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Abstract and Applied Analysis | Vol.2018, Issue. | | Pages

Multiobjective Optimization, Scalarization, and Maximal Elements of Preorders

Abstract

We characterize the existence of (weak) Pareto optimal solutions to the classical multiobjective optimization problem by referring to the naturally associated preorders and their finite (Richter-Peleg) multiutility representation. The case of a compact design space is appropriately considered by using results concerning the existence of maximal elements of preorders. The possibility of reformulating the multiobjective optimization problem for determining the weak Pareto optimal solutions by means of a scalarization procedure is finally characterized.

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Multiobjective Optimization, Scalarization, and Maximal Elements of Preorders

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Keywords

maximal elements design space weak pareto optimal solutions classical multiobjective optimization problem preorders finite richterpeleg multiutility scalarization procedure

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,.Multiobjective Optimization, Scalarization, and Maximal Elements of Preorders. 2018 (),.

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