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A Generalization of the Concept of proper efficiency in the Decomposed Multi-Objective Optimization Problems

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION 2024年第13-14期45卷 686页

作者： Foroutannia, Davoud Ahmadi, Fatemeh Vali e Asr Univ Rafsanjan Dept Math Rafsanjan Iran

In the context of multi-objective optimization, a properly efficient solution is one that is efficient while at least one of the tradeoffs between different objectives is limited. However, in some situations, it is possible that all efficient solutions have unlimited tradeoffs, which is not always appropriate. To provide new solutions that have at least one bounded tradeoff for such problems, we first introduce a new concept of efficiency by applying a family of scalarization functions for the decomposed multi-objective optimization problem. Then, we extend the concept of proper efficiency by examining the boundedness of the tradeoffs between scalar optimization subproblems and other subproblems. Another purpose of this paper is to investigate the effect of using the scalarizing functions for some subproblems in the decomposed multi-objective optimization problem. Our findings suggest that as the number of subproblems that use scalarizing functions increases, the solution set associated with the generalized proper efficiency concept becomes smaller.

关键词： efficiency multi-objective optimization proper efficiency proper efficiency with respect to a partition scalarization method

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