Вычисление объединенных мягких ограничений в задачах проектирования оптимальных технологических систем
Ключевые слова:
оптимальное проектирование, химико-технологические системы, неопределенность в исходной информации, объединенные мягкие ограничения
Аннотация
Учет неопределенности в исходной информации в задачах оптимизации химико-технологических систем приводит к учету разных форм ограничений, представляющих проектные требования к работе химико-технологических систем. В работе предложен способ решения задач проектирования оптимальных химико-технологических систем при учете объединенных вероятностных ограничений. Способ основан на использовании кусочно-линейной аппроксимации целевой функции и функций ограничений, входящих в перечень объединенных, а также аппроксимации области выполнения ограничений многомерным параллелепипедом. Это позволяет свести объединенные вероятностные ограничения к совокупности отдельных детерминированных ограничений и обеспечить их вычислимость, а также меньшее время на получение решения задачи. Уточнение используемых аппроксимаций достигается за счет разбиения области неопределенности и многомерного параллелепипеда на подобласти.
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Литература
1. Mathematical Programming Techniques for Optimization under Uncertainty and Their Application in Process Systems Engineering / I. E. Grossmann [and etc.] // Theoretical Foundations Of Chemical Engineering. – 2017. – V. 6. – No 51. – P. 961–971.
2. Hannah, L. A. Stochastic optimization / L. A. Hannah // International Encyclopedia of the Social & Behavioral Sciences / L. A. Hannah; edited by J. D. Wright. – Elsevier Ltd., 2015. – P. 473–481.
3. Exact robust counterparts of ambiguous stochastic constraints under mean and dispersion information / K. Postek [and etc.] // Optimization-Online. – 2015. URL: http://www.optimization–online.org/DB_HTML/2015/06/4946.html
4. Marti, K. Stochastic Optimization Methods. Applications in Engineering and Operations Research / K. Marti. – Springer. Engl., 2015. – 388 p.
5. Проектирование оптимальных ХТС на основе двухэтапных задач оптимизации / А. С. Сильвестрова [и др.] // Вестник Технологического университета. – 2015. – Т. 18. – No 23. – С. 110–115.
6. Xie, W. Optimized Bonferroni approximations of distributionally robust joint chance constraints / W. Xie, S. Ahmed, R. Jiang // Optimization-Online. – 2017. URL: http://www.optimization-online.org/DB_FILE/2017/02/5860.pdf
7. Bertsimas, D. Optimal inequalities in probability theory: A convex optimization approach / D. Bertsimas, I. Popescu // SIAM Journal on Optimization. – 2005. – V. 15. – No 3. – P. 780–804.
8. Baker, K. Joint Chance Constraints in AC Optimal Power Flow: Improving Bounds through Learning / K. Baker, A. Bernstein // IEEE Transactions on Smart Grid. – 2019. – Early Access. – P. 1–1.
9. On probabilistic constraints induced by rectangular sets and multivariate normal distributions / W. van Ackooij [and etc.] // Mathematical Methods of Operation Research. – 2010. – V. 71. – No 3. – P. 535–549.
10. Optimal Design and Placement of Piezoelectric Actuators using Genetic Algorithm: Application to Switched Reluctance Machine Noise Reduction // Stochastic Optimization–Seeing the Optimal for the Uncertain / O. Javier [and etc.]; edited by Dr. Ioannis Dritsas. – InTech Europe, Croatia, 2011. – Р. 95–104.
11. Covering linear programming with violations / F. Qiu [and etc.] // INFORMS Journal on Computing. – 2014. – V. 26. – No 3. – P. 531–546.
12. van Ackooij, W. Constrained bundle methods for upper inexact oracles with application to joint chance constrained energy problems / W. van Ackooij, C. Sagastizábal // SIAM Journal on Optimization. – 2014. – V. 24. – No 2. – P. 733–765.
13. Küçükyavuz, S. On mixing sets arising in chance-constrained programming / S. Küçükyavuz // Mathematical Programming. – 2012. – V. 132. – No 1–2. – P. 31–56.
