Let us discuss about the advantages, disadvantages, and use of powerful decomposition techniques like Bender's decomposition for large-scale optimization. I invite my esteemed colleagues and researchers to share important literature, ways of implementation, and potential application areas of decomposition algorithms, in this forum.
Dear R.K
Do you think that the Benders's decomposition that can be resumed as "Divide and conquer" (not my quote), can be applied to MCDM systems?
Dear Prof. Munier,
To the best of my knowledge, Bender's decomposition technique has not yet been applied to MCDM systems. I believe that saying 'no' as the answer to your question may not be fair at this moment. We never know what will happen in the future. However, my experience says that it will be difficult to apply Bender's decomposition because of the nature of the MCDM systems.
Dear R.K
You are right, we can't say no, because we don't know about new developments.
Probably, one of the reasons by which Bender's decomposition technique has not been applied to MCDM - and I share your opinion about its application - is because problems in MCDM are systems, and like that, they can't be partitioned, other than for study.
Your last paragraph resumes the same point, better than my sketchy explanation, so, we agree
Dear R.K.
Thank you.
Your agreement is very important to me since I have been saying that MCDM problems can't be partitioned because they are systems, and nobody, except you, supported me.
This is not my discovery; this fact was stated many years ago, mainly by Triantaphyllou who, with a very simple example, demonstrated that if you slice a project and add up results, and after, you solve the problem in ints integrity, you got different results. Obviously, the total is not equal to the sum of the parts, as happens in many aspects of real life.
Most, unfortunately, methods like AHP, take partition as a credo or a divine truth, and then, ignore reality.
You can divide a project to better investigate but not to solve it.
What is really strange, or perhaps not, is that none of the gurus of AHP comes to the ring to defend it.
There is only an explanation: They don't have arguments.
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