MATLAB: Generating Unique Solutions with PSO and a Tolerance Threshold

This code utilizes the Particle Swarm Optimization (PSO) algorithm to generate unique solutions within a defined tolerance threshold. The goal is to find unique solutions for the 'Shubert' function, with the PSO function used to perform the optimization.

Code Explanation:

1. Initialization:

   • glob = zeros(18,3); initializes a matrix glob with dimensions 18x3 to store the unique solutions.
   • The for i=1:1000 loop iterates 1000 times, running the PSO algorithm in each iteration.

2. PSO Optimization:

   • [xopt, yopt, fopt] = PSO(@Shubert, np, maxiter, bounds); runs the PSO algorithm for the 'Shubert' function with specific parameters np, maxiter, and bounds. The function returns the optimized values xopt, yopt, and fopt.

3. Uniqueness Check:

   • The code checks if the obtained solution [xopt, yopt, fopt] is unique within a specified tolerance threshold eps. It compares the current solution to the existing solutions in glob using abs( glob(k,1) - xopt) < eps && abs(glob(k,2) - yopt) < eps && abs(glob(k,3) - fopt) < eps.

4. Solution Storage:

   • If the solution is unique (not within the tolerance threshold of existing solutions), it is stored in the glob matrix at the current row k.
   • glob(k,1)=xopt;
   • glob(k,2)=yopt;
   • glob(k,3)=fopt;

5. Error Handling:

   • The code includes error handling for scenarios where unique solutions cannot be found within the specified tolerance threshold for all 18 rows of glob.
   • if ~flag checks if any row k of glob remains empty after the iterations. If so, it raises an error message error('Could not find unique solution for glob(%d,:)', k);.

Note: The code assumes that you have a defined PSO function, a 'Shubert' function, and the tolerance threshold eps is already set within your environment.