Physical systems can be modelled at many levels of approximation. The right model depends on the problem to be solved. In many cases, a combination of models will be more effective than a single model. Our research investigates this idea in the context of engineering design optimization. We present a family of strategies that use multiple models for unconstrained optimization of engineering designs. The strategies are useful when multiple approximations of an objective function can be implemented by compositional modelling techniques. We show how a compositional modelling library can be used to construct a variety of locally calibratable approximation schemes that can be incorporated into the optimization strategies. We analyze the optimization strategies and approximation schemes to formulate and prove sufficient conditions for correctness and convergence. We also report experimental tests of our methods in the domain of sailing yacht design. Our results demonstrate dramatic reductions in the CPU time required for optimization, on the problems we tested, with no significant loss in design quality.

Shape annealing, a computational design method applied to structural design, has been extended to the design of traditional and innovative three-dimensional domes that incorporate the design goals of efficiency, economy, utility, and elegance. In contrast to deterministic structural optimization methods, shape annealing, a stochastic method, uses lateral exploration to generate multiple designs of similar quality that form a structural language of solutions. Structural languages can serve to enhance designer creativity by presenting multiple, spatially innovative, yet functional design solutions while also providing insight into the interaction between structural form and the trade-offs involved in multi-objective design. The style of the structures within a language is a product of the shape grammar that defines the allowable structural forms and the optimization model that provides a functional measure of the generated forms to determine the desirable designs. This paper presents an application of geodesic dome patterns that have been embodied in a shape grammar to define a structural language of domes. Within this language of domes, different dome styles are generated by changing the optimization model for dome design to include the design goals of maximum enclosure space, minimum surface area, minimum number of distinct cross-sectional areas, and visual uniformity. The strengths of the method that will be shown are 1) the generation of both conventional domes similar to shape optimization results and spatially innovative domes, 2) the generation of design alternatives within a defined design style, and 3) the generation of different design styles by modifying the language semantics provided by the optimization model.

This paper is concerned with presenting guidelines to aide in the selection of the appropriate network architecture for back-propagation neural networks used as approximators. In particular, its goal is to indicate under what circumstances neural networks should have two hidden layers and under what circumstances they should have one hidden layer. Networks with one and with two hidden layers were used to approximate numerous test functions. Guidelines were developed from the results of these investigations.

This paper defines a number of general operations that accept arbitrary sets of values for two variables and general relations among three variables and generate a variety of third sets that are useful in design. Although the operations are defined without respect to mathematical or engineering domain, computing these operations depends on the specific mathematical domain, and algorithms are available for only a few domains. Appropriate software could make this complexity transparent to the designer, allowing the same conceptual operations to be used in many contexts. The paper proves a number of useful characteristics of the operations and offers examples of their potential use in design.

This paper defines, for use in design, rules for propagating “distribution constraints” through relationships such as algebraic or vector equations. Distribution constraints are predicate logic statements about the values that physical system parameters may assume. The propagation rules take into account “variation source causality”: information about when and how the values are assigned during the design, manufacturing, and operation of the system.