Good question Nolberto. Sometimes you know the answer. In some application it might be obvious if an "optimum" is not so optimal. No clear definition maybe.
Thank you for your answer, however, you say that you know the answer, and indeed it can happens, but then, if you know it, why do you need to perform a MCDM analysis?
Regarding your comment about the optimum, yes, it could be. Trouble is that you don't know that optimum, and probably you don't even know if it exists, because it may be that the problem is unfeasible
I agreed 100 % with you in that a Solver must identify unfeasibility, but my question is: How many solvers or MCDM methods do you know that have that capacity?
Only one: Linear Programming
The procedure is very simple: It compares criteria independent values, and if a solution satisfies these values. If only one criterion is not satisfied the project is unfeasible.
Nowadays, problems are 'solved' assuming that a problem is feasible, not taking into account that t hat circumstance may not exist.
I have read hundreds of comments and papers from our colleagues. How many of them posed this problem?
Nobody.
I wrote in RG almost a year ago about this problem, you can see it in my profile under the number 304, and again, in May 2020 under the number 318. Both have had some moderate reading but nobody came forward to acknowledge and discuss it. You are the only person that addresses that issue.
Regarding LocalSolver I know what it, is but my experience on it is null.