In chemical engineering, Finding the optimal operating conditions to maximize the profit or efficiency of a process is an essential task. In conventional chemical engineering, where the mathematical relationship of the target process can be known relatively accurately, the optimal solution can be effectively identified through optimization using gradient information (Nag et al., 2020). However, in modern chemical engineering with high process complexity or high dimensionality, mathematical information about the underlying function is often not known accurately. Also, even if mathematical information is known, gradient based optimization has limitations in practical application due to low reliability (Rios and Sahinidis, 2013; Sun et al., 2020). Therefore, various research on derivative-free optimization (DFO) that perform optimization by function evaluation without using mathematical information have been performed (Na et al., 2017). We divided the derivative-free algorithm into three types: deterministic global search algorithm, metaheuristic algorithm and Bayesian optimization. The deterministic global search algorithm performs optimization using a predefined search pattern, and there is a representative Divide a hyper-RECTangle (DIRECT) (Jones et al., 1993). Metaheuristic algorithms such as the Genetic algorithm use a search method inspired by nature to evaluate the search space based on probability. Bayesian optimization(BO) simultaneously performs training of a stochastic surrogate model that approximates the underlying function and optimization of an acquisition function to find the optimal location of next experiments (D. Lizotte, 2008). When applying an optimization algorithm, the selection of an appropriate algorithm directly affects the optimization resultIn (Rios and Sahinidis, 2013), performance comparison of various derivative free algorithms for various problem characteristics was performed. However, the performance of Bayesian optimization, which is known to outperforming performance in the early stage of optimization, was not compared. A total of 11 optimization algorithms were applied to maximize the thermal efficiency of the steam methane reforming process. In particular, hidden constraints that can be satisfied through the operation result of the process were treated as a penalty function. The performance of 11 algorithms (3 deterministic global search algorithm, 3 metaheuristic algorithm, 4 Bayesian optimization) was evaluated for constrained optimization. Among several algorithms, Bayesian optimization (i.e., Gaussian process (GP)-one shot knowledge gradient (OKG)), which trains past function evaluation as prior knowledge, had the best performance. The deterministic global search algorithm (i.e., DIRECT algorithm) that searches the design space based on the predefined search pattern showed poor performance. As a result, GP-OKG showed about 7.0% improved thermal efficiency compared to DIRECT.
- Lizotte, 2008. Practical Bayesian Optimization. University of Alberta.
Jones, D.R., Perttunen, C.D., Stuckman, B.E., 1993. Lipschitzian optimization without the Lipschitz constant. J. Optim. Theory Appl. 79, 157â181. https://doi.org/10.1007/BF00941892
Na, J., Lim, Y., Han, C., 2017. A modified DIRECT algorithm for hidden constraints in an LNG process optimization. Energy 126, 488â500. https://doi.org/10.1016/j.energy.2017.03.047
Nag, A., Yadav, A., Pazoki, M., 2020. Optimization Technique 77, 261â266.
Rios, L.M., Sahinidis, N. V., 2013. Derivative-free optimization: A review of algorithms and comparison of software implementations. J. Glob. Optim. 56, 1247â1293. https://doi.org/10.1007/s10898-012-9951-y
Sun, Y., Sahinidis, N. V., Sundaram, A., Cheon, M.S., 2020. Derivative-free optimization for chemical product design. Curr. Opin. Chem. Eng. 27, 98â106. https://doi.org/10.1016/j.coche.2019.11.006