>> help ga
GA    Constrained optimization using genetic algorithm.
    GA attempts to solve problems of the form:
        min F(X)  subject to:  A*X  <= B, Aeq*X  = Beq (linear constraints)
         X                     C(X) <= 0, Ceq(X) = 0 (nonlinear constraints)
                               LB <= X <= ub

    X = GA(FITNESSFCN,NVARS) finds a local unconstrained minimum X to the
    FITNESSFCN using GA. NVARS is the dimension (number of design
    variables) of the FITNESSFCN. FITNESSFCN accepts a vector X of size
    1-by-NVARS, and returns a scalar evaluated at X.

    X = GA(FITNESSFCN,NVARS,A,b) finds a local minimum X to the function
    FITNESSFCN, subject to the linear inequalities A*X <= B. Linear
    constraints are not satisfied when the PopulationType option is set to
    'bitString' or 'custom'. See the documentation for details.

    X = GA(FITNESSFCN,NVARS,A,b,Aeq,beq) finds a local minimum X to the
    function FITNESSFCN, subject to the linear equalities Aeq*X = beq as
    well as A*X <= B. (Set A=[] and B=[] if no inequalities exist.) Linear
    constraints are not satisfied when the PopulationType option is set to
    'bitString' or 'custom'. See the documentation for details.

    X = GA(FITNESSFCN,NVARS,A,b,Aeq,beq,lb,ub) defines a set of lower and
    upper bounds on the design variables, X, so that a solution is found in
    the range lb <= X <= ub. Use empty matrices for lb and ub if no bounds
    exist. Set lb(i) = -Inf if X(i) is unbounded below;  set ub(i) = Inf if
    X(i) is unbounded above. Linear constraints are not satisfied when the
    PopulationType option is set to 'bitString' or 'custom'. See the
    documentation for details.

    X = GA(FITNESSFCN,NVARS,A,b,Aeq,beq,lb,ub,NONLCON) subjects the
    minimization to the constraints defined in NONLCON. The function
    NONLCON accepts X and returns the vectors C and Ceq, representing the
    nonlinear inequalities and equalities respectively. GA minimizes
    FITNESSFCN such that C(X)<=0 and Ceq(X)=0. (Set lb=[] and/or ub=[] if
    no bounds exist.) Nonlinear constraints are not satisfied when the
    PopulationType option is set to 'bitString' or 'custom'. See the
    documentation for details.

    X = GA(FITNESSFCN,NVARS,A,b,Aeq,beq,lb,ub,NONLCON,options) minimizes
    with the default optimization parameters replaced by values in the
    structure OPTIONS. OPTIONS can be created with the GAOPTIMSET function.
    See GAOPTIMSET for details.

    X = GA(PROBLEM) finds the minimum for PROBLEM. PROBLEM is a structure
    that has the following fields:
        fitnessfcn:
             nvars:
             Aineq:
             bineq:
               Aeq:
               beq:
                lb:
                ub:
           nonlcon:
           options:
          rngstate:

    [X,FVAL] = GA(FITNESSFCN, ...) returns FVAL, the value of the fitness
    function FITNESSFCN at the solution X.

    [X,FVAL,EXITFLAG] = GA(FITNESSFCN, ...) returns EXITFLAG which
    describes the exit condition of GA. Possible values of EXITFLAG and the
    corresponding exit conditions are

      1 Average change in value of the fitness function over
         options.StallGenLimit generations less than options.TolFun and
         constraint violation less than options.TolCon.
      3 The value of the fitness function did not change in
         options.StallGenLimit generations and constraint violation less
         than options.TolCon.
      4 Magnitude of step smaller than machine precision and constraint
         violation less than options.TolCon. This exit condition applies
         only to nonlinear constraints.
      5 Fitness limit reached and constraint violation less than
         options.TolCon.
      0 Maximum number of generations exceeded.
     -1 Optimization terminated by the output or plot function.
     -2 No feasible point found.
     -4 Stall time limit exceeded.
     -5 Time limit exceeded.

    [X,FVAL,EXITFLAG,OUTPUT] = GA(FITNESSFCN, ...) returns a
    structure OUTPUT with the following information:
              rngstate:
           generations:
             funccount:
         maxconstraint: , if any
               message:

    [X,FVAL,EXITFLAG,OUTPUT,POPULATION] = GA(FITNESSFCN, ...) returns the
    final POPULATION at termination.

    [X,FVAL,EXITFLAG,OUTPUT,POPULATION,SCORES] = GA(FITNESSFCN, ...) returns
    the SCORES of the final POPULATION.


    Example:
      Unconstrained minimization of 'rastriginsfcn' fitness function of
      numberOfVariables = 2
       x = ga(@rastriginsfcn,2)

      Display plotting functions while GA minimizes
       options = gaoptimset('PlotFcns',...
         {@gaplotbestf,@gaplotbestindiv,@gaplotexpectation,@gaplotstopping});
       [x,fval,exitflag,output] = ga(@rastriginsfcn,2,[],[],[],[],[],[],[],options)

    An example with inequality constraints and lower bounds
     A = [1 1; -1 2; 2 1];  b = [2; 2; 3];  lb = zeros(2,1);
     % Use mutation function which can handle constraints
     options = gaoptimset('MutationFcn',@mutationadaptfeasible);
     [x,fval,exitflag] = ga(@lincontest6,2,A,b,[],[],lb,[],[],options);

      FITNESSFCN can also be an anonymous function:
         x = ga(@(x) 3*sin(x(1))+exp(x(2)),2)

    If FITNESSFCN or NONLCON are parameterized, you can use anonymous
    functions to capture the problem-dependent parameters. Suppose you want
    to minimize the fitness given in the function myfit, subject to the
    nonlinear constraint myconstr, where these two functions are
    parameterized by their second argument a1 and a2, respectively. Here
    myfit and myconstr are M-file functions such as

         function f = myfit(x,a1)
         f = exp(x(1))*(4*x(1)^2 + 2*x(2)^2 + 4*x(1)*x(2) + 2*x(2) + a1);

    and

         function [c,ceq] = myconstr(x,a2)
         c = [1.5 + x(1)*x(2) - x(1) - x(2);
               -x(1)*x(2) - a2];
         % No nonlinear equality constraints:
          ceq = [];

    To optimize for specific values of a1 and a2, first assign the values
    to these two parameters. Then create two one-argument anonymous
    functions that capture the values of a1 and a2, and call myfit and
    myconstr with two arguments. Finally, pass these anonymous functions to
    GA:

      a1 = 1; a2 = 10; % define parameters first
      % Mutation function for constrained minimization
      options = gaoptimset('MutationFcn',@mutationadaptfeasible);
      x = ga(@(x)myfit(x,a1),2,[],[],[],[],[],[],@(x)myconstr(x,a2),options)

    See also gaoptimset, fitnessfunction, gaoutputfcntemplate, patternsearch, @.

    Reference page in Help browser
       doc ga

3Â¥: Originally posted by libralibra at 2012-06-07 19:41:09
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>> help ga
GA    Constrained optimization using genetic algorithm.
    GA attempts to solve problems of the form:
        min F(X)  subject to:  A*X  <= B ...

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