Abordagem metaheurística para otimização estrutural

Abstract

Structural optimization aims to design structures under certain constraints to achieve better behavior. However, minimize the weight of structures can be considered as a difficult problem to solve because it makes design constraints difficult to satisfy. These constraints are non-linear, non-convex and implied with respect to the variables of design. Therefore, this has led to difficulty in the use of gradient-based optimizers. Under such circumstances, the metaheuristic algorithms can serve as appropriate alternatives due to the ability to search global minima in modal and multidimensional spaces. Although several metaheuristics have been developed in the last decades, most of them are population-based, undergo many steps along with several parameters that make them hard to code. In addition, there are same procedures in recent metaheuristics which make them similar. On the other hand, according to the No Free Lunch Theorem in the field of optimization, there is no algorithm to solve all optimization problems. This indicates that a new adapted algorithm has potential to solve a group of problems (e.g. structures design) better than the current algorithms. Contrary to previous studies, this work aims to implement and adapt a single-solution algorithm called Modified Simulated Annealing Algorithm (MSAA) to solve problem of structural optimization. To validate the algorithm, benchmark problems found in the literature are analyzed and the results are compared with previous results obtained through various existing metaheuristics. These problems are: (i) size optimization of truss structures with stresses and displacements constraints; (ii) size and shape optimization of truss structures with natural frequency constraints; and (iii) topological optimization of plane stress state models representing beam problems using finite elements developed in Strain Gradient Notation. Additionally, an improved version of MSAA is proposed to solve structural optimization problems. In the first two sets of problems, numerical results indicated that MSAA produces competitive results, compared to the other optimization metaheuristics, in terms of optimal design, number of iterations, and standard deviation of the data. In topological optimization problems, the results showed that optimized problems with corrected elements and MSAA converged to the optimal value in less time.