How to write an objective function(with complex term) to get optimization through PSO with five parameters ?

I would like to find optimize value of parameters in below equation,

Here are parameters needs to be optimize by PSO.

I have an experimental values of W and ε as follow,

and

I am able to get the solution of through lsqurvefit but It doesn't give the optimal values.

Here I wants to use all experimental values to find optimimum. How it can be incorporated in objective function?

[Alan Weiss]

When you say "complex," do you mean that the values of your parameters can have imaginary parts? And what makes you think that PSO is a good way to optimize this system? Probably, since you use lsqcurvefit, you are looking for a least-squares solution rather than an exact solution. It is possible that lsqcurvefit got stuck in a local miniimum. For ways around this problem, see MultiStart Using lsqcurvefit or lsqnonlin.

I would also suggest that you set bounds on the parameters if possible, such as nonnegativity if you believe that is applicable. Bounds can help the solver find a good solution. I encourage you to continue using lsqcurvefit, possibly with MultiStart, rather than PSO.

Alan Weiss

MATLAB mathematical toolbox documentation

[Walter Roberson]

I suspect "complex" means "complicated" in this context.

[SavanS]

Certainly it helped.

I have tried with MultiStart lscurvefit but it doesn't match the final result of PSO (which I got from leterature).

Can you help to wirite objective function for global oprimum values through PSO, incorporating experimental values?

And this is a complicated function not complex...