| Русский Русский | English English |
   
Главная Текущий номер
01 | 03 | 2021
10.14489/vkit.2021.02.pp.003-012

DOI: 10.14489/vkit.2021.02.pp.003-012

Матренин П. В.
МЕТОД РАЗДЕЛЕНИЯ ОБЛАСТИ ДОПУСТИМЫХ ЗНАЧЕНИЙ ДЛЯ УВЕЛИЧЕНИЯ ВАРИАТИВНОСТИ ТЕСТОВЫХ ЗАДАЧ НЕПРЕРЫВНОЙ ОПТИМИЗАЦИИ
(c. 3-12)

Аннотация. Рассмотрены вопросы создания тестовых задач непрерывной оптимизации с нелинейными ограничениями и разбиением области допустимых решений. Предложен метод разбиения области допустимых решений с помощью многомерной сетки запрещенных решений. Метод прост в реализации и практически не влияет на вычислительную сложность задач. Проведено исследование на ряде широко используемых тестовых задач непрерывной оптимизации и популяционных алгоритмов.

Ключевые слова:  непрерывная оптимизация; условная оптимизация; популяционные алгоритмы; генетический алгоритм; алгоритм роя частиц.

 

Matrenin P. V.
METHOD FOR SPLITTING THE FEASIBLE REGION TO INCREASE THE VARIABILITY OF CONTINUOUS OPTIMIZATION TEST PROBLEMS
(pp. 3-12)

Abstract. The solution of optimization problems is essential for the design and control of technical systems. The optimization problem arising in practice has a high dimension, nonlinear criteria, and constraints. There are a lot of continuous optimization tasks for testing and research of optimization algorithms performance. These tasks have a convex range of acceptable values limited to a specified range for each parameter. The problem of generating test multidimensional continuous optimization tasks with nonlinear constraints and splitting the feasible region is considered. A method was proposed for splitting the feasible region by separate domains using the multidimensional grid of forbidden solutions. As a result, the problem acquires properties closer to optimizing technical systems with complex constraints. The method allows creating an unlimited number of test optimization problems, which can be used to research and develop optimization algorithms. The method is simple to implement, and the impact on the computational complexity of tasks is insignificant. Research has been carried out on four widely used continuous single-objective optimization test functions, with the Genetic algorithm and the Particle Swarm Optimization algorithm. It is shown that the proposed method has an influence on the process of solving multidimensional continuous optimization problems by population algorithms and on the dependence of the accuracy of the algorithm on its heuristic coefficients.

Keywords: Continuous optimization; Constrained optimization; Population algorithms; Genetic algorithm; Particle swarm optimization.

Рус

П. В. Матренин (Новосибирский государственный технический университет, Новосибирск, Россия; Научно-технический университет «Сириус», Сочи, Россия) E-mail: Этот e-mail адрес защищен от спам-ботов, для его просмотра у Вас должен быть включен Javascript  

Eng

P. V. Matrenin (Novosibirsk State Technical University, Novosibirsk, Russia; Sirius University of Science and Technology, Sochi, Russia) E-mail: Этот e-mail адрес защищен от спам-ботов, для его просмотра у Вас должен быть включен Javascript  

