Geodesic
Evolutionary algorithms for finding approximate solutions to optimal control problems
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 30 (2024) no. 1, pp. 21-31
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

Optimal control problems with terminal constraints and with a free right end of the trajectory are considered. Each of the problems is approximated by a finite-dimensional problem. The control is subject to a constraint and is defined in the class of piecewise constant functions. Numerical algorithms are formulated to find approximate solutions to the problems. The iterative algorithms are based on the differential evolution method. A feature of the proposed approach is that the solution found is independent of the choice of the initial approximation. The results of numerical experiments on solving optimal control problems are presented. For each problem, a suboptimal control and the corresponding trajectory of the process are calculated. The results obtained are compared with solutions found by gradient methods. The comparison proves the effectiveness of using the developed evolutionary algorithms for solving optimal control problems.
Keywords: optimal control problem, differential evolution, terminal constraints, evolutionary calculations. = 
@article{TIMM_2024_30_1_a1,
     author = {E. V. Antipina and S. A. Mustafina and A. F. Antipin},
     title = {Evolutionary algorithms for finding approximate solutions to optimal control problems},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {21--31},
     year = {2024},
     volume = {30},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2024_30_1_a1/}
}
TY  - JOUR
AU  - E. V. Antipina
AU  - S. A. Mustafina
AU  - A. F. Antipin
TI  - Evolutionary algorithms for finding approximate solutions to optimal control problems
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2024
SP  - 21
EP  - 31
VL  - 30
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TIMM_2024_30_1_a1/
LA  - ru
ID  - TIMM_2024_30_1_a1
ER  - 
%0 Journal Article
%A E. V. Antipina
%A S. A. Mustafina
%A A. F. Antipin
%T Evolutionary algorithms for finding approximate solutions to optimal control problems
%J Trudy Instituta matematiki i mehaniki
%D 2024
%P 21-31
%V 30
%N 1
%U http://geodesic.mathdoc.fr/item/TIMM_2024_30_1_a1/
%G ru
%F TIMM_2024_30_1_a1
E. V. Antipina; S. A. Mustafina; A. F. Antipin. Evolutionary algorithms for finding approximate solutions to optimal control problems. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 30 (2024) no. 1, pp. 21-31. http://geodesic.mathdoc.fr/item/TIMM_2024_30_1_a1/

[1] Xue B., Yao X., “A survey on evolutionary computation approaches to feature selection”, IEEE Transactions on Evolutionary Computation, 2016, no. 20, 606–626 | DOI

[2] Mohamed A.W., Mohamed A.K., “Adaptive guided differential evolution algorithm with novel mutation for numerical optimization”, Int. J. Machine Learning and Cybernetics, 10:2 (2019), 253–277 | DOI

[3] Panteleev A.V., Metlitskaya D.V., “Primenenie geneticheskikh algoritmov s binarnym i veschestvennym kodirovaniem dlya priblizhennogo sinteza suboptimalnogo upravleniya determinirovannymi sistemami”, Avtomatika i telemekhanika, 2011, no. 11, 117–129 | Zbl

[4] Gubin P.Yu., Oboskalov V.P., “Primenenie metoda differentsialnoi evolyutsii v zadache planirovaniya remontov generiruyuschego oborudovaniya”, Izv. RAN. Energetika, 2021, no. 2, 50–64 | DOI

[5] Eremeev A.V. Tyunin N.N., “Algoritm differentsialnoi evolyutsii dlya optimizatsii napravlennosti fazirovannykh antennykh reshetok”, Mat. struktury i modelirovanie, 2022, no. 3, 57–68 | DOI | MR

[6] Kovalevich A.A., Yakimov A.I., Albkeirat D.M., “Issledovanie stokhasticheskikh algoritmov optimizatsii dlya primeneniya v imitatsionnom modelirovanii sistem”, Inform. tekhnologii, 2011, no. 8, 55–60

[7] Storn R., Price K., “Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces”, J. Global Optimi., 1997, no. 11, 341–359 | DOI | MR | Zbl

[8] Karpenko A.P., “Evolyutsionnye operatory populyatsionnykh algoritmov globalnoi optimizatsii”, Matematika i mat. modelirovanie, 2018, no. 1, 59–89 | DOI

[9] Mohamed A.W., “A novel differential evolution algorithm for solving constrained engineering optimization problems”, J. Intel. Manufact., 2018, no. 29, 659–692 | DOI

[10] Fedorenko R.P., Priblizhennye metody resheniya zadach optimalnogo upravleniya, Nauka, M., 1978, 488 pp.

[11] Rozenbrok Kh., Storn S., Vychislitelnye metody dlya inzhenerov-khimikov, Nauka, M., 1973, 444 pp.

[12] Tyatyushkin A.I., Chislennye metody i programmnye sredstva optimizatsii upravlyaemykh sistem, Nauka, Novosibirsk, 1992, 193 pp.