ga.m

一个用MATLAB编写的优化控制工具箱

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

popcount=1;         	% Initialize the generation count, 
						% set it to one, the first population

if SELF_ENTERED == 0            % Make a random initial population for
								% base-10 operation by specifying the 
								% matrix of initial traits
for pop_member = 1:POP_SIZE
      for current_trait = 1:NUM_TRAITS,
 		trait(current_trait,pop_member,popcount)=...
		(rand-(1/2))*(HIGHTRAIT(current_trait)-LOWTRAIT(current_trait))+... 
		(1/2)*(HIGHTRAIT(current_trait)+LOWTRAIT(current_trait));
			    % This starts the population off with numbers chosen randomly 
				% on the allowed range of variation, for this example.  
	  end
end 

else
								
for pop_member = 1:POP_SIZE
        for current_trait = 1:NUM_TRAITS,
            trait(current_trait,pop_member,popcount)=0;  
			% To start with a guess where all the population members are zero				
		end
end 
	
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Next, we need to set some values based on the values input by 
% the user.  In particular, we determine the length of the 
% chromosome and start point of each trait.  This information 
% will be used later in the main algorithm.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   CHROM_LENGTH=sum(SIG_FIGS)+NUM_TRAITS; % Length of the chromosome is 
  										  % the number of sig. figs. plus
  										  % the number of sign positions
   TRAIT_START(1)=1;					  % Initialize: the first trait 
   										  % starts at the first digit 
   										  % (this is the sign digit)

   for current_trait=1:NUM_TRAITS, 	% Determine the start point of the
   									% other traits - it is the start of
   									% the last trait plus the no. of sig. 
   									% figs. plus one for sign
TRAIT_START(current_trait+1)=...
   TRAIT_START(current_trait)+SIG_FIGS(current_trait)+1;
   % Yes, we compute the TRAIT_START for one extra trait - this 
   % is used for convenience in the code below.
   end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% In this next loop the fitness is calculated, the children are 
% created and it repeats until the EPSILON-DELTA termination condition
% is satisfied or MAX_GENERATION is reached.  This is the main
% loop of the GA.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

while popcount <= MAX_GENERATION 
 
% First, fix bad traits (i.e., ones that are out of the range 
% specified by HIGHTRAIT and LOWTRAIT) by saturation at the extremes

for pop_member = 1:POP_SIZE

for current_trait = 1:NUM_TRAITS,


if trait(current_trait,pop_member,popcount)>HIGHTRAIT(current_trait)

                     % The trait has went higher than the upper
                     % bound so let the trait equal to the
                     % HIGHTRAIT bound.

trait(current_trait,pop_member,popcount)=HIGHTRAIT(current_trait);

% Now consider the other case:

elseif trait(current_trait,pop_member,popcount)<LOWTRAIT(current_trait)

                     % The trait has went lower than the lower 
                     % bound so let the trait equal to the
                     % LOWTRAIT bound

trait(current_trait,pop_member,popcount)=LOWTRAIT(current_trait);
                  
		end
               
% Now that we have reset the traits to be in range, we must 
% convert them to the chromosome form for use with the genetic operators.
% First, we transfer the sign of the trait into the chromosome

               if trait(current_trait,pop_member,popcount) < 0
                  pop(TRAIT_START(current_trait),pop_member)=0;
               else
                  pop(TRAIT_START(current_trait),pop_member)=9;
               end

% Next, strip off the sign and store the resulting value in a
% temporary variable that is used in the construction of pop

temp_trait(current_trait,pop_member)=...
           abs(trait(current_trait,pop_member,popcount));  
		% temp_trait is trait without the sign of trait 

% Next, we store the numbers of the trait in the chromosome:
% First, set up a temporary trait with at most
% one nonzero digit to the left of the decimal point.
% This is used to strip off the numbers to put 
% them into a chromosome.

               for counter=1:DECIMAL(current_trait)-1,
                  
temp_trait(current_trait,pop_member)=...
       temp_trait(current_trait,pop_member)/10;
               
               end

% Encode the new trait into chromosome form 

for make_gene = TRAIT_START(current_trait)+1:TRAIT_START(current_trait+1)-1,
               
% For each gene on the trait make the gene the corresponding digit on 
% temp_trait (note that rem(x,y)=x-roundtowardszero(x/y)*y or 
% rem(x,1)=x-roundtowardszero(x) so that rem(x,1) is the fraction part
% and x-rem(x,1) is the integer part so the next line makes the location in
% pop the same as the digit to the left of the decimal point of temp_trait
  
pop(make_gene,pop_member)=temp_trait(current_trait,pop_member)-...
   rem(temp_trait(current_trait,pop_member),1);

% Next, we take temp_trait and rotate the next digit to the left so that
% next time around the loop it will pull that digit into the 
% chromosome.  To do this we strip off the leading digit then shift 
% in the next one.
  
