Search for the optimal initial composition of the reaction mixture of the polymerization process using artificial immune systems

To establish regularities of polymerization processes, it is advisable to use methods of mathematical modeling. On the basis of mathematical description of the process it is possible to determine the optimal conditions of its course, providing an increase in its efficiency, as well as the quality of produced polymers. One of the problems of optimization of polymerization processes is the problem of determining the initial composition of the reaction mixture, which ensures the achievement of given quantitative or qualitative indicators of the process. The aim of the work is to develop an algorithm for determining the initial concentrations of polymer synthesis reaction. The statement of the problem of searching for optimal concentrations of components of the polymer synthesis process and a numerical algorithm for its solution are given. Since the kinetic model of the polymerization process is an infinite system of ordinary nonlinear differential equations, its solution using classical optimization methods encounters computational difficulties. Therefore, it is proposed to apply the method of artificial immune systems to calculate the optimal initial composition of the reaction mixture of the polymerization process. This method allows to overcome local extrema in multidimensional search spaces and it is easy to implement for a particular process when the number of optimized parameters is changed. The developed algorithm based on the method of artificial immune systems includes a procedure for converting an infinite system of differential equations describing the kinetics of the polymerization process to a finite form using the method of moments. The algorithm has been tested on an industrially significant polymerization process of butadiene on a neodymium-containing catalytic system. The optimum concentrations of reagents that provide the polymer with the desired properties have been calculated.