(624c) A Surrogate-Based Framework for Feasibility Analysis and Optimization of Expensive Simulations

Simulation-based optimization has been widely studied in the field of operations research for optimization of complex systems. Compared to algebraic model-based mathematical programming, there exist several challenges in simulation-based optimization. First, the objective function and constraints are not available in algebraic form. Second, many simulations are computationally expensive to run, limiting the number of simulations that can be performed in search of the optimal solution. Third, the derivative information is usually unavailable or hard to estimate [1]. Hence, it is often impossible to utilize the conventional optimization approaches. Surrogate models have been considered to approximate expensive function evaluations using design of experiments (DOE). In addition, adaptive sampling techniques have been investigated to enrich the DOE samples, refine the surrogate model, and guide the search towards the optimum [2, 3]. The surrogate-based optimization framework has been extended to feasibility analysis, where different surrogate models have been implemented [4-9], and different methods for adaptive sampling have been discussed [10].

Most surrogate-based approaches for feasibility analysis are limited to the construction of a regression model for the feasibility function, not taking advantage of the fact that the feasibility problem is essentially a classification problem in nature. The regression model for feasibility function involves additional information regarding the degree of feasibility of each sample point, while in most feasibility problems what is of interest is whether the point is feasible or not. In this work, we consider the feasibility problem as a classification problem, and investigate the ability of classification models, such as support vector machines [11-13], to accurately characterize the design space boundary of complex systems. We integrate the classification results as constraints for process optimization and propose a modified framework for surrogate-based feasibility analysis and optimization based on the previous work of Wang et al. [14]. We also investigate adequate sampling budgets for feasibility characterization based on the complexity of the feasible space. We illustrate the efficiency of the proposed framework on a series of test problems to explore the computational complexity along with the accuracy, and compare it with existing regression-based approaches. Finally, the proposed framework is implemented on a realistic case study describing the production of solid-based drugs using wet granulation, aimed to reduce the operation cost, improve product quality, and increase process flexibility and robustness.

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