MATLAB optimization toolbox usage with genetic algorithm

Useful tutorial


http://www.mathworks.com/products/global-optimization/description3.html

Best example of implementatoin with Constraint, objective function

http://www.mathworks.com/help/gads/examples/constrained-minimization-using-the-genetic-algorithm.html

More about how to use multi-objective

http://www.mathworks.com/discovery/multiobjective-optimization.html


http://www.mathworks.com/help/gads/examples/performing-a-multiobjective-optimization-using-the-genetic-algorithm.html

http://www.mathworks.com/help/gads/examples/multiobjective-genetic-algorithm-options.html

Example GAMULTOBJ (can handle Multiple Objective)  GA(can handle 1 objective)

Constrained Minimization Problem

We want to minimize a simple fitness function of two variables x1 and x2

   min f(x) = 100 * (x1^2 - x2) ^2 + (1 - x1)^2;
    x

  min f(x) = 100 * (x1^2 + x2) ^2 + (1 + x1)^2;
    x 

such that the following two nonlinear constraints and bounds are satisfied

   x1*x2 + x1 - x2 + 1.5 <=0, (nonlinear constraint)
   10 - x1*x2 <=0,            (nonlinear constraint)
   0 <= x1 <= 1, and          (bound)
   0 <= x2 <= 13              (bound)

Implementation of  Singleobjective Function

   function y = simple_objective(x)
    y = 100 * (x(1)^2 - x(2)) ^2 + (1 - x(1))^2;

 
Implementation of  Multiobjective Function

   function y = simple_multiobjective(x)
    y(1) = 100 * (x(1)^2 - x(2)) ^2 + (1 - x(1))^2;

    y(2) = 100 * (x(1)^2 + x(2)) ^2 + (1 + x(1))^2; 

Implementation of the Constraint Function

   function [c, ceq] = simple_constraint(x)
   c = [1.5 + x(1)*x(2) + x(1) - x(2);
   -x(1)*x(2) + 10];
   ceq = [];

Implementation of the GAMULTOBJ/ GA

ObjectiveFunctionOne = @simple_objective;
ObjectiveFunctionMult = @simple_multiobjective;
nvars = 2;
A = []; b = [];
Aeq = []; beq = [];
LB = [0 0];   % Lower bound , you can also set []
UB = [1 13];  % Upper bound , you can also set []
options = gaoptimset('PlotFcns',{@gaplotpareto,@gaplotscorediversity});

[x,fval,extflag, output,pop, score] = gamultiobj( ObjectiveFunctionMult, nvars, A, b, Aeq, beq, LB, UB, options )

[x,fval,extflag, output,pop, score] = gamultiobj( ObjectiveFunctionOne, nvars, A, b, Aeq, beq, LB, UB, options )


But in GA you can add non-linear constraint

http://www.mathworks.com/help/gads/examples/constrained-minimization-using-the-genetic-algorithm.html

function [c, ceq] = simple_constraint(x)
   c = [1.5 + x(1)*x(2) + x(1) - x(2);
   -x(1)*x(2) + 10];
   ceq = [];

[x,fval,extflag, output,pop, score] = ga(ObjectiveFunctionOne,nvars,[],[],[],[],LB,UB , ConstraintFunction);

Example GAMULTOBJ (can handle Multiple Objective)  GA(can handle 1 objective) for BITSTRING

%% using gamultobj
ObjectiveFunction = @myFitnessFnc_bitString;
nvars = 2;    % Number of variables
LB = [0 0];   % Lower bound
UB = [1 13];  % Upper bound
options = gaoptimset('PopulationSize',60,...
          'ParetoFraction',0.7,'PlotFcns',@gaplotpareto, 'PopulationType','bitstring');
[x fval flag output population score] = gamultiobj(ObjectiveFunction,nvars, [],[],[],[],[] ,[] ,options )

%% using GA

%% usig ga
ObjectiveFunction = @myFitnessFnc_bitString;
nvars = 2;    % Number of variables
options = gaoptimset('PopulationSize',60,...
          'ParetoFraction',0.7,'PlotFcns',@gaplotpareto, 'PopulationType','bitstring');
[x fval flag output population score] = ga(ObjectiveFunction,nvars, options)