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Problems and methods with multiple objective functions

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Abstract

LetA be a set of feasible alternatives or decisions, and supposen different indices, measures, or objectives are associated with each possible decision ofA. How can a “best” feasible decision be made? What methods can be used or experimented with to reach some decision?

The purpose of this paper is to attempt a synthesis of the main approaches to this problem which have been studied to date. Four different classes of approaches are distinguished: (1) aggregation of multiple objective functions into a unique function defining a complete preference order; (2) progressive definition of preference together with exploration of the feasible set; (3) definition of a partial order stronger than the product of then complete orders associated with then objective functions; and (4) maximum reduction of uncertainty and incomparability.

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Roy, B. Problems and methods with multiple objective functions. Mathematical Programming 1, 239–266 (1971). https://doi.org/10.1007/BF01584088

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