14. Luedtke, J. An integer programming ap-proach for linear programs with probabilistic constraints / J. Luedtke, S. Ahmed, G. L. Nem-hauser // Mathematical Programming. – 2010. – V. 122. – No 2. – P. 247–272.
15. Luedtke, J. A branch-and-cut decomposition algorithm for solving chance-constrained mathematical programs with finite support / J. Luedtke // Mathematical Programming. – 2014. – V. 146. – No 1–2. – P. 219–244.
16. Günlük, O. Mixing mixed-integer inequalities / O. Günlük, Y. Pochet // Mathematical Programming. – 2001. – V. 90. – No 3. – P. 429–457.
17. Peña-Ordieres, A. Solving Chance-Con-strained Problems via a Smooth Sample-Based Nonlinear Approximation / A. Peña-Ordieres, J. Luedtke, A. Wächter // Cornell University Home-pape. Eprint arXiv:1905.07377. – 2019. URL: https://arxiv.org/abs/1905.07377
18. van Ackooij, W. Eventual convexity of probability constraints with elliptical distributions / W. van Ackooij, J. Malick // Mathematical Programming. – 2019. – V. 175. – No 1–2. – P. 1–27.
19. Nemirovski, A. Scenario approximations of chance constraints / A. Nemirovski // Probabilistic and randomized methods for design under uncertainty / A. Nemirovski, A. Shapiro; edited by G. Calafiore, F. Dabbene. – Springer-Verlag, London, 2006. – Р. 3–47.
20. Cheng, J. Partial sample average approx-imation method for chance constrained problems / J. Cheng, C. Gicquel, A. Lisser // Optimization Letters. – 2019. – V. 13. – No 4. – P. 657–672.
21. Baker, K. Efficient relaxations for joint chance constrained AC optimal power flow / K. Baker, B. Toomey // Electric Power Systems Research. – 2017. – No 148. – P. 230–236.
22. Ran, D. Robust Approximations to Joint Chance-constrained Problems / D. Ran, L. I. Guo-Xiang, L.I. Qi-Qiang // Acta Autom. Sin. – 2015. – V. 41. – No 10. – P. 1772–1777.
23. Zhao, M. Strong inequalities for chance- constrained program / M. Zhao, K. Huang, B. Zeng // Optimization-Online. – 2014. URL: http://www.optimization-on-line.org/DB_FILE/2014/11/4634.pdf
24. Roald, L. Chance-constrained AC optimal power flow: Reformulations and efficient algorithms / L. Roald, G. Andersson // IEEE Transactions on Power Systems. – 2018. – V. 33. – No 3. – P. 2906–2918.
25. Nemirovski, A. Convex approximations of chance constrained programs / A. Nemirovski, A. Shapiro // SIAM Journal on Optimization. – 2006. – V. 17. – No 4. – P. 969–996.
26. Watson, J.-P. Scalable heuristics for a class of chance-constrained stochastic programs / J.-P. Watson, R. J. B. Wets, D. L. Woodruff // INFORMS Journal on Computing. – 2010. – V. 22. – No 4. – P. 543–554.
27. Maußner, J. Optimization under uncertainty in chemical engineering: Comparative evaluation of unscented transformation methods and cubature rules / J. Maußner, F. Hannsjörg // Chemical Engineering Science. – 2018. – V. 183. – P. 329–345.
28. Joint Chance Constraints Under Mean and Dispersion Information / G. A. Hanasusanto [and etc.] // Operations Research. – 2017. – V. 65. – No 3. – P. 751–767.
29. Misra, S. Learning for Constrained Optimization: Identifying Optimal Active Constraint Sets / S. Misra, L. Roald, Y. Ng // URL: https://arxiv.org/pdf/1802.09639
30. Optimization of Chemical Process Design with Chance Constraints by an Iterative Partitioning Approach / G. M. Ostrovsky [and etc.] // Industrial & Engineering Chemistry Research. – 2015. – V. 13. – No 54. – P. 3412–3429.
