Writing fitness function in multi objective GA

If I need to go for a multi objective optimisation in GA, how can I bring in the two objectives in a custom made fitness function. Can someone explain in the context of the travelling salesman problem described here : https://in.mathworks.com/help/gads/custom-data-type-optimization-using-ga.html

Answer 1

[Walter Roberson]

mobj = @(x) [fun1(x); fun2(x) ]

[Hari]

Would the syntax be the same if user function evaluation is chosen as vectorized? I wrote 2 custom fitness functions and called them according to this syntax. But I am getting an error "When 'Vectorized' is 'on', your fitness function must return a vector of length equal to the size of the population"

[Walter Roberson]

You know that ga() cannot handle multi objective? gamultiobj() is needed for multi objective.

[Hari]

Yes, I have used gamultiobj() and got the error. The fitness functions worked well independently when used with ga().

[Walter Roberson]

You could try

mobj = @(x) [fun1(x), fun2(x) ]

where each of those returns a column vector

[Hari]

This too gives the same error

[Walter Roberson]

I am not getting a problem in my tests ?

fun1 = @(x) sin(pi*x(:,1)) + sinh(x(:,2));
fun2 = @(x) cos(pi*x(:,1)) + cosh(x(:,2));
mobj = @(x) [ fun1(x), fun2(x) ];

nvars = 2;
lb = [-pi -pi];
ub = [pi pi];

options1 = optimoptions(@gamultiobj, 'UseVectorized', false);
[Y1, fval1] = gamultiobj(mobj, nvars, [], [], [], [], lb, ub, [], options1);

Optimization terminated: average change in the spread of Pareto solutions less than options.FunctionTolerance.

options2 = optimoptions(@gamultiobj, 'UseVectorized', true);
[Y2, fval2] = gamultiobj(mobj, nvars, [], [], [], [], lb, ub, [], options1);

Optimization terminated: average change in the spread of Pareto solutions less than options.FunctionTolerance.

[Hari]

Yes, I tried again. The second approach worked this time. Thanks!!

Answer 2

[M Mirrashid]

https://ch.mathworks.com/matlabcentral/fileexchange/112600-transit-search-optimization-algorithm-matlab-codes