Рус

1. Карпенко А. П. Современные алгоритмы поисковой оптимизации. 2-е изд. М.: Изд-во МГТУ имени Н. Э. Баумана, 2014. 448 с.
2. Биоинспирированные методы в оптимизации / Л. А. Гладков, В. В. Курейчик, В. М. Курейчик и др. М.: Физматлит, 2009. 384 с.
3. Fevrier V. Bio-Inspired Optimization Methods // Springer Handbook of Computational Intelligence. Berlin: Springer, 2015. P. 1533 – 1538.
4. Poli R. An Analysis of Publications on Particle Swarm Optimisation Applications. Department of Computer // Journal of Artificial Evolution and Applications. 2007. Art. ID 685175. 10 p.
5. Particle Swarm Optimization: Basic Concepts, Variants and Applications in Power Systems / Y. Valle, G. K. Venayagamoorthy, S. Mohagheghi et al. // IEEE Transactions on Evolutionary Computation. 2008. V. 12, No. 2. P. 171 – 195.
6. A Decade Survey of Engineering Applications of Genetic Algorithm in Power System Optimization / C. M. Akachukwu, A. M. Aibinu, M. N. Nwohu et al. // 5th Intern. Conf. on Intelligent Systems, Modelling and Simulation. Malaysia, Langkawi. 27 – 29 Jan. 2014. P. 38 – 42.
7. Particle Swarm Optimization: Hybridization Perspectives and Experimental Illustrations / R. Thangaraj, M. Pant, A. Abraham et al. // Applied Mathematics and Computation. 2011. V. 217. P. 5208 – 5226.
8. Матренин П. В. Разработка и исследование адаптивных методов роевого интеллекта в задачах календарного планирования // Автоматика и программная инженерия. 2013. № 1(3). С. 110 – 115.
9. Abdel-Kader R. F. Hybrid Discrete PSO with GA Operators for Efficient QoS-multicast Routing // Ain Shams Eng. Journal. 2011. V. 2, No. 1. P. 21 – 31.
10. Moslehi F., Haeri, A., Martínez-Alvarez F. A Novel Hybrid GA–PSO Framework for Mining Quantitative Association Rules // Soft Computing. 2020. V. 24. P. 4645 – 4666.
11. Гладков Л. А., Курейчик В. В., Курейчик В. М. Генетические алгоритмы. М.: Физматлит, 2010. 317 с.
12. Grosan C., Abraham A.A. Novel Global Optimization Technique for High Dimensional Functions // Intern. Journal of Intelligent Systems. 2009. V. 24, No. 4. P. 421 – 440.
13. Abiyev R. H., Tunay M. Optimization of High-Dimensional Functions through Hypercube Evaluation // Computational Intelligence and Neuroscience. 2015. Art. ID 967320. 11 p.
14. Cho H., Olivera F., Guikema S. D. A Derivation of the Number of Minima of the Griewank Function // Applied Mathematics and Computation. 2014. V. 204, No. 2. P. 694 – 701.
15. Simionescu P. A., Beale D. G. New Concepts in Graphic Visualization of Objective Functions // Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Canada, Montreal, 17 – 22 Nov. 2002. 7 p.
16. Curtis F. E., Nocedal J. Flexible Penalty Functions for Nonlinear Constrained Optimization // IMA Journal of Numerical Analysis. 2008. V. 28, No. 4. P. 749 – 769.
17. New penalty Function with Differential Evolution for Constrained Optimization / C. Deng, C. Liang, B. Zhao et al. // 7th World Congress on Intelligent Control and Automation. China, Chongqing, 25 – 27 June 2008. P. 5304 – 5307.
18. Mallet O. Genetic Algorithm in C++ with Template Metaprogramming and Abstraction for Constrained Optimization. URL: https://github.com/ olmallet81/GALGO-2.0 (дата обращения: 20.08.2020).
19. Eberhart R. C., Shi Y. Particle Swarm Optimization: Developments, Applications and Resources // Congress on Evolutionary Computation. South Korea, Seoul, 27 – 30 May 2001. P. 81 – 86.
20. Матренин П. В., Манусов В. З. Адаптивный алгоритм роя частиц в задачах оперативного планирования // Вестник компьютерных и информационных технологий. 2016. № 4(142). С. 11 – 15.

