Abstract: In an example, an iterative method for generating designs includes receiving, by a computing system, a plurality of symbolic rules and a plurality of design objectives for a design of a system; generating, by the computing system, a first plurality of designs for the system based on the plurality of the symbolic rules; evaluating performance of the first plurality of designs; training a machine learning model using the first plurality of designs and performance metrics; generating a second plurality of designs; evaluating, by the computing system, using a machine learning model, performance of the second plurality of designs to filter one or more designs that meet one or more of the plurality of the design objectives; evaluating performance of the filtered designs; and updating, by the computing system, the plurality of the design objectives and/or the plurality of the symbolic rules based on the evaluated performance of the filtered designs.

Abstract: In an example, a method of designing a system or architecture includes, receiving a plurality of parameter values and a set of requirements for a plurality of objective functions related to a design problem; compressing the plurality of parameters to generate a latent representation; forward processing, with one or more Invertible Neural Networks (INNs), the latent representation to generate a plurality of objective values corresponding to the plurality of the objective functions; inverse processing the plurality of objective values; and generating, based on the latent representation, a plurality of solutions to the design problem that satisfy the set of requirements for the plurality of objective functions.

Abstract: A device for supporting a plurality of stacked caps has a concave upward element with two end portions defining mounting brackets for attachment to a wall. In one embodiment the brackets have screw holes, and in another embodiment the brackets have elongate tabs which fit into a channel defined in the wall. The device is so mounted to the wall that the concave portion faces upward and supports the front part of the crown of a lowermost one of the caps. The visor of the lowermost one of the caps is positioned in a gap defined between the concave element and the wall and faces downward. A next one of the caps is supported by a rear portion of the crown of the lowermost cap and also has its visor located in the gap. Additional caps are stacked in the same manner. The concave element inclines upwardly away from the wall to help support the stacked caps. In a further embodiment, the device stores in a planar shape, and the end portions are rotatable 90.degree.