penalty value of matlab ga optimization

Using the MATLAB Global Optimization Toolbox for calculation, the trend of the penalty value's variation is consistently as follows:

The final output in the command-line window is:

Optimization terminated: average change in the penalty fitness value less than options.FunctionTolerance

and constraint violation is less than options.ConstraintTolerance.

IdleTimeout has been reached.

Is this result the global optimum? thank you very much!

[Stephen23]

"Is this result the global optimum?"

There is no optimization routine in existence that can reliably obtain "the global optimum" of any arbitrary function.

Answer 1

[Matt J]

It is the solution that ga thinks is the global optimum.

[binbin cao]

I just want to ask, why is it that no matter how I adjust the parameters, the mean value and the best value will never coincide in the end? Later on, their curves will become parallel to each other.

[Stephen23]

"the mean value and the best value will never coincide in the end?"

The sample populaton is randomly selected and randomly modified, see an explanation of GA here:

https://www.mathworks.com/help/gads/how-the-genetic-algorithm-works.html

In general there is no reason to expect the mean and best values to coincide, no matter how long GA runs for.

By the way, you can easily find that page in the ALGORITHMS section of the GA documentation:

https://www.mathworks.com/help/gads/ga.html#d124e52882