TY - JOUR

T1 - Data-driven construction of Convex Region Surrogate models

AU - Zhang, Qi

AU - Grossmann, Ignacio E.

AU - Sundaramoorthy, Arul

AU - Pinto, Jose M.

PY - 2016/6/1

Y1 - 2016/6/1

N2 - With the increasing trend of solving more complex and integrated optimization problems, there is a need for developing process models that are sufficiently accurate as well as computationally efficient. In this work, we develop an algorithm for the data-driven construction of a type of surrogate model that can be formulated as a set of mixed-integer linear constraints, yet still provide good approximations of nonlinearities and nonconvexities. In such a surrogate model, which we refer to as Convex Region Surrogate (CRS), the feasible region is given by the union of convex regions in the form of polytopes, and for each region, the corresponding cost function can be approximated by a linear function. The general problem is as follows: given a set of data points in the parameter space and a scalar cost value associated with each data point, find a CRS model that approximates the feasible region and cost function indicated by the given data points. We present a two-phase algorithm to solve this problem and demonstrate its effectiveness with an extensive computational study as well as a real-world case study.

AB - With the increasing trend of solving more complex and integrated optimization problems, there is a need for developing process models that are sufficiently accurate as well as computationally efficient. In this work, we develop an algorithm for the data-driven construction of a type of surrogate model that can be formulated as a set of mixed-integer linear constraints, yet still provide good approximations of nonlinearities and nonconvexities. In such a surrogate model, which we refer to as Convex Region Surrogate (CRS), the feasible region is given by the union of convex regions in the form of polytopes, and for each region, the corresponding cost function can be approximated by a linear function. The general problem is as follows: given a set of data points in the parameter space and a scalar cost value associated with each data point, find a CRS model that approximates the feasible region and cost function indicated by the given data points. We present a two-phase algorithm to solve this problem and demonstrate its effectiveness with an extensive computational study as well as a real-world case study.

KW - Data-driven modeling

KW - Mixed-integer programming

KW - Multiscale optimization

KW - Polyhedral theory

KW - Surrogate modeling

UR - http://www.scopus.com/inward/record.url?scp=84946144571&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84946144571&partnerID=8YFLogxK

U2 - 10.1007/s11081-015-9288-8

DO - 10.1007/s11081-015-9288-8

M3 - Article

AN - SCOPUS:84946144571

VL - 17

SP - 289

EP - 332

JO - Optimization and Engineering

JF - Optimization and Engineering

SN - 1389-4420

IS - 2

ER -