A Kriging-Based Approach to MINLP Containing Black-Box Models and Noise

Abstract

A new MINLP algorithm is presented for a class of problems whose formulation contains black-box models. Black-box models describe process behavior when closed-form equations are absent and can be functions of continuous and/or integer variables. To address the lack of explicit equations, kriging is used to build surrogate data-driven global models because a robust process description can be obtained even when noise is present. The global models are used to identify promising solutions for local refinement, and the continuous variables are then optimized using a response surface method. The integer variables are optimized using Branch-and-Bound if a continuous relaxation exists and direct search otherwise. The four algorithms are unified into a comprehensive approach that can be used to obtain optimal process synthesis and design solutions when noise and black-box models are present. The performance of the proposed algorithm is evaluated based on its application to two industrial case studies.