A framework for design optimization across multiple concepts.

In engineering design, there often exist multiple conceptual solutions to a given problem. Concept design and selection is the first phase of the design process that is estimated to affect up to 70% of the life cycle cost of a product. Currently, optimization methods are rarely used in this phase, since standard optimization methods inherently assume a fixed (given) concept; and undertaking a full-fledged optimization for each possible concept is untenable. In this paper, we aim to address this gap by developing a framework that searches for optimum solutions efficiently across multiple concepts, where each concept may be defined using a different number, or type, of variables (continuous, binary, discrete, categorical etc.). The proposed approach makes progressive data-driven decisions regarding which concept(s) and corresponding solution(s) should be evaluated over the course of search, so as to minimize the computational budget spent on less promising concepts, as well as ensuring that the search does not prematurely converge to a non-optimal concept. This is achieved through the use of a tree-structured Parzen estimator (TPE) based sampler in addition to Gaussian process (GP), and random forest (RF) regressors. Aside from extending the use of GP and RF to search across multiple concepts, this study highlights the previously unexplored benefits of TPE for design optimization. The performance of the approach is demonstrated using diverse case studies, including design of a cantilever beam, coronary stents, and lattice structures using a limited computational budget. We believe this contribution fills an important gap and capitalizes on the developments in the machine learning domain to support designers involved in concept-based design.