Simulation Based Optimization of Expensive Flowsheet Models for Continuous Pharmaceutical Manufacturing

2011 AIChE Annual Meeting in Minneapolis

October 20, 2011

F. Boukouvala F.J. Muzzio M.G. Ierapetritou

The main purpose of this work is to develop an efficient strategy for simulation-based design and optimization for a pharmaceutical tablet manufacturing process. Simulation-based optimization is a research area that is currently attracting a lot of attention in many industrial applications, where expensive simulators are used to characterize, design and optimize real systems. Common optimization techniques cannot be applied due to the lack of knowledge of analytic derivatives, possible discontinuities caused by if-then operations, high computational cost which prohibits the realization of multiple function evaluations, and finally due to the presence of various types of noise [1]. Synthesis and design of integrated continuous manufacturing of pharmaceutical products is a field that is currently emerging through the development of large-scale flowsheet models [2]. The development of such flowsheet simulations for powder-based products require the integration of various types of models, ranging from inexpensive black-box models to costly first-principle based models, resulting in hybrid simulation models. Moreover, pharmaceutical products are typical examples of high cost products which involve expensive processes and raw materials, while at the same time must satisfy strict quality regulatory specifications, leading to the formulation of challenging and expensive optimization problems.Tablet manufacturing, is a complex process line comprised of several integrated units which aim to efficiently blend different ingredients and compress them into consistent and high-quality tablets with desired dissolution properties. A typical continuous manufacturing line for oral solid dosage products may consist of feeding, mixing, roller compaction, granulation, milling and tablet compaction processes. A common practice in the simulation-based optimization literature is surrogate based optimization [3], in order to overcome problems of computational cost and lack of knowledge of input-output first principles. Using this approach, the expensive simulation is run for a number of sample points based on which a surrogate model is built as a fast approximation of the underlying process. Surrogate-based optimization, on the other hand, has raised another significant research topic- design and analysis of computer experiments- which aims not only to efficiently plan computer experiments for global optimization of surrogate model approximations, but also to minimize sampling cost [4]. An integrated system of the aforementioned candidate processes has a large number of variables which consist of design parameters, integer decision variables, and operating conditions. The first required step for optimization of an expensive simulation using metamodeling approximations, involves the selection of the important variables and parameters which will form the design space of the underlying system and should be included as inputs to the surrogate model used for optimization. Screening techniques [5] or sensitivity analysis methods [6] are suitable for the identification of the critical inputs and can reduce the dimensionality of the problem by elimination of insignificant variables that do not contribute considerably to the overall variance of the outputs or the objective function. Once the dimensionality of the problem is identified, the feasible region of the system should also be explored in order to limit, when possible, the optimization problem inside the feasible region. Techniques in forms of penalty terms, or objective function deformation methods [7] are explored in order to drive the optimization procedure around the feasible space. In cases where the process constraints are not known in closed-form, black-box optimization techniques can be used [8]. Next, the initial experimental design and the surrogate technique used to approximate the expensive simulation must be chosen. Sampling the flowsheet model at a small number of design points based on a space-filling design (Latin Hypercube sampling), combined with a Kriging-based metamodel generation is a well established combination, proven to have high-quality results in surrogate-based optimization [9]. Kriging is a data-driven interpolating method which has the ability to provide an average error associated with each prediction [10].  Subsequently a metric must be chosen based on which new promising sampling locations are identified. Due to the inherently noisy nature of powder handling processes, the Kriging model as well as the figure of merit used should be stochastic, thus the Sequential Kriging Optimization (SKO) approach [11] which uses the stochastic Expected Improvement function (EI) as the figure of merit, is found to be most suitable for this process. The EI must concurrently favor regions where the kriging approximated objective function value is optimal (local search) but also regions where the kriging uncertainty and/or the noise is high (global search). Through an iterative procedure, the sampling set is enhanced and the optimum is updated, by locating promising new points which have a maximum EI function value. Finally, one of the critical aspects of the proposed methodology is the use of a robust optimization technique for reliable global optimization. A commonly used method for expensive optimization is the Nedler-Mead algorithm, however, its performance in the current problem which is noisy and highly non-linear is not found to be very reliable. The performance of Sequential Quadratic Programming (SQP) method is found to be more efficient for this case study. Clearly, many opportunities lie in the research for simulation-based optimization techniques in (a) designing an appropriate computer experiment, (b) identifying an efficient surrogate  approximation method which requires the minimum number of function evaluations and can also handle uncertainty caused by various sources of noise, and (c) distinguishing the suitable gradient-free optimization technique which can successfully identify the global optimum with a limited number of function evaluations in the presence of noise and possible feasibility constraints. All of the above aspects must be linked to the nature of the actual underlying process which, in this work, refers to continuous tablet manufacturing. The application of the proposed steps is shown through the optimization of a direct compression tablet manufacturing process, where the objective function is formed such that the variability of the final product properties is minimized while the constraints assure that their values are always within predefined ranges set by the Food and Drug Administration (FDA). This work aims to be one of the first attempts to formulate a multi-scale integrated pharmaceutical process as an optimization problem. The advantages of process optimization techniques which are described in this work are so far foreign to the pharmaceutical industry; however, this study aims to prove that simulation-based optimization techniques can have significant applications towards designing processes which will produce high-quality and consistent pharmaceutical products. References: 1.            Bertsimas, D., O. Nohadani, and K.M. Teo, Robust Optimization for Unconstrained Simulation-Based Problems. Oper. Res., 2010. 58(1): p. 161-178. 2.            Boukouvala, F., et al., Computer aided design and analysis of continuous pharmaceutical manufacturing processes. European Symposium of Computer Aided Process Engineering 21, Chalkidiki, Greece, 2011. 3.            Jones, D.R., A Taxonomy of Global Optimization Methods Based on Response Surfaces.Journal of Global Optimization, 2001. 21(4): p. 345-383. 4.            Papalambros, P., P. Goovaerts, and M.J. 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