hybriddemo.m

遗传算法工具包

%% Hybrid Scheme in the Genetic Algorithm

%   Copyright 2004 The MathWorks, Inc.
%   $Revision: 1.9.4.1 $  $Date: 2004/04/04 03:24:39 $

%% Introduction
% This demo uses a hybrid scheme to optimize a function using the Genetic
% Algorithm and another optimization method. GA can reach the region near
% an optimum point relatively quickly, but it can take many function
% evaluations to achieve convergence. A commonly used technique is to run
% GA for a small number of generations to get near an optimum point. Then
% the solution from GA is used as an initial point for another optimization
% solver that is faster and more efficient for local search.

%% Rosenbrock's function
% For the demo we will optimize Rosenbrock's function (also known as
% Dejong's second function):
% 
%     f(x)= 100*(x(2)-x(1)^2)^2+(1-x(1))^2 
% 
% This function is notorious in optimization because of the slow
% convergence most methods exhibit when trying to minimize this function.
% This function has a unique minimum at the point x* = (1,1) where it has a
% function value f(x*) = 0. 
%
% We can view the code for this fitness function.
type dejong2fcn.m
%%
% We use the function PLOTOBJECTIVE in the toolbox to plot the 
% function DEJONG2FCN over the range = [-2 2;-2 2].
plotobjective(@dejong2fcn,[-2 2;-2 2]);

%% Genetic Algorithm solution
% To start, we will use the Genetic Algorithm, GA, alone to find the
% minimum of Rosenbrock's function. We need to supply GA with a function
% handle to the fitness function dejong2fcn.m. Also, GA needs to know the
% how many variables are in the problem, which is two for this function.
FitnessFcn = @dejong2fcn;
numberOfVariables = 2;

%% 
% Some plot functions can be selected to monitor the performance of the
% solver.
options = gaoptimset('PlotFcns', {@gaplotbestf,@gaplotstopping});

%%
% We run GA with the above inputs.
[x,fval] = ga(FitnessFcn,numberOfVariables,options)

%% 
% The global optimum is at x* = (1,1). GA found a point near the optimum,
% but could not get a more accurate answer with the default stopping
% criteria. By changing the stopping criteria, we might find a more
% accurate solution, but it may take many more function evaluations to
% reach x* = (1,1). Instead, we can use a more efficient local search that
% starts where GA left off. The hybrid function field in GA provides this
% feature automatically.

%% Adding a hybrid function
% We will use a hybrid function to solve the optimization problem, i.e.,
% when GA stops (or you ask it to stop) this hybrid function will start
% from the final point returned by GA. Our choices are FMINSEARCH,
% PATTERNSEARCH, or FMINUNC. Since this optimization example is smooth,
% i.e., continuously differentiable, we can use the FMINUNC function from
% the Optimization toolbox as our hybrid function. Since FMINUNC has its 
% own options structure, we provide it as an additional argument when
% specifying the hybrid function.  
fminuncOptions = optimset('Display','iter', 'LargeScale','off');
options = gaoptimset(options,'HybridFcn',{@fminunc, fminuncOptions});

%%
% Run GA solver again with FMINUNC as the hybrid function.
[x,fval] = ga(@dejong2fcn,numberOfVariables,options)

%%
% The first plot shows the best and mean values of the population in every
% generation. The best value found by GA when it terminated is also shown
% in the plot title. When GA terminated, FMINUNC (the hybrid function) was
% automatically called with the best point found by GA so far. The solution
% 'x' and 'fval' is the result of using GA and FMINUNC together. As shown
% here, using the hybrid function can improve the accuracy of the
% solution efficiently.