# Writing fitness function in multi objective GA

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Hari on 25 May 2022
Answered: M Mirrashid on 5 Jun 2022
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

Walter Roberson on 25 May 2022
mobj = @(x) [fun1(x); fun2(x) ]
Walter Roberson on 27 May 2022
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 on 4 Jun 2022
Yes, I tried again. The second approach worked this time. Thanks!!

M Mirrashid on 5 Jun 2022