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European Journal of Operational Research
Volume 180, Issue 1, 1 July 2007, Pages 99-115
 
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doi:10.1016/j.ejor.2006.02.033    How to Cite or Link Using DOI (Opens New Window)
Copyright © 2006 Elsevier B.V. All rights reserved.

Discrete Optimization

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

Maria João AlvesCorresponding Author Contact Information, a, E-mail The Corresponding Author and João Clímacoa

aFaculdade de Economia da Universidade de Coimbra, INESCC, Av. Dias da Silva, 165, 3004-512 Coimbra, Portugal

Received 19 January 2005; 
accepted 16 February 2006. 
Available online 5 June 2006.

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Abstract

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.

Keywords: Integer programming; Multiple objective programming; Interactive methods

Article Outline

1. Introduction
2. Basic concepts and general results
2.1. Weighted-sum programs with additional constraints
2.2. Reference point based scalarizing programs
3. Non-interactive versus interactive methods
4. Interactive methods for MOIP/MOMIP
4.1. Biobjective integer and mixed-integer programming
4.2. Multiobjective integer and mixed-integer programming
5. Comparison of the MOIP/MOMIP interactive methods
6. Concluding remarks
References


 
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