gaoptionsdemo.m

遗传算法工具包

%% Genetic Algorithm options
% This is a demonstration of how to create and manage options for the
% genetic algorithm function GA using GAOPTIMSET in the Genetic Algorithm
% and Direct Search Toolbox.

%   Copyright 2004 The MathWorks, Inc.
%   $Revision: 1.1.4.2 $  $Date: 2004/04/04 03:24:14 $

%% Setting up a problem for GA
% GA searches for an unconstrained minimum of a function using the
% genetic algorithm. For this demo we will use GA to minimize the
% fitness function SHUFCN. SHUFCN is a real valued function of two 
% variables.

%% 
% We can use the function PLOTOBJECTIVE in the toolbox to plot the 
% function SHUFCN over the range = [-2 2;-2 2].
plotobjective(@shufcn,[-2 2; -2 2]);

%%
% To use the GA solver, we need to provide at least two input arguments, 
% a fitness function and the number of variables in the problem. The first
% two output arguments returned by GA are x, the best point found, and
% Fval, the function value at the best point. A third output argument, 
% exitFlag tells you the reason why GA stopped. GA can also return a fourth
% argument, Output, which contains information about the performance of
% the solver.
FitnessFunction = @shufcn;
numberOfVariables = 2;
%%
% Run the GA solver.
[x,Fval,exitFlag,Output] = ga(FitnessFunction,numberOfVariables);

fprintf('The number of generations was : %d\n', Output.generations);
fprintf('The number of function evaluations was : %d\n', Output.funccount);
fprintf('The best function value found was : %g\n', Fval);

%%
% Note that when you run this demo, your result may be different from the
% results shown; This will be explained in a section later in this
% demo.

%% How the Genetic Algorithm works
% The Genetic Algorithm (GA) works on a population using a set of
% operators that are applied to the population. A population is a set
% of points in the design space. The initial population is generated
% randomly by default. The next generation of the population is computed
% using the fitness of the individuals in the current generation. 

%% Adding visualization
% GA can accept one or more plot functions through an OPTIONS argument. 
% This feature is useful for visualizing the performance of the
% solver at run time. Plot functions can be selected using GAOPTIMSET. The
% help for GAOPTIMSET contains a list of plot functions to choose from.
%
% Here we use GAOPTIMSET to create an options structure to select two plot
% functions. The first plot function is GAPLOTBESTF, which plots the
% best and mean score of the population at every generation. The second
% plot function is GAPLOTSTOPPING, which plots the percentage of
% stopping criteria satisfied.
opts = gaoptimset('PlotFcns',{@gaplotbestf,@gaplotstopping});
%%
% Run the GA solver.
[x,Fval,exitFlag,Output] = ga(FitnessFunction,numberOfVariables,opts);

%% Specifying population options
% The default initial population is created using a uniform random number
% generator. Default values for the population size and the range of the 
% initial population are used to create the initial population. 

%%
% *Specify a population size*
%%
% The default population size used by GA is 20. This may not be sufficient
% for problems with a large number of variables; a smaller population size
% may be sufficient for smaller problems. Since we only have two variables,
% we specify a population size of 10. We will pass our options structure
% 'opts', created above, to GAOPTIMSET to modify the value of the parameter
% 'PopulationSize' to be 10. 
opts = gaoptimset(opts,'PopulationSize',10);

%%
% *Specify initial population range*
%%
% The initial population is generated using a uniform random number
% generator in a default range of [0;1]. This creates an initial population
% where all the points are in the range 0 to 1. For example, a population
% of size 3 in a problem with two variables could look like:
Population = rand(3,2)
%%
% The initial range can be set by changing the 'PopInitRange' option using
% GAOPTIMSET. The range must be a matrix with two rows. If the range has
% only one column, i.e., it is 2-by-1, then the range of every variable is
% the given range. For example, if we set the range to [-1; 1], then the
% initial range for both our variables is -1 to 1. To specify a different
% initial range for each variable, the range must be specified as a matrix
% with two rows and 'numberOfVariables' columns. For example if we set the
% range to 
% [-1 0; 
%   1 2], 
% then the first variable will be in the range -1 to 1, and the second 
% variable will be in the range 0 to 2 (so each column corresponds to a 
% variable).
%
% The initial range can be specifed using GAOPTIMSET. We will pass our
% options structure 'opts'  created above to GAOPTIMSET to modify the
% value of the parameter 'PopInitRange'.
opts = gaoptimset(opts,'PopInitRange',[-1 0;1 2]);
%%
% Run the GA solver. 
[x,Fval,exitFlag,Output] = ga(FitnessFunction,numberOfVariables,opts);

