Multi-Disciplinary Design Optimization of a Reentry Capsule Using Multi-Objective Differential Evolution (MODE) Algorithm

Md. Shaishab Ahmed Shetu; Tawfiqur Rahman; Ziad Bin Abdul Awal

doi:10.57159/jcmm.5.3.26733

Authors

Md. Shaishab Ahmed Shetu Department of Space System Engineering, Aviation and Aerospace University, Bangladesh
Tawfiqur Rahman Department of Space System Engineering, Aviation and Aerospace University, Bangladesh https://orcid.org/0000-0002-4919-2782
Ziad Bin Abdul Awal Department of Space System Engineering, Aviation and Aerospace University, Bangladesh https://orcid.org/0000-0001-7456-0957

DOI:

https://doi.org/10.57159/jcmm.5.3.26733

Keywords:

Differential Evolution, Latin Hypercube Sampling (LHS), Multidisciplinary Design Optimization (MDO), Pareto Optimal, Reentry Capsule, Sensitivity Analysis

Abstract

This paper presents a novel application of the Multi-Objective Differential Evolution (MODE) algorithm for the multidisciplinary design optimization of a reentry capsule. The primary design aims at maximizing the center of pressure position (Xcp) to enhance longitudinal aerodynamic stability, while simultaneously minimizing the wetted surface area (As) to reduce thermal load and structural mass, all under a volumetric constraint (V > 3.0 m³) for payload accommodation. A sphere-cone-flare geometry is parameterized using five key design variables: nose radius (RN), cone half-angle (θ1), cone length (l1), flare angle (θ2), and flare length (l2). The constrained design space is methodically navigated by the MATLAB implemented framework, which produces a Pareto optimal front that performs noticeably better than a benchmark study using NSGA-II. The optimized design strategy consistently converges to a semi-blunt configuration with parameter values of θ1 = 15.0°, l1, l2 → 1.0 m, and RN ≈ 0.462 m. This design achieves an Xcp of 1.514 m with an As of only 10.776 m², a significant improvement over previous results. The most important driver is the flare length (l2) for both objectives, according to a comprehensive global sensitivity analysis using Latin Hypercube Sampling (LHS) and Spearman rank correlation, which quantifies the impact of each design parameter. In addition to establishing a validated, Pareto optimal design family that pushes the boundaries of reentry vehicle conceptual design, this study validates MODE as a reliable and effective optimizer for complex aerospace design problems.

References

[1] Y. E. Arslantaş, T. Oehlschlägel, and M. Sagliano, "Safe landing area determination for a moon lander by reachability analysis," Acta Astronautica, vol. 128, pp. 607–615, 2016.

[2] U. Eren, D. Dueri, and B. Açıkmeşe, "Constrained reachability and controllability sets for planetary precision landing via convex optimization," Journal of Guidance, Control, and Dynamics, vol. 38, no. 11, pp. 2067–2083, 2015.

[3] R. Bhusal and K. Subbarao, "Nonlinear state estimation of re-entry vehicle using polynomial chaos-based ensemble filtering," in AAS/AIAA Astrodynamics Specialists Conference, 2020. AAS Paper 20-578.

[4] K. Balachandran and K. Subbarao, "Optimal trajectory control of a space shuttle like re-entry vehicle entering triton," in AAS/AIAA Astrodynamics Specialists Conference, 2020. AAS Paper 20-771.

[5] S. Mane, "Space radiation and its effects on environment: Conceptual study," Space, vol. 11, no. 1, 2022.

[6] J. Patel and K. Subbarao, "Reachability analysis for atmospheric reentry vehicle," Journal of Guidance, Control, and Dynamics, vol. 47, no. 1, pp. 133–142, 2024.

[7] J. Theisinger, "Hypersonic entry aeroshell shape optimization," ae8900 ms special problems report, Georgia Institute of Technology, Atlanta, GA, USA, 2007.

[8] P. Priyadarshi and S. Mittal, "Multi-objective multi-disciplinary design optimization of a semi-ballistic reentry module," in 13th AIAA/ISSMO Multidisciplinary Analysis Optimization Conference, p. 9127, 2010.

[9] Y. Shi, M. Xu, and Z. M. Wang, "Integrated optimization of aerodynamic shape with trajectory for aircraft in conceptual design," in Proceedings of the 2011 International Conference on Electronic and Mechanical Engineering and Information Technology, vol. 7, pp. 3808–3811, IEEE, 2011.

[10] 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, no. 147, pp. 10–19, 2002.

[11] J. E. Johnson, R. P. Starkey, and M. J. Lewis, "Aerothermodynamic optimization of reentry heat shield shapes for a crew exploration vehicle," Journal of Spacecraft and Rockets, vol. 44, no. 4, pp. 849–859, 2007.

[12] J. Johnson, M. Lewis, and R. Starkey, "Entry heat shield optimization for Mars return," in 47th AIAA Aerospace Sciences Meeting including The New Horizons Forum and Aerospace Exposition, p. 518, 2013.

[13] S. Kang, J. Gwon, H. Yeo, H. Nam, and K. H. Kim, "Multi-objective design optimization of reentry capsule using a machine learning-based aero-thermodynamic surrogate model," Journal of Computational Fluids Engineering, vol. 30, no. 3, pp. 20–40, 2025.

[14] 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.

[15] A. Aponte, Multidisciplinary Optimization of a Spacecraft Heat Shield for Atmospheric Entry: Coupling Non-Equilibrium Fluid Dynamics and Material Response. PhD thesis, University of Illinois at Urbana-Champaign, 2023.

[16] A. Meo, A. Aponte, A. Munafò, G. Gori, and M. Panesi, "A Bayesian framework for the shape optimization of atmospheric reentry vehicles," in AIAA Aviation Forum and Ascend 2024, p. 3563, 2024.

[17] R. Monti, M. De Stefano Fumo, and R. Savino, "Thermal shielding of a reentry vehicle by ultra-high-temperature ceramic materials," Journal of Thermophysics and Heat Transfer, vol. 20, no. 3, pp. 500–506, 2006.

[18] K. Price, "An introduction to differential evolution," in New Ideas in Optimization, pp. 77–106, McGraw-Hill Publishing Company, 1999.

[19] M. Nosratollahi, M. Hosseini, and A. Adami, "Multidisciplinary design optimization of a controllable reentry capsule for minimum landing velocity," in 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, p. 3009, 2010.

[20] M. Nosratollahi, M. Mortazavi, A. Adami, and M. Hosseini, "Multidisciplinary design optimization of a reentry vehicle using genetic algorithm," Aircraft Engineering and Aerospace Technology, vol. 82, no. 3, pp. 194–203, 2010.

[21] R. Arora and P. Kumar, "Aerodynamic shape optimization of a re-entry capsule," in AIAA Atmospheric Flight Mechanics Conference and Exhibit, p. 5394, 2003.

[22] R. Storn and K. Price, "Differential evolution: A simple and efficient heuristic for global optimization over continuous spaces," Journal of Global Optimization, vol. 11, no. 4, pp. 341–359, 1997.

[23] R. Storn, "Differential evolution: A simple and efficient adaptive scheme for global optimization over continuous spaces," Tech. Rep. 11, International Computer Science Institute, 1995.

[24] M. J. Strens and A. W. Moore, "Policy search using paired comparisons," Journal of Machine Learning Research, vol. 3, pp. 921–950, 2002.

[25] H. A. Abbass, R. Sarker, and C. Newton, "PDE: A Pareto-frontier differential evolution approach for multi-objective optimization problems," in Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No. 01TH8546), vol. 2, pp. 971–978, IEEE, 2001.

[26] N. Narasaiah, R. Varaprasad, V. S. Rao, V. Krishnamurty, and M. K. Sanyal, "Space capsule recovery: Evaluation of risk factors, safety plans and procedures and design of experiments for systems qualification," Acta Astronautica, vol. 65, no. 9-10, pp. 1224–1230, 2009.

[27] A. Del Vecchio, G. Marino, J. Thoemel, F. Ratti, and J. Gavira Izquierdo, "EXPERT: The ESA experimental re-entry vehicle: Overview of the experiments and payloads qualified and accepted for the flight," in 39th AIAA Fluid Dynamics Conference, p. 4221, 2009.

[28] F. F. J. Schrijer, F. Scarano, and B. W. van Oudheusden, "Experiments on hypersonic boundary layer separation and reattachment on a blunted cone-flare using quantitative infrared thermography," in 12th AIAA International Space Planes and Hypersonic Systems and Technologies Conference, Norfolk, Virginia, pp. 1–8, American Institute of Aeronautics and Astronautics, 2003. AIAA-2003-6967.

[29] M. D. McKay, R. J. Beckman, and W. J. Conover, "A comparison of three methods for selecting values of input variables in the analysis of output from a computer code," Technometrics, vol. 42, no. 1, pp. 55–61, 2000.

[30] S. Khan, S. B. Rayhan, M. M. Rahman, J. Sultana, and G. Varga, "Optimized ANN model for predicting buckling strength of metallic aerospace panels under compressive loading," Metals, vol. 15, no. 6, p. 666, 2025.