Optimization-driven data-based constraints identification via explicit mathematical and implicit machine-learning-based constitutives

The major aim of "data-based constraint identification" is to identify feasible regions within which a process can be operated. Our approach is based on the quantitative-feasibility information of sample points metamorphosed into single- and multiple- mathematical equations constituting the data-based constraints. We firstly devise an "overall objective function" which is capable of identifying feasible regions with multiple-constitutive inequality constraints by resorting to the technique of "constraint aggregation". We then equip our algorithm with the "form-specific constitutives" build via the generic mathematical description of some plausible inequality constraints such as the bound, linear, circular, and ellipsoidal, as single or aggregated multiple constitutives. We then build the "form-specific" and "form-free" constitutives via the "design matrix" approach, also as single or aggregated multiple constitutives. We devise the "implicit neural constitutives" as well via some Machine Learning algorithms such as Neural Networks and Extreme Learning Machines, as single implicit or aggregated multiple implicit constitutives. All of these data-based constitutive constraints are generic such that they can identify N-dimensional feasible regions. We solve the demonstrative examples with the Differential Evolution or Covariance Matrix Adaptation Evolution Strategy global optimizers. Via many diversified examples, including several chemical-engineering related ones, we show that our algorithm can identify joint, disjoint, convex, or nonconvex regions or their combinations. We also apply classification techniques, such as Probabilistic Neural Network, k-Nearest Neighbour, Support Vector Machine, Gaussian Process Regression, and Regression Trees to constraint identification. Our algorithm is also successful in identifying constraints from image boundaries, i.e., in "image-to-constraints" conversion tasks.