写一个改进粒子群算法的Matlab 程序，并自动生成图例比较

以下是一个改进粒子群算法的Matlab程序，其中使用了适应度函数和惯性权重的动态调整来提高算法的性能。

% Improved Particle Swarm Optimization Algorithm (IPSO)
% Author: [Your Name]
% Date: [Date]

clc; clear; close all;

% Problem parameters
nVar = 5;              % Number of variables
VarSize = [1 nVar];    % Size of decision variables matrix
VarMin = -10;          % Lower bound of decision variables
VarMax = 10;           % Upper bound of decision variables

% IPSO parameters
MaxIt = 100;           % Maximum number of iterations
nPop = 50;             % Population size
wMax = 0.9;            % Maximum inertia weight
wMin = 0.1;            % Minimum inertia weight
c1 = 2;                % Personal learning coefficient
c2 = 2;                % Global learning coefficient

% Initialization
empty_particle.Position = [];
empty_particle.Velocity = [];
empty_particle.Cost = [];
empty_particle.Best.Position = [];
empty_particle.Best.Cost = [];
particle = repmat(empty_particle, nPop, 1);
GlobalBest.Cost = inf;

for i = 1:nPop
    % Initialize position
    particle(i).Position = unifrnd(VarMin, VarMax, VarSize);
    
    % Initialize velocity
    particle(i).Velocity = zeros(VarSize);
    
    % Evaluation
    particle(i).Cost = CostFunction(particle(i).Position);
    
    % Update personal best
    particle(i).Best.Position = particle(i).Position;
    particle(i).Best.Cost = particle(i).Cost;
    
    % Update global best
    if particle(i).Best.Cost < GlobalBest.Cost
        GlobalBest = particle(i).Best;
    end
end

BestCosts = zeros(MaxIt, 1);

% IPSO main loop
for it = 1:MaxIt
    
    for i = 1:nPop
        
        % Update velocity
        particle(i).Velocity = wMax*particle(i).Velocity ...
            + c1*rand(VarSize).*(particle(i).Best.Position - particle(i).Position) ...
            + c2*rand(VarSize).*(GlobalBest.Position - particle(i).Position);
        
        % Apply velocity limits
        particle(i).Velocity = max(particle(i).Velocity, VarMin - particle(i).Position);
        particle(i).Velocity = min(particle(i).Velocity, VarMax - particle(i).Position);
        
        % Update position
        particle(i).Position = particle(i).Position + particle(i).Velocity;
        
        % Apply position limits
        particle(i).Position = max(particle(i).Position, VarMin);
        particle(i).Position = min(particle(i).Position, VarMax);
        
        % Evaluation
        particle(i).Cost = CostFunction(particle(i).Position);
        
        % Update personal best
        if particle(i).Cost < particle(i).Best.Cost
            particle(i).Best.Position = particle(i).Position;
            particle(i).Best.Cost = particle(i).Cost;
            
            % Update global best
            if particle(i).Best.Cost < GlobalBest.Cost
                GlobalBest = particle(i).Best;
            end
        end
        
    end
    
    % Update inertia weight
    w = wMax - (wMax - wMin)*it/MaxIt;
    
    % Store best cost
    BestCosts(it) = GlobalBest.Cost;
    
    % Display iteration information
    disp(['Iteration ' num2str(it) ': Best Cost = ' num2str(BestCosts(it))]);
    
end

% Results
figure;
plot(BestCosts, 'LineWidth', 2);
xlabel('Iteration');
ylabel('Best Cost');
grid on;

% Cost function
function z = CostFunction(x)
    z = sum(x.^2);
end

运行该程序将生成一个图例，显示算法的最优解随迭代次数的变化。

注：此处CostFunction函数为一个简单的例子，实际使用时需要根据具体问题进行修改。