temp_trait(current_trait,pop_member)=...
  (temp_trait(current_trait,pop_member)-pop(make_gene,pop_member))*10;
               
end

         end % Ends "for current_trait=..." loop
         
	 end    % Ends "for pop_member=..." loop
	 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% USER: Below is where you change the fitness function that is to be
% maximized.  This may involve changing several lines of code below.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% In the example below we want to *maximize* the function z=f(x,y).
% Important: When defining the fitness function you must remember that 
% it is a function that you are *maximizing* and that it must always be 
% positive (the selection mechanism depends on this).  For our example, 
% we are maximizing the function f.  Below, we include some ideas about
% what to do if you seek to minimize a function.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

sumfitness = 0; 		% Re-initialize for each generation

% First, determine the values of the function to be minimized for 
% each chromosome.

   for chrom_number = 1:POP_SIZE,       % Test fitness

fitness_bar(chrom_number)=...
+5*exp(-0.1*((trait(1,chrom_number,popcount)-15)^2+...
   (trait(2,chrom_number,popcount)-20)^2))...
-2*exp(-0.08*((trait(1,chrom_number,popcount)-20)^2+...
   (trait(2,chrom_number,popcount)-15)^2))...
+3*exp(-0.08*((trait(1,chrom_number,popcount)-25)^2+...
   (trait(2,chrom_number,popcount)-10)^2))...
+2*exp(-0.1*((trait(1,chrom_number,popcount)-10)^2+...
   (trait(2,chrom_number,popcount)-10)^2))...
-2*exp(-0.5*((trait(1,chrom_number,popcount)-5)^2+...
   (trait(2,chrom_number,popcount)-10)^2))...
-4*exp(-0.1*((trait(1,chrom_number,popcount)-15)^2+...
   (trait(2,chrom_number,popcount)-5)^2))...
-2*exp(-0.5*((trait(1,chrom_number,popcount)-8)^2+...
   (trait(2,chrom_number,popcount)-25)^2))...
-2*exp(-0.5*((trait(1,chrom_number,popcount)-21)^2+...
   (trait(2,chrom_number,popcount)-25)^2))...
+2*exp(-0.5*((trait(1,chrom_number,popcount)-25)^2+...
   (trait(2,chrom_number,popcount)-16)^2))...
+2*exp(-0.5*((trait(1,chrom_number,popcount)-5)^2+...
   (trait(2,chrom_number,popcount)-14)^2));

   end

% Next, compute the fitness function (this loop is only kept 
% separate from the next one in case you need to implement 
% some of the options discussed in the comments).  

   for chrom_number = 1:POP_SIZE,       % Test fitness

% The fitness function must be chosen so that it is always positive.
% To ensure this for our example we assume that we know that the value
% of f will never be below -5; so we simply add 5 to every fitness_bar value.
% Another approach would be to simply find the minimum value 
% of the fitness_bar function for every element in the population 
% and then add on its absolute value so that all the resulting 
% values will be positive

 fitness(chrom_number)= fitness_bar(chrom_number) + 5;
 
% Notice that when we turn a minimization problem into a maximization
% problem we often use 
% fitness(chrom_number)= -fitness_bar(chrom_number) + max(fitness_bar);
% as the above line.  Here, the minus sign is
% for turning the minimization problem into a maximization problem
% and max(fitness_bar) is used to make the fitness function positive.
% Another option would be to use the fitness function:
% fitness(chrom_number)=(1/(fitness_bar(chrom_number) + .1));
% The 1/fitness_bar function switches it to a maximzation problem.  
% The +.1 is to make sure that there is no divide by zero. Note that you can
% tune the GA in this case by changing the 1 in the numerator to another 
% constant and the .1 to a different value.

sumfitness = sumfitness + fitness(chrom_number);  % Store this for 
      											  % use below
   end

% Next, determine the most fit and least fit chromosome and 
% the chrom_numbers (which we call bestmember and worstmember). 

[bestfitness(popcount),bestmember]=max(fitness);
[worstfitness(popcount),worstmember]=min(fitness);

% Next, save these (if want to save worstindividual can too)

bestindividual(:,popcount)=trait(:,bestmember,popcount);
%worstindividual(:,popcount)=trait(:,worstmember,popcount);

% Compute the average fitness in case you want to plot it.

avefitness(popcount) = sumfitness / POP_SIZE;        


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Create the next generation
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% First, form the mating pool.  
% To do this we select as parents the
% chromosomes that are most fit.  
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   for pop_member = 1:POP_SIZE,
	if ELITISM ==1 & pop_member==bestmember  % If elitism on, and have
											 % the elite member
		parent_chrom(:,pop_member)=pop(:,pop_member); % Makes sure that
		                          % the elite member gets into the next
								  % generation.
	else
      pointer=rand*sumfitness; % This makes the pointer for the roulette 
                               % wheel.  
      member_count=1;        % Initialization
      total=fitness(1);

      while total < pointer,                % This spins the wheel to the 
       									    % pointer and finds the 
       									    % chromosome there - which is
       									    % identified by member_count