ABSTRACT In systems engineering, solution spaces provide a practical way to reconcile competing goals by working with sets of good designs instead of point‐based solutions. Earlier contributions, however, were restricted either by limiting the dimensionality per component or, more recently, by constraining these spaces to be convex, which can, in some cases, significantly restrict the available design freedom–usually, box‐shaped solution spaces include only a fraction of the complete solution space even in simple cases, and convex component solution spaces can still present considerable losses for problems with non‐convex complete solution spaces. In this paper, we introduce a new method to, for the first time, compute non‐convex component solution spaces for arbitrary performance functions and any number of design variables per component. By iteratively removing bad space only as so‐called corner boxes, loss of solution space is significantly reduced while maintaining crucial independence between components. Demonstrations with diverse truss structures with varying geometries and material properties, with constraints on tip deflection, show admissible regions up to eleven orders of magnitude larger than box‐shaped solutions and three orders of magnitude larger than convex component solution spaces, thus unlocking substantially more design freedom without sacrificing robustness. This can be useful in structural design for material selection before specifying geometric component details. The numerical characteristics and trade‐offs of using this new method are studied with up to 21 components and up to seven design variables per component.
Noce et al. (Mon,) studied this question.