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Title: A New Methodology to Select the Preferred Solutions from the Pareto-optimal Set: Application to Polymer Extrusion

Abstract

Most of the real world optimization problems involve multiple, usually conflicting, optimization criteria. Generating Pareto optimal solutions plays an important role in multi-objective optimization, and the problem is considered to be solved when the Pareto optimal set is found, i.e., the set of non-dominated solutions. Multi-Objective Evolutionary Algorithms based on the principle of Pareto optimality are designed to produce the complete set of non-dominated solutions. However, this is not allays enough since the aim is not only to know the Pareto set but, also, to obtain one solution from this Pareto set. Thus, the definition of a methodology able to select a single solution from the set of non-dominated solutions (or a region of the Pareto frontier), and taking into account the preferences of a Decision Maker (DM), is necessary. A different method, based on a weighted stress function, is proposed. It is able to integrate the user's preferences in order to find the best region of the Pareto frontier accordingly with these preferences. This method was tested on some benchmark test problems, with two and three criteria, and on a polymer extrusion problem. This methodology is able to select efficiently the best Pareto-frontier region for the specified relative importancemore » of the criteria.« less

Authors:
;  [1];  [2]
  1. IPC - Institute for Polymer and Composites, University of Minho, Guimaraes (Portugal)
  2. Centre for Intelligent Systems, University of Algarve, Faro (Portugal)
Publication Date:
OSTI Identifier:
21057085
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 907; Journal Issue: 1; Conference: 10. ESAFORM conference on material forming, Zaragoza (Spain), 18-20 Apr 2007; Other Information: DOI: 10.1063/1.2729621; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; ALGORITHMS; BENCHMARKS; CALCULATION METHODS; EXTRUSION; MATHEMATICAL SOLUTIONS; OPTIMIZATION; POLYMERS; STRESSES

Citation Formats

Ferreira, Jose C., Gaspar-Cunha, Antonio, and Fonseca, Carlos M.. A New Methodology to Select the Preferred Solutions from the Pareto-optimal Set: Application to Polymer Extrusion. United States: N. p., 2007. Web. doi:10.1063/1.2729621.
Ferreira, Jose C., Gaspar-Cunha, Antonio, & Fonseca, Carlos M.. A New Methodology to Select the Preferred Solutions from the Pareto-optimal Set: Application to Polymer Extrusion. United States. doi:10.1063/1.2729621.
Ferreira, Jose C., Gaspar-Cunha, Antonio, and Fonseca, Carlos M.. Sat . "A New Methodology to Select the Preferred Solutions from the Pareto-optimal Set: Application to Polymer Extrusion". United States. doi:10.1063/1.2729621.
@article{osti_21057085,
title = {A New Methodology to Select the Preferred Solutions from the Pareto-optimal Set: Application to Polymer Extrusion},
author = {Ferreira, Jose C. and Gaspar-Cunha, Antonio and Fonseca, Carlos M.},
abstractNote = {Most of the real world optimization problems involve multiple, usually conflicting, optimization criteria. Generating Pareto optimal solutions plays an important role in multi-objective optimization, and the problem is considered to be solved when the Pareto optimal set is found, i.e., the set of non-dominated solutions. Multi-Objective Evolutionary Algorithms based on the principle of Pareto optimality are designed to produce the complete set of non-dominated solutions. However, this is not allays enough since the aim is not only to know the Pareto set but, also, to obtain one solution from this Pareto set. Thus, the definition of a methodology able to select a single solution from the set of non-dominated solutions (or a region of the Pareto frontier), and taking into account the preferences of a Decision Maker (DM), is necessary. A different method, based on a weighted stress function, is proposed. It is able to integrate the user's preferences in order to find the best region of the Pareto frontier accordingly with these preferences. This method was tested on some benchmark test problems, with two and three criteria, and on a polymer extrusion problem. This methodology is able to select efficiently the best Pareto-frontier region for the specified relative importance of the criteria.},
doi = {10.1063/1.2729621},
journal = {AIP Conference Proceedings},
number = 1,
volume = 907,
place = {United States},
year = {Sat Apr 07 00:00:00 EDT 2007},
month = {Sat Apr 07 00:00:00 EDT 2007}
}