Multi-scale optimization for process systems engineering

• Three trust region-based algorithms are developed for RM-based optimization.
• The first algorithm is a gradient-based algorithm that builds on established trust region theory.
• The second algorithm avoids gradient calculations from the ODM.
• The third algorithm avoids frequent recourse to ODMs, using ϵ-exact RMs.
• Small examples and two large scale RM-based optimization case studies illustrate the algorithms.

Efficient nonlinear programming (NLP) algorithms and modeling platforms have led to powerful process optimization strategies. Nevertheless, these algorithms are challenged by recent evolution and deployment of multi-scale models (such as molecular dynamics and complex fluid flow) that apply over broad time and length scales. Integrated optimization of these models requires accurate and efficient reduced models (RMs). This study develops a rigorous multi-scale optimization framework that substitutes RMs for complex original detailed models (ODMs) and guarantees convergence to the original optimization problem. Based on trust region concepts this framework leads to three related NLP algorithms for RM-based optimization. The first follows the classical gradient-based trust-region method, the second avoids gradient calculations from the ODM, and the third avoids frequent recourse to ODM evaluations, using the concept of ϵ-exact RMs. We illustrate these algorithms with small examples and discuss RM-based optimization case studies that demonstrate their performance and effectiveness.