DOI: https://doi.org/10.20535/SRIT.2308-8893.2020.3.07

Багатокритеріальна умовна оптимізація на основі генетичних алгоритмів

Victor M. Sineglazov, Kirill D. Riazanovskiy, Olena I. Chumachenko

Анотація


Розглянуто проблему багатокритеріальної умовної оптимізації, розв’язання якої натепер є найважливішим завданням для багатьох галузей. Ця проблема є однією з найважливіших задач теперішнього часу і знаходить застосування в багатьох областях. Запропоновано повторне використання існуючих алгоритмів розв’язання безумовної оптимізації. Розглянуто різні алгоритми багатокритеріальної безумовної оптимізації. Проаналізовано переваги та недоліки кожного алгоритму. Алгоритми модифіковано для врахування обмежень. Розроблено додаткові алгоритми переходу від розв’язання задачі безумовної оптимізації до задачі умовної оптимізації, для тестування яких використано генетичний алгоритм SPEA2. Наведено приклади вирішення поставленого завдання з використанням згаданих алгоритмів. Виконано порівняльний аналіз остаточних результатів.

Ключові слова


багатокритеріальна оптимізація; умовна оптимізація; генетичний алгоритм; алгоритм лікування; SPEA2; Парето оптимізація

Повний текст:

PDF (English)

Посилання


A.P. Braga, R.H. Takahashi, M.A. Costa, and R. Teixeira, “Multi-Objective Algorithms for Neural Networks Learning”, Multi-Objective Machine Learning. Studies in Computational Intelligence, vol. 16. Berlin, Heidelberg: Springer, 2016. Available: https://doi.org/10.1007/3-540-33019-4_7

Carlos Artemio Coello Coello, “An Empirical Study of Evolutionary Techniques for Multiobjective Optimization in Engineering Design”, PhD thesis. Department of Computer Science, Tulane University, New Orleans, LA, April 1996.

C.A. Coello Coello, A comprehensive survey of evolutionary-based multiobjective optimization techniques. Laboratorio Nacional de Informatica Avanzada, Veracruz, Mexico, 1998. Available: https://doi.org/10.1007/BF03325101

E. Zitzler, M. Laumanns, and L. Thiele, “Spea2: Improving the strength pareto evolutionary algorithm for multiobjective optimization”, Evolutionary Methods for Design Optimization and Control with Applications to Industrial Problems. International Center for Numerical Methods in Engineering, Athens, Greece, 2001, pp. 95–100.

S.V. Groshev, A.P. Karpenko, and V.A. Martynyuk, “The effectiveness of population-based Pareto-approximation algorithms. Experimental comparison”, on-line journal “Naukovedenie”, 8(4), 2016. doi: 10.15862/67EVN416.

A.V. Gumennikova, “Hybrid adaptive search algorithm for solving problems of conditional multi-criteria optimization”, Siberian Journal of Science and Technology, iss. 5, pp. 70–76, 2004.

A.V. Gumennikova, “On the evolutionary approach to solving multicriteria problems of conditional optimization”, in VIII international scientific-practical conference “System analysis in the project and management”, St. Petersburg, 2004, pp. 72–76.

A.V. Gumennikova, “Solving multicriteria problems of conditional and unconditional optimization using genetic algorithms MultiobjectiveGA v.1.0”, Computer curriculum and innovation, no. 8, p. 16, 2005.

K. Deb and B.R.N. Uday, “Investigating Predator–Prey algorithms for multi-objective optimization”, KanGAL, Kanpur, Indian, Rep. 2005010, Dec. 2005.

K. Deb, S. Agrawal, A. Pratap, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II”, IEEE Trans. Evol. Comput., vol. 6, no. 2, pp. 182–197, Apr. 2002. doi: 10.1109/4235.996017

Karl O. Jones, “Comparison of genetic algorithm and particle swarm optimization”, in International Conference on Computer Systems and Technologies, 2005.

A.P. Karpenko, Modern search engine optimization algorithms. Algorithms inspired by nature, Moscow: Publishing House MSTU, 2014.

A.F. Kuri-Morales and J. Gutiérrez-García, “Penalty Function Methods for Constrained Optimization with Genetic Algorithms: A Statistical Analysis”, Lecture Notes in Computer Science, vol. 2313. Berlin, Heidelberg: Springer, 2002. Available: https://doi.org/10.1007/3-540-46016-0_12

M. Laumanns, G. Rudolph, and H.P. Schwefel, “A spatial predator-prey approach to multi-objective optimization: A preliminary study”, in Proceedings of the Parallel Problem Solving from Nature, V, pp. 241–249, 1998. Available: https://doi.org/ 10.1007/BFb0056867

David Orvosh and Lawrence Davis, “Using a Genetic Algorithm to Optimize Problems with Feasibility Constraints”, IEEE Conference on Evolutionary Computation – Proceedings, vol. 2, pp. 548–553, 1994. Available: https://doi.org/10.1109/ICEC.1994.350001

J. Schaffer, “Multiple Objective Optimization with Vector Evaluated Genetic Algorithms”, Proceedings of the First Int. Conference on Genetic Algortihms, pp. 93–100, 1985.

E.S. Semenkin, O.E. Semenkina, and S.P. Korobeinikov, Optimization of technical systems. Tutorial. Krasnoyarsk: SIBMP, 1996.

