Solving large-scale fuzzy and possibilistic optimization problems

The semantic and algorithmic differences between fuzzy and possibilistic optimization methods are presented in the context of three methods for solving large fuzzy and possibilistic optimization problems. In particular, an optimization problem in radiation therapy with various orders of complexity, 1,000-55,000 constraints, possessing (i) soft constraints, (ii) fuzzy right-hand side values and (iii) possibilistic right-hand side values, are used to illustrate the semantics and to test the performance of the three fuzzy and possibilistic optimization methods. We focus on the uncertainty in the right side which arises, in the context of the radiation therapy problem, from the fact that minimal/maximal radiation tolerances are target values rather than fixed real numbers. The results indicate that fuzzy/possibilistic optimization is a natural way to model various types of optimization under uncertainty problems and large optimization problems can be solved efficiently.