1 简介
1.1 粒子群算法
粒子群优化算法(Particle Swarm Optimization，PSO)是一种模拟自然界中生物群觅 食行为相互合作机制从而找到问题最优解的群体智算法。该算法具有原理简单、易实现、 控制参数较少等优点，从而在不同领域都得到了广泛应用。PSO 算法通过群体中各粒 子间的相互合作及竞争，实现对区域内最优解的寻找，其基本思想是在解空间中随机选 择一群粒子并将它们随机分布至解空间，每个粒子的运动速度和方向决定粒子的下一位 置，粒子本身目前找到的历史最优解和整个群体找到的历史最优解影响着每个粒子下一 次的运动速度和方向，每个粒子都看作是目标函数的一个可行解，将粒子的位置值带入 适应度函数计算并评价解的好坏，最终得到全局最优解。
2 部分代码
clc;
clear;
close all;
%% Problem Definition
model=CreateModel();
model.n=3; % number of Handle Points
CostFunction=@(x) MyCost(x,model); % Cost Function
nVar=model.n; % Number of Decision Variables
VarSize=[1 nVar]; % Size of Decision Variables Matrix
VarMin.x=model.xmin; % Lower Bound of Variables
VarMax.x=model.xmax; % Upper Bound of Variables
VarMin.y=model.ymin; % Lower Bound of Variables
VarMax.y=model.ymax; % Upper Bound of Variables
%% PSO Parameters
MaxIt=500; % Maximum Number of Iterations
nPop=150; % Population Size (Swarm Size)
w=1; % Inertia Weight
wdamp=0.98; % Inertia Weight Damping Ratio
c1=1.5; % Personal Learning Coefficient
c2=1.5; % Global Learning Coefficient
% % Constriction Coefficient
% phi1=2.05;
% phi2=2.05;
% phi=phi1+phi2;
% chi=2/(phi-2+sqrt(phi^2-4*phi));
% w=chi; % Inertia Weight
% wdamp=1; % Inertia Weight Damping Ratio
% c1=chi*phi1; % Personal Learning Coefficient
% c2=chi*phi2; % Global Learning Coefficient
alpha=0.1;
VelMax.x=alpha*(VarMax.x-VarMin.x); % Maximum Velocity
VelMin.x=-VelMax.x; % Minimum Velocity
VelMax.y=alpha*(VarMax.y-VarMin.y); % Maximum Velocity
VelMin.y=-VelMax.y; % Minimum Velocity
%% Initialization
% Create Empty Particle Structure
empty_particle.Position=[];
empty_particle.Velocity=[];
empty_particle.Cost=[];
empty_particle.Sol=[];
empty_particle.Best.Position=[];
empty_particle.Best.Cost=[];
empty_particle.Best.Sol=[];
% Initialize Global Best
GlobalBest.Cost=inf;
% Create Particles Matrix
particle=repmat(empty_particle,nPop,1);
% Initialization Loop
for i=1:nPop
% Initialize Position
if i > 1
particle(i).Position=CreateRandomSolution(model);
else
% Straight line from source to destination
xx = linspace(model.xs, model.xt, model.n+2);
yy = linspace(model.ys, model.yt, model.n+2);
particle(i).Position.x = xx(2:end-1);
particle(i).Position.y = yy(2:end-1);
end
% Initialize Velocity
particle(i).Velocity.x=zeros(VarSize);
particle(i).Velocity.y=zeros(VarSize);
% Evaluation
[particle(i).Cost, particle(i).Sol]=CostFunction(particle(i).Position);
% Update Personal Best
particle(i).Best.Position=particle(i).Position;
particle(i).Best.Cost=particle(i).Cost;
particle(i).Best.Sol=particle(i).Sol;
% Update Global Best
if particle(i).Best.Cost<GlobalBest.Cost
GlobalBest=particle(i).Best;
end
end
% Array to Hold Best Cost Values at Each Iteration
BestCost=zeros(MaxIt,1);
%% PSO Main Loop
for it=1:MaxIt
for i=1:nPop
% x Part
% Update Velocity
particle(i).Velocity.x = w*particle(i).Velocity.x ...
+ c1*rand(VarSize).*(particle(i).Best.Position.x-particle(i).Position.x) ...
+ c2*rand(VarSize).*(GlobalBest.Position.x-particle(i).Position.x);
% Update Velocity Bounds
particle(i).Velocity.x = max(particle(i).Velocity.x,VelMin.x);
particle(i).Velocity.x = min(particle(i).Velocity.x,VelMax.x);
% Update Position
particle(i).Position.x = particle(i).Position.x + particle(i).Velocity.x;
% Velocity Mirroring
OutOfTheRange=(particle(i).Position.x<VarMin.x | particle(i).Position.x>VarMax.x);
particle(i).Velocity.x(OutOfTheRange)=-particle(i).Velocity.x(OutOfTheRange);
% Update Position Bounds
particle(i).Position.x = max(particle(i).Position.x,VarMin.x);
particle(i).Position.x = min(particle(i).Position.x,VarMax.x);
% y Part
% Update Velocity
particle(i).Velocity.y = w*particle(i).Velocity.y ...
+ c1*rand(VarSize).*(particle(i).Best.Position.y-particle(i).Position.y) ...
+ c2*rand(VarSize).*(GlobalBest.Position.y-particle(i).Position.y);
% Update Velocity Bounds
particle(i).Velocity.y = max(particle(i).Velocity.y,VelMin.y);
particle(i).Velocity.y = min(particle(i).Velocity.y,VelMax.y);
% Update Position
particle(i).Position.y = particle(i).Position.y + particle(i).Velocity.y;
% Velocity Mirroring
OutOfTheRange=(particle(i).Position.y<VarMin.y | particle(i).Position.y>VarMax.y);
particle(i).Velocity.y(OutOfTheRange)=-particle(i).Velocity.y(OutOfTheRange);
% Update Position Bounds
particle(i).Position.y = max(particle(i).Position.y,VarMin.y);
particle(i).Position.y = min(particle(i).Position.y,VarMax.y);
% Evaluation
[particle(i).Cost, particle(i).Sol]=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;
particle(i).Best.Sol=particle(i).Sol;
% Update Global Best
if particle(i).Best.Cost<GlobalBest.Cost
GlobalBest=particle(i).Best;
end
end
end
% Update Best Cost Ever Found
BestCost(it)=GlobalBest.Cost;
% Inertia Weight Damping
w=w*wdamp;
% Show Iteration Information
if GlobalBest.Sol.IsFeasible
Flag=' *';
else
Flag=[', Violation = ' num2str(GlobalBest.Sol.Violation)];
end
disp(['Iteration ' num2str(it) ': Best Cost = ' num2str(BestCost(it)) Flag]);
% Plot Solution
figure(1);
PlotSolution(GlobalBest.Sol,model);
pause(0.01);
end
%% Results
figure;
plot(BestCost,'LineWidth',2);
xlabel('Iteration');
ylabel('Best Cost');
grid on;
3 仿真结果
4 参考文献
[1]秦元庆, 孙德宝, 李宁,等. 基于粒子群算法的移动机器人路径规划[J]. 机器人, 2004, 26(003):222-225.
5 MATLAB代码与数据下载地址
见博客主页
