Constrained space-filling and non-collapsing sequential design of experiments and its application for the lightweight design of cylindrical stiffened shells

Constraints widely exist in the structural optimization problems, including not only expensive constraints but also inexpensive constraints with explicit or implicit analytical expressions. Simply omitting the infeasible sampling points generated by conventional design of experiments (DoE) techniques leads to fewer feasible points than desired and to the remaining points distributed sub-optimally. This paper presents a novel constrained space-filling and non-collapsing sequential sampling (CSFSS) method for the arbitrarily constrained design space. To this end, an improved local density is firstly proposed to measure the spatial distribution of the sampling points located in the feasible region. Then, a novel formulation based on the improved local density is proposed for the criterion of sequential sampling strategies, which can guarantee the space-filling and non-collapsing properties both preferably optimal. Afterwards, several methods are proposed to tackle the challenging multimodal optimization problem posed by sequential sampling strategies. Finally, a replacement-based strategy is proposed to further elevate the quality of the design. Extensive numerical results, including an application for the lightweight design of cylindrical stiffened shells in aerospace engineering, highlight the satisfying performance of the proposed method not only in obtaining a high quality of constrained experimental designs but also in competitive contributions to constrained optimization gains.