Effective implementation of the ε-constraint method in Multi-Objective Mathematical Programming problems

As indicated by the most widely accepted classification, the Multi-Objective Mathematical Programming (MOMP) methods can be classified as a priori, interactive and a posteriori, according to the decision stage in which the decision maker expresses his/her preferences. Although the a priori methods a...

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Published in:	Applied mathematics and computation Vol. 213; no. 2; pp. 455 - 465
Main Author:	Mavrotas, George
Format:	Journal Article
Language:	English
Published:	Amsterdam Elsevier Inc 15.07.2009 Elsevier
Subjects:	Calculus of variations and optimal control Exact sciences and technology GAMS Mathematical analysis Mathematics Multi-Objective Programming Numerical analysis Numerical analysis. Scientific computation Numerical methods in mathematical programming, optimization and calculus of variations Sciences and techniques of general use ε-Constraint method ε-Constraint method GAMS Multi-Objective Programming Optimization method Iteration Mathematical method Implementation Numerical analysis Applied mathematics Optimal solution Classification Software Mathematical programming
ISSN:	0096-3003, 1873-5649
Online Access:	Get full text
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Abstract	As indicated by the most widely accepted classification, the Multi-Objective Mathematical Programming (MOMP) methods can be classified as a priori, interactive and a posteriori, according to the decision stage in which the decision maker expresses his/her preferences. Although the a priori methods are the most popular, the interactive and the a posteriori methods convey much more information to the decision maker. Especially, the a posteriori (or generation) methods give the whole picture (i.e. the Pareto set) to the decision maker, before his/her final choice, reinforcing thus, his/her confidence to the final decision. However, the generation methods are the less popular due to their computational effort and the lack of widely available software. The present work is an effort to effectively implement the ε-constraint method for producing the Pareto optimal solutions in a MOMP. We propose a novel version of the method (augmented ε-constraint method – AUGMECON) that avoids the production of weakly Pareto optimal solutions and accelerates the whole process by avoiding redundant iterations. The method AUGMECON has been implemented in GAMS, a widely used modelling language, and has already been used in some applications. Finally, an interactive approach that is based on AUGMECON and eventually results in the most preferred Pareto optimal solution is also proposed in the paper.
AbstractList	As indicated by the most widely accepted classification, the Multi-Objective Mathematical Programming (MOMP) methods can be classified as a priori, interactive and a posteriori, according to the decision stage in which the decision maker expresses his/her preferences. Although the a priori methods are the most popular, the interactive and the a posteriori methods convey much more information to the decision maker. Especially, the a posteriori (or generation) methods give the whole picture (i.e. the Pareto set) to the decision maker, before his/her final choice, reinforcing thus, his/her confidence to the final decision. However, the generation methods are the less popular due to their computational effort and the lack of widely available software. The present work is an effort to effectively implement the ε-constraint method for producing the Pareto optimal solutions in a MOMP. We propose a novel version of the method (augmented ε-constraint method – AUGMECON) that avoids the production of weakly Pareto optimal solutions and accelerates the whole process by avoiding redundant iterations. The method AUGMECON has been implemented in GAMS, a widely used modelling language, and has already been used in some applications. Finally, an interactive approach that is based on AUGMECON and eventually results in the most preferred Pareto optimal solution is also proposed in the paper.
Author	Mavrotas, George
Author_xml	– sequence: 1 givenname: George surname: Mavrotas fullname: Mavrotas, George email: mavrotas@chemeng.ntua.gr organization: Laboratory of Industrial and Energy Economics, School of Chemical Engineering, National Technical University of Athens, Zographou Campus, Athens 15780, Greece
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Snippet	As indicated by the most widely accepted classification, the Multi-Objective Mathematical Programming (MOMP) methods can be classified as a priori, interactive...
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SubjectTerms	Calculus of variations and optimal control Exact sciences and technology GAMS Mathematical analysis Mathematics Multi-Objective Programming Numerical analysis Numerical analysis. Scientific computation Numerical methods in mathematical programming, optimization and calculus of variations Sciences and techniques of general use ε-Constraint method
Title	Effective implementation of the ε-constraint method in Multi-Objective Mathematical Programming problems
URI	https://dx.doi.org/10.1016/j.amc.2009.03.037
Volume	213
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