ars.m

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function [x_min,f_min]=ARS(ARSOptions)


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%ARS->function for accelerated random search!                           %
%                                                                       %
%USAGE: [x_min,f_min]=ARS(ARSOptions)                                   %
%                                                                       %
% Arguments     : ARSOptions--> A Matlab stucture containing all ARS    %  
% related options. (see also: get_ARSOptions)                           %
%Return values: [f_min,x_min]                                           %
%                  |     |                                              %
%                  |     |_________________the minimum coordinates      %
%                  |_______________________the minimum function values  %
%                                                                       %
%History        : Author      : caodongsheng-orient                     %
%                 created on  : 2007.6.12                               %
%                 comments    :the accelerated random search(ARS)       %
%                                                                       %
%                  see also: get_ARSOptions                             %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Initializations
if nargin == 0
    arsOptions = get_ARSOptions;
end

Dim=ARSOptions.Vars.Dim;
var_flags=ARSOptions.ARSpara.flags;
 
if length(ARSOptions.Obj.lb)==1
    low=repmat(ARSOptions.Obj.lb,Dim,1);
    up=repmat(ARSOptions.Obj.ub,Dim,1);
else
      low=ARSOptions.Obj.lb;
      up=ARSOptions.Obj.ub;
    
end
if all(low<up)==0
    disp('the interval is wrong!')
    disp('Please input the correct interval!')
end
factor_contract=ARSOptions.ARSpara.factor_contract;
Nrestart_max=ARSOptions.ARSpara.Nrestart_max;
limit=ARSOptions.Vars.limit;
% Dim=size(low,1);
xx_min=[];ff_min=[];%save the best value and coordinates of every iteration!
iter_max=ARSOptions.Vars.Iterations;
tic;
% iter_max=20;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%                         BEGINNING OF ITERATION                        %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for iter=1:iter_max
if var_flags   
current_state=zeros(Dim,1);
for i=1:Dim
    current_state(i)=rand*(up(i)-low(i))+low(i);
end
else
    if  size(ARSOptions.Vars.initialvalue,1)==Dim
        current_state=ARSOptions.Vars.initialvalue;
    else
%         error('You have a wrong intial value,Please repeat input!')
         disp('You have a wrong intial value!')
         disp('Please repeat to input!')
         break;
    end
end
if all(current_state>=low&current_state<=up)
    original_state=current_state;%get the initial result!
    f2eval=ARSOptions.Obj.f2eval;
    f_current=feval(f2eval,original_state);
else 
    disp('the initial value is not in the interval!')
    disp('Please input the correct initial value!')
    break;
end
    
% f_current=obj_fun(original_state)%get the intial obj value!
 
% xx_min=[xx_min,current_state];
% ff_min=[ff_min,f_current];

% limit=ARSOptions.Vars.limit;
% limit=0.000000001;
radius=ARSOptions.ARSpara.radius;
% radius=2;%initalize the radius equals 1!
time=1;
% Nrestart_max=ARSOptions.ARSpara.Nrestart_max;
% Nrestart_max=4;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%restart
while time<Nrestart_max
    
flag=1;
while flag
    vr=2*rand(Dim,1)-1; 
    vr=vr/norm(vr,2);
    x_cycle=vr.*radius+current_state;
    lamda=rand;
    x_current=lamda*current_state+(1-lamda)*x_cycle;
     
%     x_cycle=current_state+vr;
%     x_current=(1-lamda).*current_state+lamda.*x_cycle;
%     if radius==1
%     x_cycle=current_state+vr;
%     x_current=lamda*current_state+(radius-lamda)*x_cycle;
%     else
%     x_cycle=current_state+vr;
%     x_current=lamda*current_state+(1-lamda)*x_cycle;
%     x_current=x_current.* radius;
%     end
%  x_current=current_state+vr.*radius;

%ensure the new coordinate between the low and up!
%         for i=1:Dim
                 if all(x_current>=low&x_current<=up)
                     flag=0;
                 else
                      flag=1;
                 end
%         end  
   
end

% f2eval=ARSOptions.Obj.f2eval;
f_x=feval(f2eval,x_current);%obtain the new coordinate's functional values!
% f_x=obj_fun(x_current);%%get the current obj value!
 

if f_x<f_current
   current_state=x_current;
   xxx_min=x_current;
   fff_min=f_x;
   xx_min=[xx_min,xxx_min];
   ff_min=[ff_min,fff_min];
   radius=ARSOptions.ARSpara.radius;
%    radius=1;
%    f2eval=ARSOptions.Obj.f2eval;
   f_current=feval(f2eval,current_state);
   % f_current=obj_fun(current_state);
else
%     current_state=current_state;
%     xx_min=[xx_min,current_state];
%     ff_min=[ff_min,f_current];
% factor_contract=ARSOptions.ARSpara.factor_contract;
%     factor_contract=2;
    radius=radius/factor_contract;%generate  a (0.1] radius,
    if radius<limit
        radius=1;
        time=time+1;
    end
end

end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%print the every iteration's results!
if  rem(iter_max,1)==0
     disp(sprintf('%4d\t\t\t%.8g\t\t\t%5d', iter, fff_min, iter*time));
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%                           END OF ITERATION                            %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%compute the time of iteration 
run_time=toc
%obtain the best value and the coordinate'sopsitions.
[f_min,opsition]=min(ff_min);
%obtain the the best value's coordinate.
x_min=xx_min(:,opsition);