On the improvement of design space subsets formulation for iteratively optimizing structural systems

Abstract Structural optimization is the process of identifying the optimal set of design parameters for a structural system. Optimization techniques provide an effective approach for rationally improving structural engineering design, both for the structural system with deterministic and uncertain parameters. It is unanimously agreed that in engineering design applications, knowledge about a planned system is never comprehensive. These uncertainties resulting from incomplete information are often assessed probabilistically. In this probabilistic framework, the system design process is referred to as stochastic system design, and the concomitant design optimization problem is alluded to as stochastic optimization. The stochastic optimization process has been widely used in civil, mechanical, and aeronautical engineering designs. Stochastic system optimization includes two stages where initially the performance measure is approximated either by Taylor series approximation or the metamodels, and in the second stage, the approximated performance function is optimized by implementing the available optimization techniques such as nonlinear programming methods, gradient-based methods, metaheuristic methods, etc. Approaches available in literature can effectively take into account the uncertainties, but still, achieving higher accuracy and lower computational cost remains a challenging task for designing complex and realistic structural systems. To obliviate these aforementioned limitations, a simulation-based approach known as Stochastic Subset Optimization (SSO) is found to be very effective. The basic principle in the original SSO is to reduce the design space size iteratively, which has high plausibility of containing the optimal design solution. However, the success of the approach depends on the shape selection of the design space while implementing the SSO. Therefore, in the present study, the dependency of the original SSO over the selection of the shape of the design subset is overcome by exploring the design space based on the density of simulated design samples with the design space. This improves the applicability of the SSO to the complex, realistic problem. Two benchmark optimization problems: a 2-dimensional bowl-shaped sphere function and a helical compression spring design, are solved with the proposed approach to demonstrate the efficiency of the proposed approach.