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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Vydané v:	European journal of operational research Ročník 228; číslo 2; s. 397 - 404
Hlavný autor:	Nguyen, Duy Van
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Amsterdam Elsevier B.V 16.07.2013 Elsevier Elsevier Sequoia S.A
Predmet:	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
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Abstract	► 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.
AbstractList	The UTAs (UTilite Additives) type methods for constructing nondecreasing additive utility functions were first proposed by Jacquet-Lagreze 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. [PUBLICATION ABSTRACT] ► 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.
Author	Nguyen, Duy Van
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Snippet	► We propose an algorithm for globally maximizing UTA function for convex multi-objective optimization problems. ► This is a finite branch and bound... The UTAs (UTilite Additives) type methods for constructing nondecreasing additive utility functions were first proposed by Jacquet-Lagreze and Siskos in 1982...
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SubjectTerms	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
Title	Global maximization of UTA functions in multi-objective optimization
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