Have a look at:

Article Solving large-scale global optimization problems using enhan...

And...there is not something like "the best " approach!

@J. W. Nieuwenhuis

Yes that true.

However, I am wondering if there are comparative studies between decomposition and non decomposition approaches.

Dear Abdennour Boulesnane,

I suggest you to see links and attached files on topic.

https://titan.csit.rmit.edu.au/~e46507/publications/lsgo-cec15.pdf

https://arxiv.org/pdf/1607.01668.pdf

https://scholar.princeton.edu/sites/default/files/ghall/files/georgina_hall_proquest_version.p

Best regards

dear Abdennour Boulesnane ,

algorithms-based decomposition

Farmalend Fertility algorithm is one of the best algorithm for this issue. please find at this:

https://www.sciencedirect.com/science/article/abs/pii/S1568494618304216

https://ieeexplore.ieee.org/document/8789943

There is no method that can solve all problems. We would need to know much more in order to have a chance to give advise - the information is not at all enough!

If there is a special structure to the problem, then it may be beneficial to use decomposition based approaches. Even then, it may or may not work, depending on the problem. You should have an open mind and consider all options.

The authors of the paper on farmland fertility can't even spell right!! I wouldn't go near it!

Remember: if the title of the paper - or of the method - is exotic, it probably is a scam - probably a lousy metaheuristic borrowed and adjusted a little. Geez - can't these people just go away ... ?

Notice also that the people who propose these methods do not even mention FOR WHAT PROBLEM! "Large-scale problems" could be anything!

Michael Patriksson , thank you for your reply, sir, that clear, in several situations, there is no one standard method that fits all.

But if we have a non-separable large-scale problem where all variables interact, how could we deal with it? Knowing that in this case, methods-based decomposition are not recommended !!

I Find a nice answer here:

Conference Paper On the Selection of Decomposition Methods for Large Scale Fu...

Thank you all

Best regards

Abdennour Boulesnane, if the problem is non-separable, then there are still methods that can be used to hopefully make the problem easier to solve. You have to consider the formulation first: can you formulate the problem in different ways? Are there additional variables and/or constraints that you can consider? Sometimes additional constraints will strengthen the formulation and make it easier to solve. You can take a look at the following book for a comprehensive treatment of large scale linear and integer optimization:

Book Large Scale Linear and Integer Optimization: A Unified Approach