Eng

1. Karpenko A. P. (2014). Modern algorithms for search engine optimization. 2nd ed. Moscow: Izdatel'stvo MGTU imeni N. E. Baumana. [in Russian language]
2. Gladkov L. A., Kureychik V. V., Kureychik V. M. et al. (2009). Bioinspired methods in optimization. Moscow: Fizmatlit. [in Russian language]
3. Fevrier V. (2015). Bio-Inspired Optimization Methods. Springer Handbook of Computational Intelligence, pp. 1533 – 1538. Berlin: Springer.
4. Poli R. (2007). An Analysis of Publications on Particle Swarm Optimisation Applications. Department of Computer. Journal of Artificial Evolution and Applications, Article ID 685175.
5. Valle Y., Venayagamoorthy G. K., Mohagheghi S. et al. (2008). Particle Swarm Optimization: Basic Concepts, Variants and Applications in Power Systems. IEEE Transactions on Evolutionary Computation, Vol. 12, (2), pp. 171 – 195.
6. Akachukwu C. M., Aibinu A. M., Nwohu M. N. et al. (2014). A Decade Survey of Engineering Applications of Genetic Algorithm in Power System Optimization. 5th International Conference on Intelligent Systems, Modelling and Simulation, pp. 38 – 42. Langkawi.
7. Thangaraj R., Pant M., Abraham A. et al. (2011). Particle Swarm Optimization: Hybridization Perspectives and Experimental Illustrations. Applied Mathematics and Computation, Vol. 217, pp. 5208 – 5226.
8. Matrenin P. V. (2013). Development and research of adaptive methods of swarm intelligence in scheduling problems. Avtomatika i programmnaya inzheneriya, 3(1), pp. 110 – 115. [in Russian language]
9. Abdel-Kader R. F. (2011). Hybrid Discrete PSO with GA Operators for Efficient QoS-multicast Routing. Ain Shams Engineering Journal, Vol. 2, (1), pp. 21 – 31.
10. Moslehi F., Haeri, A., Martínez-Alvarez F. (2020). A Novel Hybrid GA–PSO Framework for Mining Quantitative Association Rules. Soft Computing, Vol. 24, pp. 4645 – 4666.
11. Gladkov L. A., Kureychik V. V., Kureychik V. M. (2010). Genetic algorithms. Moscow: Fizmatlit. [in Russian language]
12. Grosan C., Abraham A. A. (2009). Novel Global Optimization Technique for High Dimensional Functions. International Journal of Intelligent Systems, Vol. 24, (4), pp. 421 – 440.
13. Abiyev R. H., Tunay M. (2015). Optimization of High-Dimensional Functions through Hypercube Evaluation. Computational Intelligence and Neuroscience, Article ID 967320.
14. Cho H., Olivera F., Guikema S. D. (2014). A Derivation of the Number of Minima of the Griewank Function. Applied Mathematics and Computation, Vol. 204, (2), pp. 694 – 701.
15. Simionescu P. A., Beale D. G. (2002). New Concepts in Graphic Visualization of Objective Functions. Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Montreal.
16. Curtis F. E., Nocedal J. (2008). Flexible Penalty Functions for Nonlinear Constrained Optimization. IMA Journal of Numerical Analysis, Vol. 28, (4), pp. 749 – 769.
17. Deng C., Liang C., Zhao B. et al. (2008). New penalty Function with Differential Evolution for Constrained Optimization. 7th World Congress on Intelligent Control and Automation, pp. 5304 – 5307. Chongqing.
18. Mallet O. (2020). Genetic Algorithm in C++ with Template Metaprogramming and Abstraction for Constrained Optimization. Available at: https://github.com/olmallet81/GALGO-2.0 (Accessed: 20.08.2020).
19. Eberhart R. C., Shi Y. (2001). Particle Swarm Optimization: Developments, Applications and Resources. Congress on Evolutionary Computation, pp. 81 – 86. Seoul.
20. Matrenin P. V., Manusov V. Z. (2016). Adaptive particle swarm optimization for the operational scheduling problem. Vestnik komp'yuternyh i informatsionnyh tekhnologiy, 142(4), pp. 11 – 15. [in Russian language]

Рус

Статью можно приобрести в электронном виде (PDF формат).

Стоимость статьи 350 руб. (в том числе НДС 18%). После оформления заказа, в течение нескольких дней, на указанный вами e-mail придут счет и квитанция для оплаты в банке.

После поступления денег на счет издательства, вам будет выслан электронный вариант статьи.

Для заказа скопируйте doi статьи:

10.14489/vkit.2021.02.pp.003-012

и заполните  форму 

Отправляя форму вы даете согласие на обработку персональных данных.

.

 

Eng

This article  is available in electronic format (PDF).

The cost of a single article is 350 rubles. (including VAT 18%). After you place an order within a few days, you will receive following documents to your specified e-mail: account on payment and receipt to pay in the bank.

After depositing your payment on our bank account we send you file of the article by e-mail.

To order articles please copy the article doi:

10.14489/vkit.2021.02.pp.003-012

and fill out the  form  

 

.

 

 

 
Поиск
Журнал КОНТРОЛЬ. ДИАГНОСТИКА
Баннер
Баннер
Баннер
Rambler's Top100 Яндекс цитирования