A Fuzzy Dynamic Programming Approach for the Mixed-Discrete Optimization of Mechanical Systems

Many engineering optimization problems can be considered as multistage decision- making problems. If the system involves uncertainty in the form of linguistic parameters and vague data, a fuzzy approach is to be used for its description. The solution of such problems can be accomplished through fuzzy dynamic programming. However, most of the existing fuzzy dynamic programming algorithms cannot deal with mixed-discrete design variables in the optimization of mechanical systems containing fuzzy information. They often assumed that a fuzzy goal is imposed only on the final state for simplicity, the values of fuzzy goal and other parameters need to be predefined, and an optimal solution is obtained in the continuous design space only. To better reflect the nature of uncertainties present in real-life optimization problems, a mixed-discrete fuzzy dynamic programming (MDFDP) approach is proposed in this work for solving multistage decision-making problems in mixed-discrete design space with a fuzzy goal and a fuzzy state imposed on each stage. The method can also be extended to solve general mixed-discrete fuzzy nonlinear programming problems if their corresponding crisp problems can be solved using dynamic programming approaches. The feasibility and versatility of the proposed method are illustrated by considering the design of a four-bar truss and the reliability-based optimization of a gearbox. To the authors' knowledge, this work represents the first fuzzy dynamic programming method reported in the literature for dealing with mixed-discrete optimization problems.