fprintf('The number of generations was : %d\n', Output.generations);
fprintf('The number of function evaluations was : %d\n', Output.funccount);
fprintf('The best function value found was : %g\n', Fval);
 
%% Reproducing your results 
% By default, GA starts with a random initial population which is
% created using MATLAB random number generators. The next generation is
% produced using GA operators that also use these same random number
% generators. Every time a random number is generated, the state of the
% random number generators change. This means that even if you do
% not change any options, when you run again you may get different
% results.
%
% Here we run the solver twice to show this phenomenon.

%%
% Run the GA solver.
[x,Fval,exitFlag,Output] = ga(FitnessFunction,numberOfVariables);
fprintf('The best function value found was : %g\n', Fval);
%%
% Run GA again.
[x,Fval,exitFlag,Output] = ga(FitnessFunction,numberOfVariables);
fprintf('The best function value found was : %g\n', Fval);

%% 
% In the previous two runs GA might give different results. The results are
% different because the states of the random number generators have changed
% from one run to another.

%%
% We can reproduce our results if we reset the states of the random
% number generators by using information returned by GA. GA returns the
% states of the random number generators at the time you call GA in the 
% output argument. This information can be used to reset the states.  
% Here we reset the states using this output information so the results 
% of the next two runs are the same.

%% 
% Run the GA solver.
[x,Fval,exitFlag,Output] = ga(FitnessFunction,numberOfVariables);
fprintf('The best function value found was : %g\n', Fval);
%%
% Reset the states. 
rand('state',Output.randstate);
randn('state',Output.randnstate);
%%
% Run GA again.
[x,Fval,exitFlag,Output] = ga(FitnessFunction,numberOfVariables);
fprintf('The best function value found was : %g\n', Fval);

%% Modifying the stopping criteria
% GA uses four different criteria to determine when to stop the
% solver. GA stops when the maximum number of generations is reached; by
% default this number is 100. GA also detects if there is no change in the
% best fitness value for some time given in seconds (stall time limit),
% or for some number of generations (stall generation limit). Another
% criteria is the maximum time limit in seconds. Here we modify the
% stopping criteria to increase the maximum number of generations to
% 150 and the stall generations limit to 100.
opts = gaoptimset(opts,'Generations',150,'StallGenLimit', 100);
%%
% Run the GA solver again.
[x,Fval,exitFlag,Output] = ga(FitnessFunction,numberOfVariables,opts);

fprintf('The number of generations was : %d\n', Output.generations);
fprintf('The number of function evaluations was : %d\n', Output.funccount);
fprintf('The best function value found was : %g\n', Fval);

%% Choosing GA operators
% GA starts with a random set of points in the population and uses
% operators to produce the next generation of the population. The
% different operators are scaling, selection, crossover, and mutation.
% The toolbox provides several functions to choose from for each operator.
% Here we choose FITSCALINGPROP for 'FitnessScalingFcn' and
% SELECTIONTOURNAMENT for 'SelectionFcn'.
opts = gaoptimset('SelectionFcn',@selectiontournament, ...
    'FitnessScalingFcn',@fitscalingprop);
%%
% Run the GA solver.
[x,Fval,exitFlag,Output] = ga(FitnessFunction,numberOfVariables,opts);

fprintf('The number of generations was : %d\n', Output.generations);
fprintf('The number of function evaluations was : %d\n', Output.funccount);
fprintf('The best function value found was : %g\n', Fval);

%%
% The best function value may improve or it may get worse by choosing
% different operators. Choosing a good set of operators for your problem is
% often best done by experimentation. The GATOOL provides a wonderful
% environment for easily experimenting with different options and then
% trying them out by running the GA solver.