Fuzzy Genetic Algorithm for Optimization of Steel Structures

Abstract

In the traditional optimization algorithms, constraints are satisfied within a tolerance defined by a crisp number. In actual engineering practice, constraint evaluation involves many sources of imprecision and approximation. When an optimization algorithm is forced to satisfy the design constraints exactly, it can miss the global optimum solution within the confine of commonly acceptable approximations. Extending the augmented Lagrangian genetic algorithm (GA) of Adeli and Cheng, a fuzzy augmented Lagrangian GA is presented for optimization of steel structures subjected to the constraints of the AISC allowable stress design specifications taking into account the fuzziness in the constraints. The membership function for the fuzzy domain is found by the intersection of the fuzzy membership function for the objective function and the constraints using the max-min procedure of Bellman and Zadeh. Nonlinear quadratic fuzzy membership functions are used for objective function and constraints. The algorithm is applied to two space axial-load structures including a large 37-story structure with 1,310 members. The features and advantages of the new fuzzy GA include acknowledging the imprecision and fuzziness in the code-based design constraints, increased likelihood of obtaining the global optimum solution, improved convergence, and reduced total computer processing time.