31. Ostrovsky, G. M. Optimal design of chemical processes under uncertainty / G. M. Ostrovsky, T. V. Lapteva, N. N. Ziyatdinov // Theoretical Foundations Of Chemical Engineering. – 2014. – V. 48. – No 5. – P. 583–593.
32. Ke, S. Filter Trust Region Method for Nonlinear SemiInfinite Programming Problem / S. Ke, X. Chun, L. Ren // Mathematical Problems in Engineering. – 2018. – V. 2018. – P. 1–9.
2. Hannah, L. A. Stochastic optimization / L. A. Hannah // International Encyclopedia of the Social & Behavioral Sciences / L. A. Hannah; edited by J. D. Wright. – Elsevier Ltd., 2015. – P. 473–481.
3. Exact robust counterparts of ambiguous stochastic constraints under mean and dispersion information / K. Postek [and etc.] // Optimization-Online. – 2015. URL: http://www.optimization–online.org/DB_HTML/2015/06/4946.html
4. Marti, K. Stochastic Optimization Methods. Applications in Engineering and Operations Research / K. Marti. – Springer. Engl., 2015. – 388 p.
5. Проектирование оптимальных ХТС на основе двухэтапных задач оптимизации / А. С. Сильвестрова [и др.] // Вестник Технологического университета. – 2015. – Т. 18. – No 23. – С. 110–115.
6. Xie, W. Optimized Bonferroni approximations of distributionally robust joint chance constraints / W. Xie, S. Ahmed, R. Jiang // Optimization-Online. – 2017. URL: http://www.optimization-online.org/DB_FILE/2017/02/5860.pdf
7. Bertsimas, D. Optimal inequalities in probability theory: A convex optimization approach / D. Bertsimas, I. Popescu // SIAM Journal on Optimization. – 2005. – V. 15. – No 3. – P. 780–804.
8. Baker, K. Joint Chance Constraints in AC Optimal Power Flow: Improving Bounds through Learning / K. Baker, A. Bernstein // IEEE Transactions on Smart Grid. – 2019. – Early Access. – P. 1–1.
9. On probabilistic constraints induced by rectangular sets and multivariate normal distributions / W. van Ackooij [and etc.] // Mathematical Methods of Operation Research. – 2010. – V. 71. – No 3. – P. 535–549.
10. Optimal Design and Placement of Piezoelectric Actuators using Genetic Algorithm: Application to Switched Reluctance Machine Noise Reduction // Stochastic Optimization–Seeing the Optimal for the Uncertain / O. Javier [and etc.]; edited by Dr. Ioannis Dritsas. – InTech Europe, Croatia, 2011. – Р. 95–104.
11. Covering linear programming with violations / F. Qiu [and etc.] // INFORMS Journal on Computing. – 2014. – V. 26. – No 3. – P. 531–546.
12. van Ackooij, W. Constrained bundle methods for upper inexact oracles with application to joint chance constrained energy problems / W. van Ackooij, C. Sagastizábal // SIAM Journal on Optimization. – 2014. – V. 24. – No 2. – P. 733–765.
13. Küçükyavuz, S. On mixing sets arising in chance-constrained programming / S. Küçükyavuz // Mathematical Programming. – 2012. – V. 132. – No 1–2. – P. 31–56.
14. Luedtke, J. An integer programming ap-proach for linear programs with probabilistic constraints / J. Luedtke, S. Ahmed, G. L. Nem-hauser // Mathematical Programming. – 2010. – V. 122. – No 2. – P. 247–272.
15. Luedtke, J. A branch-and-cut decomposition algorithm for solving chance-constrained mathematical programs with finite support / J. Luedtke // Mathematical Programming. – 2014. – V. 146. – No 1–2. – P. 219–244.
16. Günlük, O. Mixing mixed-integer inequalities / O. Günlük, Y. Pochet // Mathematical Programming. – 2001. – V. 90. – No 3. – P. 429–457.
