Global maximization of UTA functions in multi-objective optimization

► We propose an algorithm for globally maximizing UTA function for convex multi-objective optimization problems. ► This is a finite branch and bound algorithm.The most expensive tasks are performed in the space of the objectives. ► The algorithm works well for problems, in which the number of object...

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Bibliographic Details
Published in:European journal of operational research Vol. 228; no. 2; pp. 397 - 404
Main Author: Nguyen, Duy Van
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 16.07.2013
Elsevier
Elsevier Sequoia S.A
Subjects:
Algorithms
Branch & bound algorithms
Branch-and-bound algorithm
Decision analysis
Global optimization
Mathematical programming
Multiple criteria decision making
Multiple objective optimization
Optimization algorithms
Studies
UTA functions
UTA type methods
Utility function program
Utility functions
Utility function program
Global optimization
UTA type methods
UTA functions
Multiple objective optimization
Branch-and-bound algorithm
ISSN:0377-2217, 1872-6860
Online Access:Get full text
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Summary:► We propose an algorithm for globally maximizing UTA function for convex multi-objective optimization problems. ► This is a finite branch and bound algorithm.The most expensive tasks are performed in the space of the objectives. ► The algorithm works well for problems, in which the number of objectives is much smaller than the number of variables. The UTAs (UTilité Additives) type methods for constructing nondecreasing additive utility functions were first proposed by Jacquet-Lagrèze and Siskos in 1982 for handling decision problems of multicriteria ranking. In this article, by UTA functions, we mean functions which are constructed by the UTA type methods. Our purpose is to propose an algorithm for globally maximizing UTA functions of a class of linear/convex multiple objective programming problems. The algorithm is established based on a branch and bound scheme, in which the branching procedure is performed by a so-called I-rectangular bisection in the objective (outcome) space, and the bounding procedure by some convex or linear programs. Preliminary computational experiments show that this algorithm can work well for the case where the number of objective functions in the multiple objective optimization problem under consideration is much smaller than the number of variables.
Bibliography:SourceType-Scholarly Journals-1
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ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2012.06.022