real and integer variables

How can I perform an optimization with the ga function using both real and integer variables, and what mean banality, how to use it

can anyone help me to solve this sample : optimize y with simple GA and plot it using real une integer variable decision and penality.

y=(1.002)-((1-exp(-0.00003*x+(0.000675)))/(0.00003*(x-21)+(0.00063*(1-exp(-0.00003*x+(0.000675))))))

lb=24 ub=720

[dal]

tank you for your help

Answer 1

[John D'Errico]

No. We won't do what is surely your homework assignment. But why not TRY IT!

First, plotting it is trivial. LEARN TO USE a tool like fplot. So, first, learn to write it as a function!

Read the help about function handles, and anonymous functions.

functions

For example, here is a function handle. For a different function. No, I won't do your homework. That is your job, not ours.

Fun = @(x) 0.1*x.^2 + 2 - 0.025*x.^3 + x;

Decide where it lives. I'll pick the interval from -5 to +8.

fplot(Fun,[-5,8])

However, the rest of your question makes little sense. There is only one variable. You want to optimize it with one integer variable, and penalty? What does a penalty have to do with anything? GA is not a solver that uses a penalty function in any form anyway, since it allows bound constraints. And since there is only one variable, ALL of the one variables are integer in your question.

Regardless, READ THE HELP DOCS FOR ga. In there, you will find examples of how to use ga. If you want to specify some of a set of variables, look at the input argument intcon, as it allows you to designate which variabes are integer, and which ones are allowed to be continuous.

You can use the links I gave by clicking on ga above for the complete documentation on GA. You can also read the help for ga here:

help ga

 ga - Find minimum of function using genetic algorithm
    This MATLAB function finds a local unconstrained minimum, x, to the
    objective function, fun.

    Syntax
      x = ga(fun,nvars)
      x = ga(fun,nvars,A,b)
      x = ga(fun,nvars,A,b,Aeq,beq)
      x = ga(fun,nvars,A,b,Aeq,beq,lb,ub)
      x = ga(fun,nvars,A,b,Aeq,beq,lb,ub,nonlcon)
      x = ga(fun,nvars,A,b,Aeq,beq,lb,ub,nonlcon,options)
      x = ga(fun,nvars,A,b,Aeq,beq,lb,ub,nonlcon,intcon)
      x = ga(fun,nvars,A,b,Aeq,beq,lb,ub,nonlcon,intcon,options)
      x = ga(problem)
      [x,fval] = ga(___)
      [x,fval,exitflag,output] = ga(___)
      [x,fval,exitflag,output,population,scores] = ga(___)

    Input Arguments
      fun - Objective function
        function handle | function name
      nvars - Number of variables
        positive integer
      A - Linear inequality constraints
        real matrix
      b - Linear inequality constraints
        real vector
      Aeq - Linear equality constraints
        real matrix
      beq - Linear equality constraints
        real vector
      lb - Lower bounds
        [] (default) | real vector or array
      ub - Upper bounds
        [] (default) | real vector or array
      nonlcon - Nonlinear constraints
        function handle | function name
      options - Optimization options
        output of optimoptions | structure
      intcon - Integer variables
        vector of positive integers
      problem - Problem description
        structure

    Output Arguments
      x - Solution
        real vector
      fval - Objective function value at the solution
        real number
      exitflag - Reason ga stopped
        integer
      output - Information about the optimization process
        structure
      population - Final population
        matrix
      scores - Final scores
        column vector

    Examples
      openExample('globaloptim/OptimizeANonsmoothFunctionUsingGaExample')
      openExample('globaloptim/MinimizeANonsmoothFunctionWithLinearConstraintsExample')
      openExample('globaloptim/MinimizeNonsmoothFunctionLinearEqualityInequalityExample')
      openExample('globaloptim/OptimizeWithLinearConstraintsAndBoundsExample')
      openExample('globaloptim/OptimizeWithNonlinearConstraintsUsingGaExample')
      openExample('globaloptim/MinimizeWithNondefaultOptionsExample')
      openExample('globaloptim/MinimizeANonlinearFunctionWithIntegerConstraintsExample')
      openExample('globaloptim/ObtainTheSolutionAndFunctionValueExample')
      openExample('globaloptim/ObtainDiagnosticInformationExample')
      openExample('globaloptim/ObtainFinalPopulationAndScoresExample')

    See also gamultiobj, optimoptions, particleswarm, patternsearch,
      Optimize

    Introduced in Global Optimization Toolbox before R2006a
    Documentation for ga
       doc ga

Which gives an abbreviated documentaiton.

So to minimize Fun, on the interval [-5 to 8, with x an integer, we would do

lb = -5;
ub = 8;
nvars = 1; % ony one variable, x.
intcon = 1; % ALL of the variables are integer.

[xval,fval,exitflag] = ga(Fun,nvars,[],[],[],[],lb,ub,[],intcon)

ga stopped because the average change in the penalty function value is less than options.FunctionTolerance and 
the constraint violation is less than options.ConstraintTolerance.

xval = -3

fval = 0.5750

exitflag = 1

On the interval we chose, with x an integer, that is the minimum. You can see that from the plot.

In a more complicated case with multiple variables, where some variables are integer and some are continuous, you would tell GA which ones were integer, by listing the index of only the integer variables in intcon.