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Solving Large-Scale Fuzzy and Possibilistic Optimization Problems

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Abstract

Fuzzy and possibilistic optimization methods are demonstrated to be effective tools in solving large-scale problems. In particular, an optimization problem in radiation therapy with various orders of complexity from 1000 to 62,250 constraints for fuzzy and possibilistic linear and nonlinear programming implementations possessing (1) fuzzy or soft inequalities, (2) fuzzy right-hand side values, and (3) possibilistic right-hand side is used to demonstrate that fuzzy and possibilistic optimization methods are tractable and useful. We focus on the uncertainty in the right side of constraints which arises, in the context of the radiation therapy problem, from the fact that minimal and maximal radiation tolerances are ranges of values, with preferences within the range whose values are based on research results, empirical findings, and expert knowledge, rather than fixed real numbers. The results indicate that fuzzy/possibilistic optimization is a natural and effective way to model various types of optimization under uncertainty problems and that large fuzzy and possibilistic optimization problems can be solved efficiently.

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Authors and Affiliations

  1. Department of Mathematics, University of Colorado at Denver, Campus Box 170, P.O. Box 173364, Denver, CO, 80217-3364, USA

    Weldon A. Lodwick

  2. Department of Mathematics, University of Colorado at Denver, Campus Box 170, P.O. Box 173364, Denver, CO, 80217-3364, USA

    Katherine A. Bachman

Authors
  1. Weldon A. Lodwick
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  2. Katherine A. Bachman
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Correspondence to Weldon A. Lodwick.

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Lodwick, W.A., Bachman, K.A. Solving Large-Scale Fuzzy and Possibilistic Optimization Problems. Fuzzy Optim Decis Making 4, 257–278 (2005). https://doi.org/10.1007/s10700-005-3663-4

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  • DOI: https://doi.org/10.1007/s10700-005-3663-4

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