Bayesian Network Structure Optimization for Improved Design Space Mapping for Design Exploration With Materials Design Applications

Modern design problems present both opportunities and challenges, including multifunctionality, high dimensionality, highly nonlinear multimodal responses, and multiple levels or scales. These factors are particularly important in materials design problems and make it difficult for traditional optimization algorithms to search the space effectively, and designer intuition is often insufficient in problems of this complexity. Efficient machine learning algorithms can map complex design spaces to help designers quickly identify promising regions of the design space. In particular, Bayesian network classifiers (BNCs) have been demonstrated as effective tools for top-down design of complex multilevel problems. The most common instantiations of BNCs assume that all design variables are independent. This assumption reduces computational cost, but can limit accuracy especially in engineering problems with interacting factors. The ability to learn representative network structures from data could provide accurate maps of the design space with limited computational expense. Population-based stochastic optimization techniques such as genetic algorithms (GAs) are ideal for optimizing networks because they accommodate discrete, combinatorial, and multimodal problems. Our approach utilizes GAs to identify optimal networks based on limited training sets so that future test points can be classified as accurately and efficiently as possible. This method is first tested on a common machine learning data set, and then demonstrated on a sample design problem of a composite material subjected to a planar sound wave. INTRODUCTION Advances in manufacturing processes and simulation capabilities have made it possible to design more complex materials and structures. These complex engineering system design problems are commonly broken down into subproblems, at which point the high-level challenge becomes managing the dependencies between the subproblems and identifying highperformance system-wide solutions. This is often a cumbersome process of iteratively adjusting candidate designs in pursuit of optimal performance. The expense of this optimization process grows with the problem’s dimensionality, the degree of coupling between variables and subsystems, the nonlinearity of the underlying relationships, and the computational expense of the underlying simulation models. As a means of addressing these complex systems design problems, design exploration techniques aim to explore the design space to identify sets of promising designs. Set-based design exploration methods, in particular, focus on identifying sets of satisfactory performance for each subproblem in a complex systems design problem instead of identifying unique optimal point-wise solutions. These sets of solutions can be intersected across subproblems to identify system-wide solutions with fewer total iterations compared to traditional point-wise optimization [1]. Figure 1 presents a simplified illustration of the set-based design paradigm. A key challenge in the set-based approach is mapping the sets of promising solutions, especially for problems with complex, highly nonlinear design spaces. Interval-based Proceedings of the ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference