دانش و فناوری هوافضا

دانش و فناوری هوافضا

تحلیل همگرایی جبهه‌های پارتو در بهینه‎ سازی سه‎هدفه طراحی یک کپسول زیستی به روش شاخص اَبَرحجم نسبی

نوع مقاله : مقاله پژوهشی

نویسندگان
1 استادیار پژوهشگاه هوافضا، وزارت علوم، تحقیقات و فناوری
2 دانشجوی دکتری پژوهشگاه هوافضا، وزارت علوم، تحقیقات و فناوری
چکیده
این مقاله به بررسی روش شاخص اَبَرحجم نسبی (RHV) به‌عنوان ابزاری مؤثر برای ارزیابی همگرایی در مسائل بهینه‌سازی چندهدفه می‌پردازد. اکثر مسائل مهندسی فاقد جبهه پارتوی واقعی هستند و ارزیابی همگرایی در آن‌ها با چالش مواجه می‌شود. برای این منظور، الگوریتم ژنتیک چندهدفه (MOGA) برای هر مسئله ۳۰ بار اجرا می‌شود تا ۳۰ جبهه پارتو تقریبی به دست آید. سپس تمامی راه‌حل‌های حاصل با هم ترکیب شده و یک فیلتر غلبه پارتو برای شناسایی راه‌حل‌های غیرمغلوب اعمال می‌شود تا جبهه پارتوی واقعی و ابرحجم مرتبط با آن تعیین گردد. این روش برای سه مسئله بهینه‌سازی سه‌هدفه در طراحی کپسول زیستی فضایی مورد استفاده قرار گرفته است. تحلیل حساسیت پارامترهای طراحی با روش نمونه‌برداری ابرمکعب لاتین (LHS) و اجرای MOGA نشان داد که هر سه مسئله در کمتر از ۳۷۳ نسل به همگرایی رضایت‌بخش رسیدند، که تعداد نسل مناسبی برای مسائل چندهدفه مقید محسوب می‌شود و کارآمدی روش پیشنهادی را نشان می‌دهد. نتایج حاکی از تولید جبهه‌های پارتو سه‌بعدی با کیفیت بالا (شاخص RHV بین ۰.۸۷ تا ۰.۹۳) است و مقایسه با داده‌های کپسول بومی نشان داد برخی پیکربندی‌ها بهینه بوده و برخی دیگر نیاز به بازنگری در پارامترها دارند.
کلیدواژه‌ها

موضوعات


عنوان مقاله English

Convergence analysis of pareto fronts in three-objective optimization of a bio-capsule design using relative hypervolume metric

نویسندگان English

hassan Naseh 1
Hadiseh Karimaei 1
Mohammad Lesani fadafan 2
1 Assistant Professor of Aerospace Research Institute, Ministry of Science, Research and Technology, Tehran, Iran
2 Ph.D. Student of Aerospace Research Institute, Ministry of Science, Research and Technology, Tehran
چکیده English

This paper examines the application of the Relative Hypervolume (RHV) metric as a powerful tool for assessing convergence in multi-objective optimization problems. Most engineering optimization problems lack a true Pareto front, which makes convergence assessment challenging. In this approach, the Multi-Objective Genetic Algorithm (MOGA) is executed 30 times for each problem, generating 30 approximate Pareto fronts. All solutions from these runs are then combined into a merged set, and a Pareto dominance filter is applied to identify the non-dominated solutions, allowing the determination of the true Pareto front along with its associated hypervolume. The method is applied to three three-objective optimization problems in the design of a space biocapsule. Sensitivity analysis using Latin Hypercube Sampling (LHS) and MOGA execution showed that all three problems achieved satisfactory convergence in fewer than 373 generations, which is appropriate for constrained multi-objective optimization problems and demonstrates the efficiency of the proposed approach. Results indicate that the method successfully generates high-quality three-dimensional Pareto fronts with RHV values ranging from 0.87 to 0.93. Comparison with native capsule data revealed that while some configurations were optimal, others required redesign of parameters.

کلیدواژه‌ها English

Bio-capsule
Design optimization
Tri-objective
Relative Hypervolume
Multi-Objective GA
[1] K. Deb, Multi-objective optimization using evolutionary algorithms. New York, NY: John Wiley & Sons, Inc., 2001.
[2] E. Zitzler and L. Thiele, “Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach,” IEEE Transactions on Evolutionary Computation, vol. 3, no. 4, pp. 257–271, 2002.
[3] H. Ishibuchi, R. Imada, Y. Setoguchi, and Y. Nojima, “Reference point specification in hypervolume calculation for fair comparison and efficient search,” in Proceedings of the Genetic and Evolutionary Computation Conference, pp. 585–592, July 2017.
[4] N. Beume, C. M. Fonseca, M. Lopez-Ibanez, L. Paquete, and J. Vahrenhold, “On the complexity of computing the hypervolume indicator,” IEEE Transactions on Evolutionary Computation, vol. 13, no. 5, pp. 1075–1082, 2009.
[5] A. Liefooghe and B. Derbel, “A correlation analysis of set quality indicator values in multiobjective optimization,” in Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2016), pp. 581–588, July 2016.
[6] M. Tava and S. Suzuki, “Multidisciplinary design optimization of the shape and trajectory of a reentry vehicle,” Transactions of the Japan Society for Aeronautical and Space Sciences, vol. 45, pp. 10–19, 2002.
[7] R. Arora and P. Kumar, “Aerodynamic shape optimization of a re-entry capsule,” in AIAA Conference Proceedings, 2003.
[8] J. Theisinger, R. Braun, and I. Clark, “Aerothermodynamic shape optimization of hypersonic entry aeroshells,” in 13th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, 2010.
[9] N. Mehran, M. Mortazavi, A. Adami, and M. Hosseini, “Multidisciplinary design optimization of a reentry vehicle using genetic algorithm,” Aircraft Engineering and Aerospace Technology, vol. 82, pp. 194–203, 2010.
[10] A. Adami, N. Mehran, M. Mortazavi, and M. Hosseini, “Multidisciplinary design optimization of a manned reentry mission considering trajectory and aerodynamic configuration,” in Proceedings of the 5th International Conference on Recent Advances in Space Technologies (RAST2011), pp. 598–603, 2011.
[11] D. Dirkx and E. Mooij, “Optimization of entry-vehicle shapes during conceptual design,” Acta Astronautica, vol. 94, pp. 198–214, 2014.
[12] N. Stander and T. Goel, “An assessment of geometry-based convergence metrics for multi-objective evolutionary algorithms,” in 13th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, p. 9232, 2010.
[13] I. Bunescu, M. Pricop, G. Stoican, and A. Dina, “Aerothermodynamic shape optimization for re-entry capsule using genetic algorithms,” INCAS Bulletin, 2019.
[14] M. Brchnelova and E. Mooij, “Re-entry shape optimisation using the axisymmetric analogue method with modified Newtonian technique resolved inviscid flowfield,” in AIAA Conference Proceedings, 2021.
[15] H. Naseh, H. Karimaei, and M. Lesani, “Two-objective structural optimization of space capsule with thin-walled cylindrical approximation,” Journal of Space Science, Technology & Applications (in Persian), vol. 2, no. 2, pp. 158–170, 2022.
[16] M. Kabganian, S. M. Hashemi, and J. Roshanian, “Multidisciplinary design optimization of a re-entry spacecraft via Radau pseudospectral method,” Applied Mechanics, vol. 3, no. 4, pp. 1176–1189, 2022.
[17] A. Aprovitola, L. Iuspa, G. Pezzella, and A. Viviani, “Aerodynamic optimization of airfoils shape for atmospheric flight on Mars planet,” Acta Astronautica, vol. 212, pp. 580–594, 2023.
[18] A. Aprovitola, L. Iuspa, G. Pezzella, and A. Viviani, “Flows past airfoils for the low-Reynolds number conditions of flying in Martian atmosphere,” Acta Astronautica, vol. 221, pp. 94–107, 2024.
[19] H. Naseh, H. Karimaei, and M. Lesani Fadafan, “Multi-objective design optimization of a re-entry bio-capsule based on sensitivity analysis of the main configuration parameters,” Aerospace Knowledge and Technology Journal, vol. 13, no. 2, pp. 81–94, 2025.
[20] T. J. Sooy and R. Z. Schmidt, “Aerodynamic predictions, comparisons, and validations using Missile DATCOM (97) and Aeroprediction 98 (AP98),” Journal of Spacecraft and Rockets, vol. 42, pp. 257–265, 2005.
[21] C. Thibault, N. Merlinge, and R. Wuilbercq, “3DoF simulation model and specific aerodynamic control capabilities for SpaceX's Starship-like atmospheric reentry vehicle,” 2019. [Online preprint].
[22] A. Aprovitola, N. Montella, L. Iuspa, G. Pezzella, and A. Viviani, “An optimal heat-flux targeting procedure for LEO re-entry of reusable vehicles,” Aerospace Science and Technology, 2021.
[23] W. G. Vincenti, J. W. Boyd, and G. E. Bugos, “H. Julian Allen: an appreciation,” Annual Review of Fluid Mechanics, vol. 39, pp. 1–17, 2007.
[24] D. Montgomery, Design and analysis of experiments, 8th ed. Hoboken, NJ: John Wiley & Sons, Inc., 2013.
[25] A. Saltelli, M. Ratto, T. Andres, F. Campolongo, J. Cariboni, D. Gatelli, M. Saisana, and S. Tarantola, Global Sensitivity Analysis: The Primer. Chichester: John Wiley & Sons, 2008.
[26] X. Liu, F. Wang, Y. Liu, and L. Li, “A multi-objective black-winged kite algorithm for multi-UAV cooperative path planning,” Drones, vol. 9, no. 2, p. 118, 2025.