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Abstract Supervised machine learning techniques have proven to be effective tools for engineering design exploration and optimization applications, in which they are especially useful for mapping promising or feasible regions of the design space. The design space mappings can be used to inform early-stage design exploration, provide reliability assessments, and aid convergence in multiobjective or multilevel problems that require collaborative design teams. However, the accuracy of the mappings can vary based on problem factors such as the number of design variables, presence of discrete variables, multimodality of the underlying response function, and amount of training data available. Additionally, there are several useful machine learning algorithms available, and each has its own set of algorithmic hyperparameters that significantly affect accuracy and computational expense. This work elucidates the use of machine learning for engineering design exploration and optimization problems by investigating the performance of popular classification algorithms on a variety of example engineering optimization problems. The results are synthesized into a set of observations to provide engineers with intuition for applying these techniques to their own problems in the future, as well as recommendations based on problem type to aid engineers in algorithm selection and utilization. 

Exploration of a design space is the first step in identifying sets of high-performing solutions to complex engineering problems. For this purpose, Bayesian network classifiers (BNCs) have been shown to be effective for mapping regions of interest in the design space, even when those regions of interest exhibit complex topologies. However, identifying sets of desirable solutions can be difficult with a BNC when attempting to map a space where high-performance designs are spread sparsely among a disproportionately large number of low-performance designs, resulting in an imbalanced classifier. In this paper, a method is presented that utilizes probabilities of class membership for known training points, combined with interpolation between those points, to generate synthetic high-performance points in a design space. By adding synthetic design points into the BNC training set, a designer can rebalance an imbalanced classifier and improve classification accuracy throughout the space. For demonstration, this approach is applied to an acoustics metamaterial design problem with a sparse design space characterized by a combination of discrete and continuous design variables. Paper No: DETC2018-85274 

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.