Can a search method that optimizes one criteria and uses other as a tie-breaker be called multi-objective? If yes, is there a subcategory in which it falls? If not, what is it called?
Thank you.
Interesting question
In my opinion, if the the alternatives are subject to both criteria, it can be considered a multi objective. Needs to be seen which is the specific objective of this second criterion. It it is used only as a breaker, well it is an objective as any other and then I believe that the process credits to be considered multicriteria
Dear Victor,
It all depends on the problem to solve. If the second criterion is related to the first but does not optimize it, it can serve as a restrictive condition for optimization under the primary criterion. If the criteria have objectives this is milticriteria optimization model.
Hello Victor,
The tie-breaker may be considered as a constraint according to the explanation of Svetla Stoilova, Nolberto Munier, and probably your statement too (... tie-breaker). Therefore, I suggest that your problem is called single objective constrained (linear/non-linear) optimization problem.
Dear Victor,
Judging by your question, you possibly have a situation with ordered criteria: you are looking for a solution that is optimal with respect to the first criterion and amongst these solutions, you are looking for a solution that is optimal with respect to the second criterion.
If my description is valid, then the terminology question has the following answer. The above approach to solving multicriteria problems is called an ordered criteria approach or a lexicographic approach.
Please, be careful: you should guarantee that the found solution is really optimal with respect to the second criterion amongst all solutions that are optimal with respect to the first criterion. To guarantee this, you should prove, for example, that IN EACH STEP, your ALGORITHM GENERATES ALL POSSIBLE ALTERNATIVES for the first criterion. Otherwise, the final solution may not be optimal with respect to the second criterion.
More than that, even if you generate all alternatives, you should guarantee, that the local choice in each step gives a global optimum with respect to the second criterion. If you have no such guarantees, you cannot speak about solving a multicriteria problem and your approach has no any special name.
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