A Framework for the Optimization of Complex Cyber-Physical Systems via Directed Acyclic Graph

Mathematical modeling and data-driven methodologies are frequently required to optimize industrial processes in the context of Cyber-Physical Systems (CPS). This paper introduces the PipeGraph software library, an open-source python toolbox for easing the creation of machine learning models by using Directed Acyclic Graph (DAG)-like implementations that can be used for CPS. scikit-learn's Pipeline is a very useful tool to bind a sequence of transformers and a final estimator in a single unit capable of working itself as an estimator. It sequentially assembles several steps that can be cross-validated together while setting different parameters. Steps encapsulation secures the experiment from data leakage during the training phase. The scientific goal of PipeGraph is to extend the concept of Pipeline by using a graph structure that can handle scikit-learn's objects in DAG layouts. It allows performing diverse operations, instead of only transformations, following the topological ordering of the steps in the graph; it provides access to all the data generated along the intermediate steps; and it is compatible with GridSearchCV function to tune the hyperparameters of the steps. It is also not limited to (X,y) entries. Moreover, it has been proposed as part of the scikit-learn-contrib supported project, and is fully compatible with scikit-learn. Documentation and unitary tests are publicly available together with the source code. Two case studies are analyzed in which PipeGraph proves to be essential in improving CPS modeling and optimization: the first is about the optimization of a heat exchange management system, and the second deals with the detection of anomalies in manufacturing processes.