What is the meaning of function count in the genetic algorithm in matlab optimization?

Where is the function count coming from? Why does it not increase the same amount between generations?

Function:

 function y = fitness(x)
 a=1;
 b=1;
 c=1;
 y =sin(a*x(1)^2+b*x(2)+c);

Constraint Function:

function [c, ceq] = constraint(x)
   c = [];
 ceq = [];

Optimization Code:

ObjectiveFunction = @fitness;

nvars = 2;    % Number of variables
LB = [,];   % Lower bound
UB = [,];  % Upper bound
ConstraintFunction = @constraint;

for i=1:5

options = gaoptimset('MutationFcn',{@mutationuniform, .01}, 'Display','iter',...
    'Generations',100,'FitnessLimit', -.9999,...
    'PopulationSize',127);

[x,fval,exitflag, output] = ga(ObjectiveFunction,nvars,[],[],[],[],LB,UB,...
    ConstraintFunction,[],options)
%record = [record; fval];
z(i)=output.generations
k(i)=output.funccount
end

Answer 1

[Alan Weiss]

When you use a nonlinear constraint in ga, the solution algorithm is different than without the nonlinear constraint. See nonlinear constraint solver. In particular, note the paragraph:

 Each subproblem solution represents one generation.
 The number of function evaluations per generation is
 therefore much higher when using nonlinear constraints
 than otherwise.

Even though your constraint function is not calculating anything, the fact that you have a nonlinear constraint function means that ga uses the nonlinear constraint solver. If you really don't have a nonlinear constraint, set the ConstraintFunction argument to [].

Alan Weiss

MATLAB mathematical toolbox documentation

[Emily Senay]

Thank You!

Shouldn't the function count not exceed the number of generations multiplied by the population size? When I specify that I want to use integers (using IntCon) this is the case, but when I'm not using IntCont the function count exceeds to number of generations multiplied by the population size.

[Alan Weiss]

No, you misunderstand how the nonlinear constraint solver works. Read the link that I gave. There can be many iterations in each subproblem solution, so the number of function evaluations can be large.

Alan Weiss

MATLAB mathematical toolbox documentation

[Emily Senay]

I see now. So if I get rid of the nonlinear constraint shouldn't what I stated above be true..that the function count should equal or be less than the number of generations multiplied by the population size?