Copyright © 2006 Elsevier B.V. All rights reserved.
Discrete Optimization
A review of interactive methods for multiobjective integer and mixed-integer programming
Received 19 January 2005;
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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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