O.E. Semenkina and V.V. Zhidkov, Optimization of management of complex systems by the method of generalized local search. MAKS Press, 2002.

Tomio Umeda and Atsunobu Ichikawa, “A Modified Complex Method for Optimization”, Industrial & Engineering Chemistry Process Design and Development, 10 (2), pp. 229–236, 1971. doi: 10.1021/i260038a016

Yu.I. Zhuravlev and Yu.Yu. Finkelstein, “Local Algorithms for Linear Integer Programming Problems”, Cybernetics problems, iss. 14, pp. 289–295, 1965.


Пристатейна бібліографія ГОСТ


1. A.P. Braga, R.H. Takahashi, M.A. Costa, and R. Teixeira, “Multi-Objective Algorithms for Neural Networks Learning”, Multi-Objective Machine Learning. Studies in Computational Intelligence, vol. 16. Berlin, Heidelberg: Springer, 2016. Available: https://doi.org/10.1007/3-540-33019-4_7

2. Carlos Artemio Coello Coello, “An Empirical Study of Evolutionary Techniques for Multiobjective Optimization in Engineering Design”, PhD thesis. Department of Computer Science, Tulane University, New Orleans, LA, April 1996.

3. C.A. Coello Coello, A comprehensive survey of evolutionary-based multiobjective optimization techniques. Laboratorio Nacional de Informatica Avanzada, Veracruz, Mexico, 1998. Available: https://doi.org/10.1007/BF03325101

4. E. Zitzler, M. Laumanns, and L. Thiele, “Spea2: Improving the strength pareto evolutionary algorithm for multiobjective optimization”, Evolutionary Methods for Design Optimization and Control with Applications to Industrial Problems. International Center for Numerical Methods in Engineering, Athens, Greece, 2001, pp. 95–100.

5. S.V. Groshev, A.P. Karpenko, and V.A. Martynyuk, “The effectiveness of population-based Pareto-approximation algorithms. Experimental comparison”, on-line journal “Naukovedenie”, 8(4), 2016. doi: 10.15862/67EVN416.

6. A.V. Gumennikova, “Hybrid adaptive search algorithm for solving problems of conditional multi-criteria optimization”, Siberian Journal of Science and Technology, iss. 5, pp. 70–76, 2004.

7. A.V. Gumennikova, “On the evolutionary approach to solving multicriteria problems of conditional optimization”, in VIII international scientific-practical conference “System analysis in the project and management”, St. Petersburg, 2004, pp. 72–76.

8. A.V. Gumennikova, “Solving multicriteria problems of conditional and unconditional optimization using genetic algorithms MultiobjectiveGA v.1.0”, Computer curriculum and innovation, no. 8, p. 16, 2005.

9. K. Deb and B.R.N. Uday, “Investigating Predator–Prey algorithms for multi-objective optimization”, KanGAL, Kanpur, Indian, Rep. 2005010, Dec. 2005.

10. K. Deb, S. Agrawal, A. Pratap, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II”, IEEE Trans. Evol. Comput., vol. 6, no. 2, pp. 182–197, Apr. 2002. doi: 10.1109/4235.996017

11. Karl O. Jones, “Comparison of genetic algorithm and particle swarm optimization”, in International Conference on Computer Systems and Technologies, 2005.

12. A.P. Karpenko, Modern search engine optimization algorithms. Algorithms inspired by nature, Moscow: Publishing House MSTU, 2014.

13. A.F. Kuri-Morales and J. Gutiérrez-García, “Penalty Function Methods for Constrained Optimization with Genetic Algorithms: A Statistical Analysis”, Lecture Notes in Computer Science, vol. 2313. Berlin, Heidelberg: Springer, 2002. Available: https://doi.org/10.1007/3-540-46016-0_12

14. M. Laumanns, G. Rudolph, and H.P. Schwefel, “A spatial predator-prey approach to multi-objective optimization: A preliminary study”, in Proceedings of the Parallel Problem Solving from Nature, V, pp. 241–249, 1998. Available: https://doi.org/ 10.1007/BFb0056867

15. David Orvosh and Lawrence Davis, “Using a Genetic Algorithm to Optimize Problems with Feasibility Constraints”, IEEE Conference on Evolutionary Computation – Proceedings, vol. 2, pp. 548–553, 1994. Available: https://doi.org/10.1109/ICEC.1994.350001

16. J. Schaffer, “Multiple Objective Optimization with Vector Evaluated Genetic Algorithms”, Proceedings of the First Int. Conference on Genetic Algortihms, pp. 93–100, 1985.

17. E.S. Semenkin, O.E. Semenkina, and S.P. Korobeinikov, Optimization of technical systems. Tutorial. Krasnoyarsk: SIBMP, 1996.

18. O.E. Semenkina and V.V. Zhidkov, Optimization of management of complex systems by the method of generalized local search. MAKS Press, 2002.

19. Tomio Umeda and Atsunobu Ichikawa, “A Modified Complex Method for Optimization”, Industrial & Engineering Chemistry Process Design and Development, 10 (2), pp. 229–236, 1971. doi: 10.1021/i260038a016

20. Yu.I. Zhuravlev and Yu.Yu. Finkelstein, “Local Algorithms for Linear Integer Programming Problems”, Cybernetics problems, iss. 14, pp. 289–295, 1965.