Análise comparativa no uso de algoritmos genéticos e baseados em gradiente aplicados à otimização estrutural.

Abstract

When designing structures, it is crucial that safety and action conditions are met during their useful life in order to guarantee their stability without causing damage and excessive deformation. Offering a better structural design, considered from a function, respecting the parameters and limitations that each element imposes, optimization has been one of the themes that has been extensively studied in recent decades to remedy the setbacks in structural design. This study aims to compare results of optimization of a dam and a concrete beam from different mathematical methods, namely, DDO (Deterministic Design Optimization) and RBDO (ReliabilityBased Design Optimization), using Matlab software routines. For the formulation of algorithms, routines based on gradients (fmincon) and heuristic algorithms (particle swarm optimization PSO) were implemented. The achieved results demonstrate that the use of fmincon to solve RBDO problems can be ineffective, being able to vary the value of the function according to the initial guess. The PSO, on the other hand, obtained a reliable performance, always converging to the global optimal value in the DDO and RBDO problems. Even so, in the RBDO analyses, there was an expected increase in the value of the objective function in relation to the DDO analyses, in order to guarantee the stability and safety of the building since it will be subject to a probability of failure. Finally, with the results achieved using the PSO/RBDO method, together with Matlab, it proved to be an efficient alternative to find the best optimization solutions, with a simple methodology and low processing cost, contributing to obtaining measurements that guarantee structure stability and cost reduction.