Comparison of Derivative-Free Optimization: Energy Optimization of Steam Methane Reforming Process

In modern chemical engineering, various derivative-free optimization (DFO) studies have been conducted to identify operating conditions that maximize energy efficiency for efficient operation of processes. Although DFO algorithm selection is an essential task that leads to successful designs, it is a nonintuitive task because of the uncertain performance of the algorithms. In particular, when the system evaluation cost or computational load is high (e.g., density functional theory and computational fluid dynamics), selecting an algorithm that quickly converges to the near-global optimum at the early stage of optimization is more important. In this study, we compare the optimization performance in the early stage of 12 algorithms. The performance of deterministic global search algorithms, global model-based search algorithms, metaheuristic algorithms, and Bayesian optimization is compared by applying benchmark problems and analyzed based on the problem types and number of variables. Furthermore, we apply all algorithms to the energy process optimization that maximizes the thermal efficiency of the steam methane reforming (SMR) process for hydrogen production. In this application, we have identified a hidden constraint based on real-world operations, and we are addressing it by using a penalty function. Bayesian optimizations explore the design space most efficiently by training infeasible regions. As a result, we have observed a substantial improvement in thermal efficiency of 12.9% compared to the base case and 7% improvement when compared to the lowest performing algorithm.