha(3));
        F(3) = (cos(alpha(1)) + cos(alpha(2)) - cos(alpha(3))) - M;
        F_dot=dot(F,F)
        end

So the scalar value returned is a dot product of F with itself. I want to minimize F_dot to zero, but when i use PSO i get the following result

Unfortunately PSO does not converge to zero, it does not do anything in my case.

Obviously I am doing something wrong, but I am not sure what

Any help will be appreciated!

[Walter Roberson]

fun = @(alpha) pwm_equations_multilevel_pso(alpha0,1,2,harmonics)

Your objective function ignores the current state vector, alpha, and always calculates the equations on the same inputs, alpha0, 1, 2, harmonics . That is not going to change with the state vector, so you are going to get constant output instead of minimization.

[RAN]

Hi Walter,

Thank you for your reply.

Yes you are right, changing 'alpha0' to 'alpha' did the trick.

However it still does not converge to zero which is what i want. I have attached the plot. I tried to use ObjectiveLimit option to +0.01 and -0.01, in that case since the value of the first swarms being considered is already less than 0.01, the iteration stop.

Again would be nice if you can help me out here

[Walter Roberson]

Please post enough so that we can test your code -- in particular we need the value of harmonics

Question: why do you have harmonic_cancellation as a parameter of the function when you do not use it?

[RAN]

Hello Walter,

harmonics = [5 7]

Actually the objective function looks as follows

function F_dot = pwm_equations_multilevel_pso(alpha,M,harmonic_cancellation,harmonics)

% Cancellation of 5th harmonic
    if harmonic_cancellation == 1
        F(1) = cos(harmonics(1)*alpha(1)) + cos(harmonics(1)*alpha(2));
        F(2) = 4/pi*(cos(alpha(1)) + cos(alpha(2))) -M;
    end


% Cancellation of 5th, 7th harmonics
    if harmonic_cancellation == 2
        F(1) = cos(harmonics(1)*alpha(1)) + cos(harmonics(1)*alpha(2)) - cos(harmonics(1)*alpha(3));
        F(2) = cos(harmonics(2)*alpha(1)) + cos(harmonics(2)*alpha(2)) - cos(harmonics(2)*alpha(3));
        F(3) = (cos(alpha(1)) + cos(alpha(2)) - cos(alpha(3))) - M;
        F_dot=sqrt(dot(F,F));
    end
end

Its just different set of equations depending on the number of harmonics cancelled.

However i found a bug in my code, and after solving that the algorithm seems to work ok. I am posting the picture below

So now PSO tries to converge it to zero. But if the objective function already solves to a negative value in the first iteration then PSO stops.

Now the question remains is how to put constraints on alpha while solving the equations. I have ub and lb set as mentioned above for each alpha, but i also want to restrict the solutions such that alpha1<alpha2<alpha3. Is there a way to do that as well?

[Walter Roberson]

particleswarm() does not offer any constraints other than lb / ub .

You could add a penalty to the output for inputs that are out of order.

[RAN]

Ok, I already found some constrained based PSO.

Thank you for your help, now i got the hang of PSO.

Answer 1

[Nishma Sai]

can u just provide the entire code as i got some errors with my code

[Walter Roberson]

You could post your attempt, along with the error message, and we could help you debug the problems.