请用matlab语言编写粒子群算法代码注释尽量详细

% Particle Swarm Optimization (PSO) Algorithm

% Initialize the parameters clear; clc; num_particles = 50; % Number of particles num_iterations = 100; % Number of iterations inertia_weight = 0.8; % Inertia weight cognitive_weight = 2; % Cognitive weight social_weight = 2; % Social weight max_velocity = 5; % Maximum velocity min_position = -5; % Minimum position max_position = 5; % Maximum position

% Initialize the particles particles_position = min_position + (max_position-min_position)*rand(num_particles,2); particles_velocity = zeros(num_particles,2); particles_best_position = particles_position; particles_best_fitness = zeros(num_particles,1);

% Evaluate the fitness function for i = 1:num_particles particles_best_fitness(i) = fitness(particles_position(i,:)); end

% Find the global best position and fitness global_best_fitness = min(particles_best_fitness); global_best_position = particles_position(find(particles_best_fitness == global_best_fitness),:);

% Update the particles for iteration = 1:num_iterations for i = 1:num_particles % Update the velocity particles_velocity(i,:) = inertia_weightparticles_velocity(i,:) + ... cognitive_weightrand(1,2).(particles_best_position(i,:) - particles_position(i,:)) + ... social_weightrand(1,2).*(global_best_position - particles_position(i,:)); particles_velocity(i,:) = min(particles_velocity(i,:),max_velocity);

    % Update the position
    particles_position(i,:) = particles_position(i,:) + particles_velocity(i,:);
    particles_position(i,:) = max(particles_position(i,:),min_position);
    particles_position(i,:) = min(particles_position(i,:),max_position);
    
    % Evaluate the fitness function
    fitness_value = fitness(particles_position(i,:));
    
    % Update the personal best
    if fitness_value < particles_best_fitness(i)
        particles_best_fitness(i) = fitness_value;
        particles_best_position(i,:) = particles_position(i,:);
    end
    
    % Update the global best
    if fitness_value < global_best_fitness
        global_best_fitness = fitness_value;
        global_best_position = particles_position(i,:);
    end
end

% Display the results
fprintf('Iteration: %d, Best Fitness: %f\n', iteration, global_best_fitness);

end

% Plot the results x = linspace(min_position,max_position,100); y = linspace(min_position,max_position,100); [X,Y] = meshgrid(x,y); Z = zeros(size(X)); for i = 1:length(x) for j = 1:length(y) Z(i,j) = fitness([x(i),y(j)]); end end surf(X,Y,Z); hold on; scatter3(particles_position(:,1),particles_position(:,2),particles_best_fitness,'filled','r'); scatter3(global_best_position(1),global_best_position(2),global_best_fitness,'filled','g'); xlabel('x'); ylabel('y'); zlabel('fitness');

% Define the fitness function function f = fitness(x) f = -20exp(-0.2sqrt(0.5*(x(1)^2+x(2)^2))) - exp(0.5*(cos(2pix(1))+cos(2pix(2)))) + exp(1) + 20; end