(578e) Simulation-Based Optimization with Embedded Dynamic Models Using a Data-Driven Spatial Branch-and-Bound Algorithm

Rigorous dynamic computer simulations are used routinely for decision-making in chemical and biological process systems engineering to explain complex underlying phenomena accurately^1,2. These dynamic models are often nonlinear and constrained, and this results in many challenges when trying to directly embed them within related inverse optimization problems ³. Typical dynamic optimization problems come in two forms: (a) estimation of parameters of the dynamic simulation, and (b) optimization of simulation outputs by manipulating simulation inputs (i.e., optimal process operation and/or design). In all cases, globally optimal solutions are strongly desired since local solutions may lead to inaccurate conclusions, especially in the case of parameter estimation ⁴. There are currently two main ways to solve such problems, by either using rigorous dynamic optimization methods ⁵, or by treating the dynamic model as a “black-box” and optimization relies on the input-output data⁴. Some of the main advantages of the former are the direct use of physics-based equations, the ability to use equation-based local and global optimization solvers, and the consistency in identifying optimal solutions that satisfy derivative-based criteria. However, often this approach suffers from tractability issues and challenges in finding feasible solutions. The data-driven approach typically leads to reduced formulations but is often criticized due to the uncertainty introduced by sampling, fitting surrogate models, and lack of convergence guarantees.

In this work, we showcase the capabilities and performance of a novel data-driven spatial branch-and-bound algorithm for several types of dynamic simulation-based optimization case studies with continuous variables, known and unknown constraints. Although this algorithm employs data-driven techniques, we have previously shown that through the use of branch-and-bound procedures and data-driven underestimators, it has a globally convergent behavior and provides an estimation of lower bounds given a limited amount of samples. The case studies are selected from various chemical and biological applications such as the parameter estimation and design of a batch fermentation process, design of a steam reforming process, and design of a carbon-capture process. The performance of the data-driven spatial branch-and-bound algorithm is compared with state-of-art data-driven solvers as well as rigorous dynamic optimization solutions in terms of solution accuracy, consistency, and computational cost.

References:

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5. Esposito WR, Floudas CA. Global Optimization for the Parameter Estimation of Differential-Algebraic Systems. Industrial & Engineering Chemistry Research. 2000;39(5):1291-1310.