Multiple objective (fuzzy) dynamic programming problems: a survey and some applications

Many real-world problems involve sequential or multistage decision making. Dynamic programming (DP) is a powerful optimization technique that is particularly applicable to many complex problems requiring a sequence of interrelated decisions. A new methodology, multiobjective dynamic programming (MODP), which relies heavily on conventional dynamic programming, is developed as a technique for solving problems that involve conflicting objectives that obey DP characteristics. In the past two decades, a major development of multiobjective dynamic optimization has been made: MODP, one of the most provocative topics within the broader subject. A natural extension of DP is its use in conjunction with fuzzy sets. This involves the perturbation of its components in a manner that admits of systematic fuzzification. Fuzzy dynamic programming (FDP) represents an advance on the Theory of DP. This paper reviews the major concepts used in MODP and FMODP and examines the current progress made in the development of the corresponding theory and methodology.