Global and Dynamic Optimization using the Artificial Chemical Process Paradigm and Fast Monte Carlo Methods for the Solution of Population Balance Models

Abstract

Global and dynamic optimization of engineering problems usually involves complex physico-chemical models as constraints. These models are in general highly non-linear, resulting in multimodal optimization problems. The model may have discontinuous behavior and/or include a very large set of variables. As the complexity of the systems increases, equation-free modeling is becoming more common (Kevrekidis, Gear and Hummer, 2004). For example, in particle dynamics, population balance models are sometimes more effectively solved by the Monte Carlo method. Stochastic global optimization methods are very important algorithms for the solution of these types of problems. They have been successfully applied to solve challenging problems that cannot be solved using gradient based methods. Stochastic optimization methods have also been used in many algorithms, in which solution of optimization problems is part of the algorithm. Global stochastic optimization strategies have been utilized in learning phase of pattern recognition algorithms using fuzzy logic (Irizarry, 2005b) and neuro-fuzzy systems (Lin, 2008). These methods have been used for the optimization of complex engineering designs involving computational fluid mechanics such as aerodynamics applications (Duvigneau and Visonneau, 2004). Other applications include the determination of molecular structures, including protein structure prediction and protein-small molecule interactions among others (Sahinis, 2009). Batch scheduling problems are another type of problem were stochastic optimization can be very efficient (Liu et al., 2010). In particular, the solution of dynamic optimization problems is also of great industrial importance for process development and process optimization, since most processes are dynamic. In this type of problem an optimal profile function is sought (vs. an optimal value for a set of variables). For example, in a fed-batch fermenter, the feed-rate schedule is optimized to maximize production of antibiotics, vitamins, enzymes, and other products (Banga et al., 2003). Another example is the determination of optimal temperature profiles in crystallization processes to control crystal size distribution (Ma, Tafti and Braatz, 2002). Dynamic optimization is also of central importance to the application of process control