MATLAB Examples

# Particle Swarm Optimization Simulation

Simulates the movements of a swarm to minimize the objective function

The swarm matrix is

swarm(index, [location, velocity, best position, best value], [x, y components or the value component])

Author: Wesam ELSHAMY (wesamelshamy@yahoo.com)

## Initialization

Parameters

```clear clc iterations = 30; inertia = 1.0; correction_factor = 2.0; swarm_size = 49; % ---- initial swarm position ----- index = 1; for i = 1 : 7 for j = 1 : 7 swarm(index, 1, 1) = i; swarm(index, 1, 2) = j; index = index + 1; end end swarm(:, 4, 1) = 1000; % best value so far swarm(:, 2, :) = 0; % initial velocity ```

## Iterations

```for iter = 1 : iterations %-- evaluating position & quality --- for i = 1 : swarm_size swarm(i, 1, 1) = swarm(i, 1, 1) + swarm(i, 2, 1)/1.3; %update x position swarm(i, 1, 2) = swarm(i, 1, 2) + swarm(i, 2, 2)/1.3; %update y position x = swarm(i, 1, 1); y = swarm(i, 1, 2); val = (x - 15)^2 + (y - 20)^2; % fitness evaluation (you may replace this objective function with any function having a global minima) if val < swarm(i, 4, 1) % if new position is better swarm(i, 3, 1) = swarm(i, 1, 1); % update best x, swarm(i, 3, 2) = swarm(i, 1, 2); % best y postions swarm(i, 4, 1) = val; % and best value end end [temp, gbest] = min(swarm(:, 4, 1)); % global best position %--- updating velocity vectors for i = 1 : swarm_size swarm(i, 2, 1) = rand*inertia*swarm(i, 2, 1) + correction_factor*rand*(swarm(i, 3, 1) - swarm(i, 1, 1)) + correction_factor*rand*(swarm(gbest, 3, 1) - swarm(i, 1, 1)); %x velocity component swarm(i, 2, 2) = rand*inertia*swarm(i, 2, 2) + correction_factor*rand*(swarm(i, 3, 2) - swarm(i, 1, 2)) + correction_factor*rand*(swarm(gbest, 3, 2) - swarm(i, 1, 2)); %y velocity component end %% Plotting the swarm clf plot(swarm(:, 1, 1), swarm(:, 1, 2), 'x') % drawing swarm movements axis([-2 30 -2 30]); pause(.2) end ```