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Dynamic optimization of batch emulsion polymerization using simulated annealing
Abstract
The aim of this paper is to present a global approach to dynamic optimization of batch emulsion polymerization reactors using a stochastic optimizer. The objective is to minimize the final batch time with constraints on the final conversion and molecular weight, using the reactor temperature as the manipulated variable. First, results from the standard SQP-based approach are presented to illustrate how this problem is prone to be stuck in local minima. Then, in this study, the applicability of MSIMPSA, a simulated annealing-based algorithm, is evaluated. The results obtained are only marginally superior to those reported in the literature. However, the main outcomes of this study are: (i) MSIMPSA can be applied in an easy and straightforward manner to such optimal control problems. (ii) Though MSIMPSA is a stochastic algorithm, the best obtained solution is so good that it cannot be improved further by local optimization methods.
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Related concepts (32)
Global optimization
Global optimization is a branch of applied mathematics and numerical analysis that attempts to find the global minima or maxima of a function or a set of functions on a given set. It is usually described as a minimization problem because the maximization of the real-valued function is equivalent to the minimization of the function . Given a possibly nonlinear and non-convex continuous function with the global minima and the set of all global minimizers in , the standard minimization problem can be given as that is, finding and a global minimizer in ; where is a (not necessarily convex) compact set defined by inequalities .
Simulated annealing
Simulated annealing (SA) is a probabilistic technique for approximating the global optimum of a given function. Specifically, it is a metaheuristic to approximate global optimization in a large search space for an optimization problem. For large numbers of local optima, SA can find the global optima. It is often used when the search space is discrete (for example the traveling salesman problem, the boolean satisfiability problem, protein structure prediction, and job-shop scheduling).
Mathematical optimization
Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries.
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