Code covered by the BSD License

# Differential Evolution

### Markus Buehren (view profile)

03 Feb 2008 (Updated )

Optimization using the evolutionary algorithm of Differential Evolution.

demo3
```function demo3
%DEMO3  Demo for usage of DIFFERENTIALEVOLUTION.
%   DEMO3 starts searching the minimum of Shekel's Foxholes as a demo. This
%   demo is similar to DEMO2 except that it uses a function to check
%   parameter vectors for validity. Modify this function for your first
%   optimization.
%
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%   Markus Buehren
%

% set title
optimInfo.title = 'Demo 3 (Shekel''s Foxholes with constraint)';

% specify objective function
objFctHandle = @foxholes;

% define parameter names, ranges, quantizations and initial values :
paramDefCell = {'', [-65 65; -65 65], [0; 0], [0; -30]};
% (single vector-valued parameter with no name, as function foxholes is
% called with a parameter vector as only input)

% no additional function parameters needed
objFctSettings = {};

% no parameter vector needed
objFctParams = [];

% get default DE parameters
DEParams = getdefaultparams;

% set number of population members (often 10*D is suggested; here we use
% more as we know that the Foxholes functions has many local minima).
DEParams.NP = 50;

% do not use slave processes here
DEParams.feedSlaveProc  = 0;

% use a subfunction to check parameter vectors for validity
DEParams.validChkHandle = @demo3_constraint;

% set times
DEParams.maxiter  = 20;
DEParams.maxtime  = 30;  % in seconds
DEParams.maxclock = [];

% set display options
DEParams.infoIterations = 1;
DEParams.infoPeriod     = 10;  % in seconds

% do not send E-mails
emailParams = [];

% set random state in order to always use the same population members here
setrandomseed(1);

% start differential evolution
[bestmem, bestval, bestFctParams, nrOfIterations, resultFileName] = differentialevolution(...
DEParams, paramDefCell, objFctHandle, objFctSettings, objFctParams, emailParams, optimInfo); %#ok

disp(' ');
disp('Best parameter set returned by function differentialevolution:');
disp(bestFctParams);

if DEParams.saveHistory

disp(' ');
disp(textwrap2(sprintf(...
disp(' ');

DEParams.maxiter  = 100;
DEParams.maxtime  = 60;  % in seconds

[bestmem, bestval, bestFctParams] = differentialevolution(...
DEParams, paramDefCell, objFctHandle, objFctSettings, objFctParams, emailParams, optimInfo, ...
resultFileName); %#ok

disp(' ');
disp('Best parameter set returned by function differentialevolution:');
disp(bestFctParams);
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function valid = demo3_constraint(x)
% constraint function must accept the same input arguments as the objective
% function!

x0 = [-30, -30];
r0 = 40;

% as an example, set values outside some circle to invalid
valid = (x(1) - x0(1))^2 + (x(2) - x0(2))^2 < r0^2;
```