REPAIRS: Gaussian Mixture Model-based Completion and Optimization of Partially Specified Systems

Most system optimization techniques focus on finding the values of the system components to achieve the best performance. Searching over all component values gives the search methodology the freedom to explore the entire design space to determine the best system configuration. However, real-world systems often require searching in a restricted space over only a subset of component values while freezing some of the components to fixed values. Rather than optimizing from scratch to search over the subset of components, incorporating the past simulation logs (search performed when all components were allowed to vary) enables the optimization mechanism to utilize knowledge from past system behavior. In addition, when the system gives the same response over different combinations of input values, the designer may prefer one combination over another. Furthermore, real-world data often contain errors. To avoid catastrophic consequences of making decisions based on incorrect data points, we need a mechanism to identify and correct the resulting error. We propose REPAIRS, a methodology to complete/optimize partially specified systems. It also performs data integrity checks and identifies/corrects errors after detecting an anomaly in the data. We use a Gaussian mixture model to learn the joint distribution of the system inputs and the corresponding output response (objectives/constraints). We use the learned model to complete a partially specified system where only a subset of the component values and/or the system response is specified. When the system response exhibits multiple modes (e.g., same response for different combinations of input values), REPAIRS determines the combinations of input values that correspond to the several modes. Using past simulation logs, it searches over various subsets of system inputs to improve the performance of the reference solution. We also present a framework for verifying the integrity of a given data instance. When the integrity check fails, we provide a mechanism to identify the error location and correct the error. REPAIRS provides an explanation for the decision it makes for the different use cases described in this article. We provide results of REPAIRS in the context of completion, partial optimization, and data integrity check of real-world systems. REPAIRS achieves a hypervolume that is better than that obtained using a baseline method by up to 50%. It successfully identifies the error location and predicts the correct value of the erroneous feature with an error less than 0.2%. It detects error locations with a mean accuracy of up to 95% even when three feature values have an error.