Advances in Fuzzy Dynamic Programming

Introduction

While deterministic optimization problems are formulated with known parameters, very often real-world problems include unknown parameters (Delgado et al., 1987). When the parameters are only known to remain within given bounds, one way to tackle such problems is through robust optimization (Ben-Tal et al., 2009). When probability distributions are available for their values, stochastic optimization techniques (Ruszczynski et al., 2003) may be used to provide the most expected feasible solution. An intermediate approach adopting the fuzzy formalism to represent the parameter uncertainties has been also developed (Zimmermann, 1986). These three approaches lead in general to cumbersome computations. Also, in many situations the optimal solution cannot be applied exactly according to implementation constraints which have not been considered explicitly in the formulation of the problem. In that case post optimization sensibility analysis (Gal et al., 1997) resulting often in an important computational effort must be performed.