optimizing iterated objective function - containing ∑- sum operator

I am writing MATLAB code to minimize objective function f(x,y) - please see attached image. P and Q are readily available (known) arrays of equal size n. My major challenge is on how to deal with P and Q to formulate the objective function f(x,y) for input to the optimization algorithm (genetic algorithm). I tried using a loop to iterate through all P and Q before the optimization process but i could not understand the resulting objective function and how to apply it in the optimization algorithm. Same challenge exists with the first constraint, dealing with P and Q. Is there any possible way i can resolve this? (n,a,b,R,K and L are all known constants). Thanks in advance.

Answer 1

[Wycliff Dembe]

I later figured it out. I had to apply loops and function handles and it worked.

[Kedar Karpe]

Please share your solution. Thanks!

Answer 2

[Wycliff Dembe]

Define a custom objective function as:

function f_sum = objectiveFun(inParam)

global N p q

 x = inParam(1);
 y = inParam(2);
 
for i=1:N
   f_xy(i) = sqrt((x-p(i))^2+(y-q(i))^2); 
end
f_sum = sum(f_xy);
end

Define a custom constraint function as:

function [ c, ceq ] = constraintsFun(inParam)
global R 
a = rand; b = rand;
x = inParam(1);
y = inParam(2);
 
%inequality constraint. please note I didn't use the first constraint during implementation so I haven't written it here
c = (x-a)^2 + (y-b)^2 - R;

%equality constraint 
ceq = []; % none
end

Invoke the matlab built-in ga function as:

 clc
 clear
 
global N p q R

 R = randi(5);
 N = randi(20);
 p = rand(1,N);
 q = rand(1,N);
 
 nvars = 2; % x and y
 min_bound = [-rand -rand]; % -K,-L
 max_bound = [rand rand]; % K,L

[optim_x_y,f_min,exitflag] = ga(@objectiveFun,nvars,[],[],[],[],min_bound,max_bound,@constraintsFun)

Anything you might want to customise in ga can be passed via options using gaoptimset

[Muhammad Ali Zakria]

What is the following line doing? Is it taking some constant value from the input paramter?

x = inParam(1);

[Wycliff Dembe]

The dimensions of the input parameter (inParam) are defined in nvars.

With nvars gives as 2 (because we have x and y), we define the first dimension of inParam as x and the second dimension of inParam as y. The two can be accessed as:

x = inParam(1)

y = inParam(2)

[Shahrooz Pouryousef]

Hi Wycliff, I need your help. I have almost the same objective function. But I have sum over three different sets in my objective function and also for each variable I need to call a function. Would you please help me on this? I can explain more if you are here.

Answer 3

[Hanne Vanduffel]

Could you please share your code?

Thanks in advance!