Optimization of the temperature profile in a chemical process using a genetic algorithm

   This study addresses the problem of finding an optimal temperature profile for a complex physico-chemical process. The greatest difficulties arise in the study and optimization of multicomponent systems, which determines both scientific and practical interest in developing the most effective tools for identifying optimal production regimes. One of the key aspects is the consideration of dynamic constraints that affect the rate of change of control parameters and ensure the construction of physically feasible trajectories of temperature variation. To solve this problem, a modified genetic algorithm is proposed, allowing for the incorporation of predefined constraints. An optimization problem is formulated for a complex physico-chemical process, aiming to determine the optimal temperature profile that maximizes (or minimizes) a given target parameter while satisfying constraints on the rate of temperature change. The method is based on discretizing the total process duration and representing the temperature profile as a piecewise linear function, with segment values determined using a genetic optimization algorithm. The main stages of the genetic algorithm have been modified and presented as an adaptive evolutionary search scheme that accounts for permissible control parameter variations. These modifications enhance the algorithm robustness against local extrema and ensure more precise adherence to predefined constraints. The efficiency of the algorithm, the functionality of the software module, and the interaction mechanism were tested through a computational experiment investigating the kinetics of the reaction of dimethyl carbonate with alcohols in the presence of dicobalt octacarbonyl. Numerical simulations demonstrated that the temperature regime significantly influences reaction kinetics, and computational trials enabled the unambiguous identification of the optimal temperature profile under constraints on temperature increase and an additional requirement for the linear variation of the target product concentration. The proposed modification of the genetic algorithm significantly improved its robustness against local extrema and ensured stricter compliance with technological constraints. In particular, an analysis of the obtained profiles showed that the proposed method allows for solutions that ensure a more uniform distribution of the target product concentration, which is especially important in the design of reaction systems highly sensitive to parameter variations. This optimization approach can be useful for the design and scaling of chemical-technological processes, and the conducted study confirms the effectiveness of numerical methods and evolutionary algorithms for optimizing chemical reaction conditions.

1. Marpaung T.J. Optimization of temperature on the concentration of a mixture of substances in liquid waste treatment process palm oil. Journal of Physics: Conference Series, 2019, vol. 1235, no. 1, pp. 012123. doi: 10.1088/1742-6596/1235/1/012123

2. Shevchuk V.P., Sharovina S.O. The control of the temperature profile of the rectification column dish type. Instruments and Systems: Monitoring, Control, and Diagnostics, 2013, no. 3, pp. 39–47. (in Russian)

3. Slinko M.G. Kinetic model as a basis for mathematical modeling of catalytic processes. Teoreticheskie Osnovy Khimicheskoi Tekhnologii, 1976, vol. 10, no. 1, pp. 137–146. (in Russian)

4. Bykov V.I., Tcybenova S.B. Nonlinear Models of Chemical Kinetics. Moscow, Kom-Kniga Publ., 2010, 350 p. (in Russian)

5. Vasilev F.P. Numerical Methods for Extreme Problems Solving. Moscow: Nauka Publ., 1988, 552 p. (in Russian)

6. Panteleev A.V., Skavinskaia D.V., Aleshina E.A. Metaheuristic Algorithms for Searching of the Optimal Program Control. Moscow: Infra-M Publ., 2020, 396 p. (in Russian)

7. Miftakhov E.N., Kashnikova A.P., Ivanov D.V. Using genetic algorithms to solve the problem of finding the optimal composition of the reaction mixture. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2024, vol. 24, no. 4, pp. 637–644. (in Russian). doi: 10.17586/2226-1494-2024-24-4-637-644

8. Katoch S., Chauhan S.S., Kumar V. A review on genetic algorithm: past, present, and future. Multimedia Tools and Applications, 2021, vol. 80, no. 5, pp. 8091–8126. doi: 10.1007/s11042-020-10139-6

9. Miftakhov E.N., Ivanov D.V. Searching for the optimal composition of the reaction mixture using a simulated annealing algorithm. Avtometriya, 2024, vol. 60, no. 5, pp. 120–128. (in Russian). doi: 10.15372/AUT20240514

10. Miftakhov E.N. Algorithm for searching the optimal regulator supply mode in the process of manufacturing polymer products. Engineering Technologies and Systems, 2024, vol. 34, no. 4, pp. 597–614. (in Russian). doi: 10.15507/2658-4123.034.202404.597-614

11. Awad A., Hawash A., Abdalhaq B. A Genetic Algorithm (GA) and swarm-based Binary Decision Diagram (BDD) reordering optimizer reinforced with recent operators. IEEE Transactions on Evolutionary Computation, 2023, vol. 27, no. 3, pp. 535–549. doi: 10.1109/tevc.2022.3170212

12. Yang D., Rao K., Xu B., Sheng W. PIR sensors deployment with the accessible priority in smart home using genetic algorithm. International Journal of Distributed Sensor Networks, 2015, vol. 11, no. 11, pp. 146270. doi: 10.1155/2015/146270

13. Antipina E.V., Mustafina S.A., Antipin A.F. Automation of search for optimal values of the ethylene oligomerization process parameters. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2024, vol. 24, no. 4, pp. 563–570. (in Russian). doi: 10.17586/2226-1494-2024-24-4-563-570

14. Zhou T., Fang W. Two-point crossover operator in genetic algorithm for deep learning compiler. Proc. of the Companion Conference on Genetic and Evolutionary Computation, 2023, pp. 347–350. doi: 10.1145/3583133.3590536

15. Bell O. Applications of Gaussian Mutation for self adaptation in evolutionary genetic algorithms. arXiv, 2022, doi: 10.48550/arXiv.2201.00285

16. Tinós R., Yang S. Evolution strategies with q-Gaussian mutation for dynamic optimization problems. Proc. of the 11^th Brazilian Symposium on Neural Networks, 2010, pp. 223–228. doi: 10.1109/sbrn.2010.46

17. Koledina K.F., Koledin S.N., Schadneva N.A., Mayakova Y.Yu., Gubaydullin I.M. Kinetic model of the catalytic reaction of dimethylcarbonate with alcohols in the presence Co₂ (CO)₈ and W(CO)₆. Reaction Kinetics, Mechanisms and Catalysis, 2017, vol. 121, no. 2, pp. 425–438. doi: 10.1007/s11144-017-1181-3

18. Fiorani G., Perosa A., Selva M. Dimethyl carbonate: a versatile reagent for a sustainable valorization of renewables. Green Chemistry, 2018, vol. 20, no. 2, pp. 288–322. doi: 10.1039/c7gc02118f

19. Koledina K.F., Koledin S.N., Shchadneva N.A., Gubaidullin I.M. Kinetics and mechanism of the catalytic reaction between alcohols and dimethyl carbonate. Russian Journal of Physical Chemistry A, 2017, vol. 91, no. 3, pp. 442–447. doi: 10.1134/s003602441703013x

20. Koledina K.F. Multi-Criteria Optimization and Optimal Control of Chemical Processes Based on a Detailed Kinetic Model. Ufa, UFRC RAS, 2020, 334 p. (in Russian)