An Interactive Multiple Objective Linear Programming Method for a Class of Underlying Nonlinear Utility Functions

Zionts, Stanley; Wallenius, Jyrki

doi:10.1287/mnsc.29.5.519

Cited by 321 publications

(61 citation statements)

References 14 publications

(4 reference statements)

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“…Another version of the algorithm exists for a class of pseudoconcave value functions (Zionts and Wallenius, 1983). As the method is based on piecewise linear approximations of the functions, we will briefly describe it for MOLP problems representing one of these piecewise approximations.…”

Section: Some Trade-off Based Methodsmentioning

confidence: 99%

Introduction to Multiobjective Optimization: Interactive Approaches

Miettinen

Ruiz

Wierzbicki

2008

Multiobjective Optimization

200

197

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Abstract. We give an overview of interactive methods developed for solving nonlinear multiobjective optimization problems. In interactive methods, a decision maker plays an important part and the idea is to support her/him in the search for the most preferred solution. In interactive methods, steps of an iterative solution algorithm are repeated and the decision maker progressively provides preference information so that the most preferred solution can be found. We identify three types of specifying preference information in interactive methods and give some examples of methods representing each type. The types are methods based on trade-off information, reference points and classification of objective functions. IntroductionSolving multiobjective optimization problems typically means helping a human decision maker (DM) in finding the most preferred solution as the final one. By the most preferred solution we refer to a Pareto optimal solution which the DM is convinced to be her/his best option. Naturally, finding the most preferred solution necessitates the participation of the DM who is supposed to have insight into the problem and be able to specify preference information related to the objectives considered and different solution alternatives, as discussed in Chapter 1. There we presented four classes for multiobjective optimization methods according to the role of the DM in the solution process.

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Section: Some Trade-off Based Methodsmentioning

confidence: 99%

Introduction to Multiobjective Optimization: Interactive Approaches

Miettinen

Ruiz

Wierzbicki

2008

Multiobjective Optimization

200

197

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show abstract

“…The method employs a modified version of the MOLP method of Zionts and Wallenius (1983) within a branch-and-bound framework. The DM's preference structure is assessed using pairwise comparisons.…”

Section: Biobjective Integer and Mixed-integer Programmingmentioning

confidence: 99%

A review of interactive methods for multiobjective integer and mixed-integer programming

Alves

Clímaco

2007

European Journal of Operational Research

132

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This paper makes a review of interactive methods devoted to multiobjective integer and mixed-integer programming (MOIP/MOMIP) problems. The basic concepts concerning the characterization of the non-dominated solution set are first introduced, followed by a remark about non-interactive methods vs. interactive methods. Then, we focus on interactive MOIP/MOMIP methods, including their characterization according to the type of preference information required from the decision maker, the computing process used to determine non-dominated solutions and the interactive protocol used to communicate with the decision maker. We try to draw out some contrasts and similarities of the different types of methods.

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“…Une classe importante de ces méthodes utilise ces fonctions d'utilité d'une manière interactive dans le but de générer un ensemble de solutions efficaces d'utilité croissante [2,11,13] ou même d'estimer une solution unique d'utilité maximale [4], En effet, dans ces méthodes le décideur doit répondre à plusieurs types de questions (/. e. taux de substitution explicite, classement d'alternatives, .…”

Section: G N (X))unclassified

Méthode d'estimation d'utilités additives concaves en programmation linéaire multiobjectifs

Despotis¹,

Yannacopoulos²

1990

RAIRO-Oper. Res.

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An Interactive Multiple Objective Linear Programming Method for a Class of Underlying Nonlinear Utility Functions

Cited by 321 publications

References 14 publications

Introduction to Multiobjective Optimization: Interactive Approaches

Introduction to Multiobjective Optimization: Interactive Approaches

A review of interactive methods for multiobjective integer and mixed-integer programming

Méthode d'estimation d'utilités additives concaves en programmation linéaire multiobjectifs

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