Modeling and Optimization of Process Engineering Problems Containing Black-box Systems and Noise
Surrogate data-driven models can be alternatively generated, but many substitute models may need to be built, especially in the case of process synthesis problems. Although model reliability can be improved using additional information, resource constraints can limit the number of additional experiments allowed. Since it may not be possible to a priori estimate the problem cost in terms of the number of experiments required, there is a need for strategies targeted at the generation of sufficiently accurate surrogate models at low resource cost. The problem addressed in this work focuses on the development of model-based optimization algorithms targeted at obtaining the best solutions based on limited sampling. A centroid-based sampling algorithm for global modeling has also been developed to accelerate accurate global model generation and improve subsequent local optimization. The developed algorithms enable the superior local solutions of problems containing black-box models and noisy input-output data to be obtained when the problem contains both continuous and integer variables and is defined by an arbitrary convex feasible region. The proposed algorithms are applied to many numerical examples and industrial case studies to demonstrate the improved optima attained when surrogate models are built prior to optimization.
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Local Optimization Employing Response Surface Models
Global Optimization Employing Kriging and Response Surface Models
MixedInteger Optimization Considering
Optimization Considering MixedInteger BlackBox Models
CentroidBased Sampling Strategy for KrigingBased Global Modeling 191 6 1 Introduction
additional sampling attained B&B tree based on application black-box models built cells central composite design centrifuge centroid-based sampling centroids constraints continuous variables convergence convex polytope covariance function Delaunay triangulation deterministic DS-RSM employed factorial design feasible region flowchart formulated function calls Gillespie algorithm given by Equation given in Problem global model global optimum identified input variables integer integer variables iteration index KC-R algorithm kg/h KNC-R kriging model kriging predictor kriging solutions kriging-RSM algorithm locations method methodology MINLP mol/L NLP subproblem node nominal sampling set normally distributed number of function number of sampling objective function given objective value obtained for Problem optimal solution Optimization results obtained output variable predictions protein Ptot refined kriging relaxed NLP response surface methodology RSM algorithm RSM-G RSM-S sampling data sampling expense sampling points sampling vector search directions semivariance shown in Figure simulation starting iterates surrogate models t-BMA techniques test point