Numerical algorithm for searching the optimal temperature regime of a chemical process based on the method of artificial immune systems
The paper presents an algorithm for calculating the optimal temperature regime of a chemical process in the presence of terminal constraints. The formulation of the problem of optimal control of a chemical process is given, in which constraints on the control parameter and phase variables are given. A method of solving this problem based on the penalty method and artificial immune systems is given. The penalty method allows to reduce the problem with terminal constraints to the problem without constraints by changing the optimality criterion. The new optimal control problem without terminal constraints is solved by the method of artificial immune systems. The sequence of solutions of the new optimal control problem tends to the solution of the original problem with terminal constraints when the value of the penalty parameter increases. Approbation of the algorithm on the example of the reaction of aminomethylation of thiols is carried out. The mathematical description of the reaction, which is a system of ordinary differential equations, is given. The problem of searching the optimal temperature regime with terminal constraints is formulated. As a result of the calculations, approximate optimal concentrations of substances and approximate optimal temperature regime providing close to the maximum yield of the target reaction product at fulfillment of terminal restrictions are determined.