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Abstract and Applied Analysis
Volume 2018 (2018), Article ID 3804742, 6 pages
https://doi.org/10.1155/2018/3804742
Research Article

Multiobjective Optimization, Scalarization, and Maximal Elements of Preorders

1DIA, Università di Trieste, 34127 Trieste, Italy
2DEAMS, Università di Trieste, 34127 Trieste, Italy
3DEM, Università di Brescia, 25122 Brescia, Italy

Correspondence should be addressed to Gianni Bosi

Received 31 July 2017; Accepted 17 December 2017; Published 28 January 2018

Academic Editor: Simeon Reich

Copyright © 2018 Paolo Bevilacqua et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.