The cross-over and the mutation operators are used for global and local optimum, respectively. So, if you use the correct operators, you can find the optimum.

Yes. It's very possible. The performance of GA and the likes, largely depend on exhaustive searching of the hyper space. Disregarding some option as you said will limit this searching, thus, the possibility of missing the global optimum. Again if the control parameters like the crossover and mutation are wrongly selected, it could also have effect on the performance of GA.

Dear Mohammad Royapoor,

Indeed it can happen that the GA algorithm does not converge towards a global optimum and this result depends mainly on the fitness function. This problem can be alleviated by using a different fitness function. It is therefore imperative to adapt an appropriate technique for each class of process in order to guide the algorithm towards the overall optimum.

Also i suggest you to see links on topic.

https://www.daaam.info/Downloads/Pdfs/proceedings/proceedings_2019/018.pdf

https://www.cambridge.org/core/books/abs/global-optimization-methods-in-geophysical-inversion/genetic-algorithms/ED12FE3DAE5E3643F3C4EB59B1B9D19F

Article A Review on Genetic Algorithm: Past, Present, and Future

Best regards

Finding the global optimum can only guarantee the launch of the genetic algorithm an infinite number of times.

Dear Mohammad Royapoor , I really like this question. It addresses an especially important design issue. First, I would like to question what is to be understood as a true global optimum. By applying a GA optimisation tool that divides the space of possibilities into subsets, to perform hypercube sampling within each subset introduces some error which influences the fitness function. The suggestion of Mohamed-Mourad Lafifi is therefore to be considered. But there is another issue I would like to address and that is de method used dividing the space of dimensions into subsets. This depends on the objective function (i.e. the model) and the question whether the space of dimensions can be sliced in such a way that we can determine whether the true global solution must exist. The ordening of the unit type must be preserved and the reversal of the ordening must also be preserved (i.e. bivariant). Under these conditions you can say something about the distributions in subspaces and their global behavior. A model may miss the global true solution so will the tool implementing the model using an EA.

Furthermore, I like to refer to the work of Paul Griffioen. A Unit-Aware Matrix Language and its Application in Control and Auditing - https://pure.uva.nl/ws/files/42206706/Thesis.pdf

Again, thank you for putting the question.

Kind regards

It will fin an optimal but depending on the design it could fail.

I would like to invite you to have a look on the following links.

SSO: https://www.mathworks.com/matlabcentral/fileexchange/92150-sperm-swarm-optimization-sso

HSSOGSA: https://www.mathworks.com/matlabcentral/fileexchange/92130-hssogsa?s_tid=srchtitle

MOSFP: https://github.com/sh7adeh1990/MOSFP

Dear Mohammad Royapoor,

GA is a metaheuristic. In a limited number of iterations, no one can claim that a metaheuristic always and for all problems can find a globally optimum solution (even a near-optimum solution).

this is a natural thing in mathematics there is no perfect solution especially the no linear problem, and most metaH utilized in the no linear problem, so you need always to expect and accept that fact, and keep improving the study of the metaH

The balancing between the exploration by using an appropriate mutation rate and exploitation by using an appropriate crossover rate plays an important role for getting the optimal solution in reasonable time.

Yes, in fact its not just the sampling method that may overlook the global optimum, you're actually starting from a deficit by using the GA algorithm as well. Since its a stochastic optimizer, the likelihood of ever reaching the true global optimum is slim. I don't fully understand the true parameters of your study, but if the problem is complex enough so as to prevent the use of deterministic techniques, then near-global optimal solutions is the best you can hope for.

Good luck