Fuzzy Multistage Optimization of Large-Scale Trusses

Fuzzy membership functions are implemented in the multistage optimization technique to improve its performance for the minimum weight design of truss structures of fixed topology. First, a large truss is split into several smaller substructures that are optimized separately. However, to preserve the unity of the original truss, interaction-balance equality constraints are introduced to account for the compatibility of deformations, and the equality of the action and reaction of forces at the points of the separation of the substructures. A penalty function, containing the equilibrium equations and interaction constraints as well as other constraints, is defined for each substructure. Then, a fuzzy membership function, returning a value between 0 and 1, is introduced for each of the equality constraints to provide some fuzzy evaluation of the degree of satisfaction. This measure is then used in the determination of an appropriate penalty parameter. The design procedure is iterative and continues until convergence is achieved for all of the objective functions corresponding to the substructures. It has been found that this technique has significantly improved the convergence speed at the expense of increasing the minimum weight by a negligible amount.