optimizing iterated objective function - containing ∑- sum operator

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Wycliff Dembe on 3 Mar 2018
Edited: Wycliff Dembe on 24 Oct 2019
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.

Wycliff Dembe on 23 Aug 2018
I later figured it out. I had to apply loops and function handles and it worked.
Kedar Karpe on 4 Feb 2019

Wycliff Dembe on 9 Apr 2019
Edited: Wycliff Dembe on 24 Oct 2019
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
Wycliff Dembe on 24 Oct 2019
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)

Hanne Vanduffel on 9 Apr 2019