Annals of Operations Research

, Volume 197, Issue 1, pp 47–70

Improving the computational efficiency in a global formulation (GLIDE) for interactive multiobjective optimization

Article

DOI: 10.1007/s10479-010-0831-x

Cite this article as:
Ruiz, F., Luque, M. & Miettinen, K. Ann Oper Res (2012) 197: 47. doi:10.1007/s10479-010-0831-x

Abstract

In this paper, we present a new general formulation for multiobjective optimization that can accommodate several interactive methods of different types (regarding various types of preference information required from the decision maker). This formulation provides a comfortable implementation framework for a general interactive system and allows the decision maker to conveniently apply several interactive methods in one solution process. In other words, the decision maker can at each iteration of the solution process choose how to give preference information to direct the interactive solution process, and the formulation enables changing the type of preferences, that is, the method used, whenever desired. The first general formulation, GLIDE, included eight interactive methods utilizing four types of preferences. Here we present an improved version where we pay special attention to the computational efficiency (especially significant for large and complex problems), by eliminating some constraints and parameters of the original formulation. To be more specific, we propose two new formulations, depending on whether the multiobjective optimization problem to be considered is differentiable or not. Some computational tests are reported showing improvements in all cases. The generality of the new improved formulations is supported by the fact that they can accommodate six interactive methods more, that is, a total of fourteen interactive methods, just by adjusting parameter values.

Keywords

Multiobjective programming Multiple objectives Interactive methods Reference point methods Classification Marginal rates of substitution Global system Pareto optimality 

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Francisco Ruiz
    • 1
  • Mariano Luque
    • 1
  • Kaisa Miettinen
    • 2
  1. 1.University of MalagaMalagaSpain
  2. 2.Department of Mathematical Information TechnologyUniversity of JyväskyläUniversity of JyväskyläFinland

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