Finding optimal values for a linear combination using PSO

Hello, I want to find the optimal values of x1-x4 of the linear combination CCIQ(X,Y)=x1*ECC(X,Y) + x2*H(X,Y) + x3*R + x4*AMBE(X,Y) using PSO algorithm.

ECC(X,Y), H(X,Y), R and AMBE(X,Y) are computed knwown values which corresponds to edge based contrast criterion, entropy, corelation coef and absolute mean brightness error respectively. Any help on this would be greatly appreciated!

[Matt J]

Why not use linprog?

[Claudia Alonzo]

I tried using the built in problem solver and it tried solving the problem using linprog as you suggested. I got an error saying that the problem is unbounded. I posted the code below, I'm not sure if i'm missing anything. I essentially want to find the weights so that a1+a2+a3+a4 == 1

a1 = optimvar('a1');

a2 = optimvar('a2');

a3 = optimvar('a3');

a4 = optimvar('a4');

prob = optimproblem;

prob.Objective = a1*ECC_XY+a2*H_XY+a3*R_XY+a4*AMBE_XY;

prob.Constraints.cons1 = a1+a2+a3+a4==1;

sol = solve(prob)