Mixed-discrete fuzzy programming for nonlinear engineering optimization

Engineering optimization often contains a mix of continuous, integer and discrete types of design variables. The design domain and constraints frequently are fuzzy and cannot be defined precisely. This paper proposes an algorithm of mathematical programming in which the λ-formulation of fuzzy optimization combines the modified branch-and-bound with max-partial derivative branching techniques for solving mixed discrete fuzzy optimization problems. The construction of a membership function of a design goal is extremely important in order to obtain the true optimum. The paper proposes a strategy to construct and select the preferred objective membership function. Optimal designs of a reinforced concrete beam and a pressure vessel illustrate this strategy. The numerical results and the feasibility of the proposed methodology are presented and discussed.