ps101010.m

多为函数极小化程序 可以用来测试PSO优化函数

% 多维数自变量的函数极小优化问题程序

function [xmin, fxmax, iter] = PSO() 

num_success = 0;              %success counter 
sucrate = 0;
sumf = 0;
avestep=0;
sumstep=0;

%%%%%%%%%%%%%%%%%%%%%%
%不同的实验需要改变的参数：实验次数
trialnum = 100;                %trial counter
%%%%%%%%%%%%%%%%%%%%%%

% 实验数次循环体开始执行
for num=1:1:trialnum 
   
% Initializing variables  
%%%%%%%%%%%%%%%%%%%%%%
%每更改一个函数需要改变的量：函数名称、自变量的上下界限和函数理论极小值
f = 'Rastrigrin';                  % Objective Function
upbnd = 5.12;                      % Upper bound for init. of the swarm 
lwbnd = -5.12;                    % Lower bound for init. of the swarm 
foptimal = 0;                          % minimum fitness value
%%%%%%%%%%%%%%%%%%%%%%
%粒子数和最大迭代次数也需要改变
PopSize = 20;                % Size of the swarm 
MaxIt = 20000;                % Maximum number of iterations 
%%%%%%%%%%%%%%%%%

flag_suc = 0;               % Success flag
iter = 0;                   % Iterations’counter 
fevals = 0;                     % Function evaluations’ counter 
maxw=0.9;                       % maximum inertia weight's value
minw=0.2;                       % minimum inertia weight's value
weveryit=floor(0.75*MaxIt);     % Inertia decr.step, floor为取最小的整数，不四舍五入
c1 = 2;                         % PSO parameter C1 
c2 = 2;                         % PSO parameter C2 
inertdec=(maxw-minw)/weveryit;  % inertia weight's decrement
%w = 0.6;                       % inertia weight 
w=maxw;                         % initial inertia weight               
dim = 10;                       % Dimension of the problem 
GM = 0;                         % Global minimum (used in the stopping criterion) 
ErrGoal = 1;              % Desired accuracy 

% Initializing swarm and velocities 
popul = rand(dim, PopSize)*(upbnd-lwbnd) + lwbnd;    %initialize location x,维数为D*m，popul代表位置x
vel = rand(dim, PopSize);                            %initialize velocity v,维数为D*m,代表速度v

%Evaluate initial population
for i = 1:PopSize, 
   fpopul(i) = feval(f, popul(:,i));        %一个粒子对应一个解，适应度个数为解的个数，所以循环体采用的是Popsize
   fevals = fevals + 1; 
end 

%initializing best positions'matrix and the corresponding function values
bestpos = popul;                 %bestpos 为最好位置
fbestpos = fpopul;               %fbestpos 为最好适应度函数

% Finding best particle in initial population 
[fbestpart,g] = min(fpopul); 
lastbpf = fbestpart; 


%swarm evolution loop * start*
while  (flag_suc == 0) & (iter < MaxIt),     
   iter = iter + 1; 
   
   %update the value of the inertia weight w
   if (iter<=weveryit)
      w=maxw-(iter-1)*inertdec;                   %w linearly decreasing
   end
   
   % velocity update
   for i=1:PopSize, 
       A(:,i) = bestpos(:,g); 
   end 
   R1 = rand(dim, PopSize); 
   R2 = rand(dim, PopSize); 
   vel = w*vel + c1*R1.*(bestpos-popul) + c2*R2.*(A-popul); 

   % swarm update
   popul = popul + vel; 
   % Evaluate the new swarm 
   for i = 1:PopSize, 
       fpopul(i) = feval(f,popul(:,i)); 
       fevals = fevals + 1; 
    end 
    
   % Updating the best position for each particle 
   changeColumns = fpopul < fbestpos; 
   fbestpos = fbestpos.*( 1-changeColumns) + fpopul.*changeColumns; 
   bestpos(:, find(changeColumns)) = popul(:, find(changeColumns)); 
   % Updating index g 
   [fbestpart, g] = min(fbestpos); 
   %currentTime = etime(clock,startTime); 
   % Checking stopping criterion if abs(fbestpart-GM)<=ErrGoal
   %fopt(iter)=fbestpos(g);
      if abs(fbestpart-GM) <= ErrGoal 
       flag_suc = 1; 
   else 
       lastbpf = fbestpart; 
   end 
end 
%Swarm evolution loop *end*

% Output arguments 
xopt = popul(:,g); 
fopt(num) = fbestpos(g);
sumf=sumf+fopt(num);
fstep(num)=iter;
sumstep=sumstep+fstep(num);
if (abs(fopt(num)-foptimal)<ErrGoal)
  num_success = num_success+1;
end
end
fmean=sumf/trialnum;
success_rate = num_success*100/trialnum;
avestep=sumstep/trialnum;
fopt;


fprintf(' The success rate is : '); 
fprintf('---  %g ',success_rate); 
fprintf('%%');
fprintf('\n');
fprintf(' The mean fitness value is : '); 
fprintf('---  %g ',fmean); 
fprintf('\n');
fprintf(' The best fitness value is : '); 
fprintf('---  %g ',foptimal); 
fprintf('\n');
fprintf(' The mean iteration steps is : '); 
fprintf('---  %g ',avestep); 
fprintf('\n');
fprintf('\n');

%优化的函数定义
%========================================== 
%%function1----DeJong函数，-10<x1,x2<10,fmin=0
%%1个全局最优点x=(0,0)
%寻优率100%
function DeJong = DeJong(x) 
DeJong = sum(x.^2); 
%==========================================
%%function2----Rastrigrin函数，-10<x1,x2<10,fmin=0
%%多个局部极值，1个全局最优点x=(0，0)
%寻优率
function Rastrigrin = Rastrigrin(x)
Rastrigrin = sum((x.^2-10*cos(2*pi*x)+10));
%==========================================