Genetic Algorithm for Multi-Objective Optimization of Dynamic Systems Using an Infinite-Dimensional Model

This article investigates the multi-objective problem of optimizing polymerization process parameters. The complexity of the mathematical description of the polymerization process stems from the fact that the reaction system contains an unlimited number of components. Therefore, the mathematical model of the polymerization process is an infinite-dimensional system of differential equations. To solve this multi-objective problem of polymerization process optimization, the article proposes a genetic algorithm based on the Pareto dominance principle. A key feature of the algorithm is the procedure for reducing the infinite system of equations to a final form using the moment method. An advantage of the algorithm is the absence of the need to prioritize the optimization criteria. The article presents the results of a computational experiment on the polymerization of butadiene on a neodymium-containing catalytic system. The experiment allowed determining such parameters as the synthesis duration and the initial concentrations of the monomer and organoaluminum compound that ensure maximum monomer conversion at a given polydispersity index of the final product. The solution to the problem of the multi-objective optimization of the butadiene polymerization process was compared to the solutions obtained by minimizing each criterion separately. It was found that the use of the developed algorithm allows for a significant improvement in the indicators of the highest monomer conversion and the polydispersity index of polymers.