Shape and size optimization of truss structures considering dynamic constraints through modern metaheuristic algorithms

Abstract

Mass optimization on shape and sizing with multiple natural frequency constraints are highly nonlinear dynamic optimization problems. Multiple natural frequency constraints normally cause difficult dynamic sensitivity analysis and, in addition, two different types of design variables, nodal coordinates and cross-sectional areas, often lead to divergence. Thus, the choice of the appropriated method to solve this kind of problem is of paramount importance. Within this context, in this paper two of the most recent metaheuristic algorithms developed in the last decade, Harmony Search (HS) and Firefly Algorithm (FA), are used, for the first time here, to solve truss shape and sizing optimization with multiple natural frequency constraints. Since these metaheuristic algorithms are not a gradient-based search, they avoid most of the pitfalls of any gradient-based search algorithms. The effectiveness of Harmony Search and Firefly Algorithm is demonstrated through four benchmark structural optimization problems for solving shape and sizing optimization of trusses with multiple frequency constraints. The results showed that both metaheuristic algorithms reached, in a relatively low computational time, better results than the literature in three of the four examples considered, and in the other example the structure is approximately equal to the best one found, emphasizing the excellent capacity of both methods.