(233b) Combined Task Bayesian Optimization for Efficient Scale-up and Technology Transfer

Operating condition optimization is crucial to assure product quality and reduce operation cost in any industry. In particular, one of the most challenging problems is to optimize operating conditions of commercial-scale equipment when only a small number of data are available just after scale-up from pilot-scale equipment. Such a situation is quite common because the experimental cost is significantly higher with commercial-scale equipment than pilot-scale equipment. In the present work, we aim to solve this problem and propose a new operating condition optimization method, which is referred to as combined task Bayesian optimization (CTBO). The proposed method is applicable not only to the scale-up problem but also to the problem of technology transfer from a mother plant to a copy plant; that is, when two plants are the same but operating conditions need to be optimized at the copy plant due to various uncertainties.

A conventional method builds a model that relates product qualities with operating conditions, and then optimizes the operating conditions by using the model so that the target product qualities are realized and operation cost is minimized under various constraints. Unfortunately, this method does not work well when only little data is available at a commercial-scale plant, because it is difficult to build an accurate model. Such a situation always occurs just after scale-up from a pilot-scale plant. The optimization performance would be improved if data of the pilot-scale plant could be used jointly with data of the commercial-scale plant. However, combining data of different scales is not straightforward because pilot-scale and commercial-scale plants have different numbers and types of sensors, which are operated under different conditions.

The goal of this research is to develop a new method that can efficiently and accurately derive optimal operating conditions by using data obtained from a commercial-scale plant and a pilot-scale plant even when only little data is available at the commercial-scale plant. The proposed method uses Bayesian optimization (BO).

BO can systematically determine a plan for new operating conditions to be evaluated for further optimization. Thus, without experimental design, BO can find a better solution through fewer experiments than conventional methods. BO uses two important tools: Gaussian process regression (GPR) and an acquisition function. GPR is used as a nonlinear regression method, and the acquisition function is used to determine new operating conditions to be evaluated by taking account of the trade-off between exploration and exploitation. By combining them, BO can efficiently optimize operating conditions.

Transfer learning aims to exploit knowledge from one or more source tasks and to apply the knowledge to the target task. A key idea of the present work is that transfer learning is useful for solving the scale-up problem by regarding the source task and the target task as the pilot-scale plant and the commercial-scale plant, respectively. Among transfer learning algorithms, adaptive transfer learning and frustratingly easy domain adaptation are used in this work. The former is an algorithm established for GPR, and the latter is a famous, simple algorithm.

Conventional transfer learning algorithms assume that the number of input variables in the source task is the same as that in the target task. In practice, however, the number and types of sensors of a pilot-scale plant are different from those of a commercial-scale plant. Thus, to apply transfer learning to the scale-up problem, we introduce a transformation matrix, which transforms data of the pilot-scale plant into data of the commercial-scale plant so that data from both can be used for modeling the commercial-scale plant. To derive the transformation matrix automatically, we propose to use Markov Chain Monte Carlo (MCMC), which is also used to determine GPR hyperparameters.

In the present work, combined task Bayesian optimization (CTBO) is proposed by integrating BO, transfer learning, and the transformation matrix. To validate the effectiveness of the proposed method, CTBO was compared with BO and LW-PLS + jDE (locally weighted partial least squares + self-adaptive differential evolution) through their applications to numerical examples and a pharmaceutical granulation process. Two types of CTBO were tested: CTBO(ATGP), i.e., CTBO with adaptive transfer learning, and CTBO(DAGP), i.e., CTBO with frustratingly easy domain adaptation.

The results of the numerical examples showed that the optimization performance of BO was superior to that of LW-PLS + jDE since BO appropriately determined operating conditions one by one. CTBO further improved the optimization performance by combining data of both the source task and the target task. Similarly, in the pharmaceutical granulation process, CTBO outperformed LW-PLS + jDE and BO. The improvement rate of CTBO(DAGP) compared with LW-PLS + jDE and BO were 48.6% and 15.2%, respectively, when the number of samples on the commercial-scale plant was 10. The results demonstrated that CTBO used data of the pilot-scale plant effectively to optimize the operating conditions of the commercial-scale plant.