The authors present a Generative Adversarial Network (GAN) model that learns how to generate 3D models in their native format so that they can either be evaluated using complex simulation environments, or realized using methods such as additive manufacturing. Once initially trained, the GAN can create additional training data itself by generating new designs, evaluating them in a physics-based virtual environment, and adding the high performing ones to the training set. A case study involving a GAN model that is initially trained on 4045 3D aircraft models is used for demonstration, where the training data set updated with GAN-generated and evaluated designs, results in enhanced model generation, both in the geometric feasibility and performance of the designs. Z-tests on the performance scores of the generated aircraft models indicate a statistically significant improvement in the functionality of the generated models after three iterations of the training-evaluation process. In the case study, a number of techniques are explored to structure the generate-evaluate process in order to balance the need to generate feasible designs with the need for innovative designs.

Recent advancements in computing power and speed provide opportunities to revolutionize trade space exploration, particularly for the design of complex systems such as automobiles, aircraft, and spacecraft. In this paper, we introduce three visual steering commands to support trade space exploration and demonstrate their use within a powerful data visualization tool that allows designers to explore multidimensional trade spaces using glyph, 1D and 2D histograms, 2D scatter, scatter matrix, and parallel coordinate plots, linked views, brushing, preference shading, and Pareto frontier display. In particular, we define three user-guided samplers that enable designers to explore (1) the entire design space, (2) near a point of interest, or (3) within a region of high preference. We illustrate these three samplers with a vehicle configuration model that evaluates the technical feasibility of new vehicle concepts. Future research is also discussed.

Abstract4ne of the goals of early stage conceptual design is to execute broad trade studies of possible design concepts, evaluating them for their capability to meet minimum requirements, and choosing the one that best satisfies the goals of the project. To support trade space exploration, we have developed the Advanced Trade Space Visualizer (ATSV) that facilitates a design by shopping paradigm, which allows a decision-maker to form a preference a posteriori and use this preference to select a preferred satellite. Design automation has allowed us to implement this paradigm, since a large number of designs can be synthesized in a short period of time. The ATSV uses multidimensional visualization techniques, preference shading, and Pareto frontier display to visualize satellite trade spaces.

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In this paper we present results from analytical and experimental investigations into the performance of divide & conquer algorithms for determining Pareto points in multidimensional data sets of size n and dimension d. The focus in this work is on the worst-case, where all points are Pareto, but extends to problem sets where only a partial subset of the points is Pareto. Analysis supported by experiment shows that the number of comparisons is bounded by two different curves, one that is O(n (log n)^(d-2)), and the other that is O(n^log 3). Which one is active depends on the relative values of n and d. Also, the number of comparisons is very sensitive to the structure of the data, varying by orders of magnitude for data sets with the same number of Pareto points. Nomenclature n = number of points in a data set d = dimension of the data set , , T Z … = Table of n records, each record having d attributes , , t z … = A record with d attributes , , i i t z … = The ith attribute in a record DC = Divide & Conquer algorithm pbf[n,d] = estimator for number of comparisons in DC algorithm, n points and dimension d mbf[n,d] = estimator for number of comparisons in marriage step of DC algorithm I.