17. Peña-Ordieres, A. Solving Chance-Con-strained Problems via a Smooth Sample-Based Nonlinear Approximation / A. Peña-Ordieres, J. Luedtke, A. Wächter // Cornell University Home-pape. Eprint arXiv:1905.07377. – 2019. URL: https://arxiv.org/abs/1905.07377
18. van Ackooij, W. Eventual convexity of probability constraints with elliptical distributions / W. van Ackooij, J. Malick // Mathematical Programming. – 2019. – V. 175. – No 1–2. – P. 1–27.
19. Nemirovski, A. Scenario approximations of chance constraints / A. Nemirovski // Probabilistic and randomized methods for design under uncertainty / A. Nemirovski, A. Shapiro; edited by G. Calafiore, F. Dabbene. – Springer-Verlag, London, 2006. – Р. 3–47.
20. Cheng, J. Partial sample average approx-imation method for chance constrained problems / J. Cheng, C. Gicquel, A. Lisser // Optimization Letters. – 2019. – V. 13. – No 4. – P. 657–672.
21. Baker, K. Efficient relaxations for joint chance constrained AC optimal power flow / K. Baker, B. Toomey // Electric Power Systems Research. – 2017. – No 148. – P. 230–236.
22. Ran, D. Robust Approximations to Joint Chance-constrained Problems / D. Ran, L. I. Guo-Xiang, L.I. Qi-Qiang // Acta Autom. Sin. – 2015. – V. 41. – No 10. – P. 1772–1777.
23. Zhao, M. Strong inequalities for chance- constrained program / M. Zhao, K. Huang, B. Zeng // Optimization-Online. – 2014. URL: http://www.optimization-on-line.org/DB_FILE/2014/11/4634.pdf
24. Roald, L. Chance-constrained AC optimal power flow: Reformulations and efficient algorithms / L. Roald, G. Andersson // IEEE Transactions on Power Systems. – 2018. – V. 33. – No 3. – P. 2906–2918.
25. Nemirovski, A. Convex approximations of chance constrained programs / A. Nemirovski, A. Shapiro // SIAM Journal on Optimization. – 2006. – V. 17. – No 4. – P. 969–996.
26. Watson, J.-P. Scalable heuristics for a class of chance-constrained stochastic programs / J.-P. Watson, R. J. B. Wets, D. L. Woodruff // INFORMS Journal on Computing. – 2010. – V. 22. – No 4. – P. 543–554.
27. Maußner, J. Optimization under uncertainty in chemical engineering: Comparative evaluation of unscented transformation methods and cubature rules / J. Maußner, F. Hannsjörg // Chemical Engineering Science. – 2018. – V. 183. – P. 329–345.
28. Joint Chance Constraints Under Mean and Dispersion Information / G. A. Hanasusanto [and etc.] // Operations Research. – 2017. – V. 65. – No 3. – P. 751–767.
29. Misra, S. Learning for Constrained Optimization: Identifying Optimal Active Constraint Sets / S. Misra, L. Roald, Y. Ng // URL: https://arxiv.org/pdf/1802.09639
30. Optimization of Chemical Process Design with Chance Constraints by an Iterative Partitioning Approach / G. M. Ostrovsky [and etc.] // Industrial & Engineering Chemistry Research. – 2015. – V. 13. – No 54. – P. 3412–3429.
31. Ostrovsky, G. M. Optimal design of chemical processes under uncertainty / G. M. Ostrovsky, T. V. Lapteva, N. N. Ziyatdinov // Theoretical Foundations Of Chemical Engineering. – 2014. – V. 48. – No 5. – P. 583–593.
32. Ke, S. Filter Trust Region Method for Nonlinear SemiInfinite Programming Problem / S. Ke, X. Chun, L. Ren // Mathematical Problems in Engineering. – 2018. – V. 2018. – P. 1–9.
Опубликован
2019-08-27
Как цитировать
Лаптева, Т. В., Зиятдинов, Н. Н., & Нгуен, Т. К. (2019). Вычисление объединенных мягких ограничений в задачах проектирования оптимальных технологических систем. Вестник ВГУ. Серия: Системный анализ и информационные технологии, (3), 18-28. https://doi.org/10.17308/sait.2019.3/1302
Выпуск
Раздел
Математические методы системного анализа и управления
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