An algorithm for the use of surrogate models in modular flowsheet optimization

Abstract

in Wiley InterScience (www.interscience.wiley.com).In this work a methodology is presented for the rigorous optimization of nonlinear programming problems in which the objective function and (or) some constraints are represented by noisy implicit black box functions. The special application considered is the optimization of modular process simulators in which the derivatives are not available and some unit operations introduce noise preventing the calculation of accurate derivatives. The black box modules are substituted by metamodels based on a kriging interpolation that assumes that the errors are not independent but a function of the independent variables. A Kriging metamodel uses non-Euclidean measure of distance to avoid sensitivity to the units of measure. It includes adjustable parameters that weigh the importance of each variable for obtaining a good model representation, and it allows calculating errors that can be used to establish stopping criteria and provide a solid base to deal with ''possible infeasibility'' due to inaccuracies in the metamodel representation of objective function and constraints. The algorithm continues with a refining stage and successive bound contraction in the domain of independent variables with or without kriging recalibration until an acceptable accuracy in the metamodel is obtained. The procedure is illustrated with several examples.

Global optimization advances in Mixed-Integer Nonlinear Programming, MINLP, and Constrained Derivative-Free Optimization, CDFO

“…Conejo et al (2013) develop a method which uses local quadratic models of the objective function for problems with a known convex feasible region. General constrained CDFO problems have been studied by Caballero and Grossmann (2008) and Sankaran et al (2010) using local kriging models for the objective and constraints; Powell (1994Powell ( , 2013a developed the COBYLA algorithm which uses local linear approximations for the unknown objective and the unknown constraints which is an approach revisited recently by March and Willcox (2012); Conn and Le Digabel (2013) employ quadratic models for the objective and constraints; Müller et al (2013) use radial-basis function models; and finally Müller and Shoemaker (2014) use an ensemble of various surrogate-models to best fit the objective and constraints of the problem. A recent extension of the BOBYQA algorithm for mixed variable programming has been published which uses quadratic approximations and local integer search, with guaranteed identification of locally optimal points (Newby and Ali, 2014).…”

Large scale optimization of a sour water stripping plant using surrogate models

“…Important studies have been performed with Kriging models by disaggregating parts of the model (Caballero & Grossmann, 2008) or using the full system approach (Davis & Ierapetritou, 2007;D. Huang et al, 2006;Palmer & Realff, 2002).…”

“…An interesting summary of Kriging simulation applications can be found in the review by Kleijnen (2009). Caballero and Grossmann (2008) studied modular flowsheet (disaggregated) optimization using Kriging models to represent process units with low-level noise. Complete process Kriging models were used by Davis and Ierapetritou (2007) to find global model solutions and later refine them using local response surface around the optima.…”

“…In the optimization field, surrogate models have become popular due to their applicability (Caballero & Grossmann, 2008;Queipo et al, 2005;Wang & Shan, 2006) and we can differentiate two approaches. The first locates the most relevant variables of the entire flowsheet through a sensitivity analysis and then generates a surrogate model based on these variables.…”

Integration of different models in the design of chemical processes: Application to the design of a power plant

“…To generate data that sets up the kriging model [54][55][56]60] a gas turbine model was created in Aspen Hysys TM . See Figure 3.The model consists of a compressor that receives air at ambient conditions.…”