Skip to main content

Hull-form stochastic optimization via computational-cost reduction methods


The paper shows how cost-reduction methods can be synergistically combined to enable high-fidelity hull-form optimization under stochastic conditions. Specifically, a multi-objective hull-form optimization is presented, where (a) physics-informed design-space dimensionality reduction, (b) adaptive metamodeling, (c) uncertainty quantification (UQ) methods, and (d) global multi-objective algorithm are efficiently and effectively combined to achieve high-fidelity simulation-based design optimization (SBDO) solutions. The application pertains to the multi-objective optimization for resistance and seakeeping (operational efficiency and effectiveness) of a destroyer-type vessel. Two hierarchical multi-objective SBDO problems are presented, with a level of complexity decreasing from the most general (stochastic sea state, heading, and speed) to the least general (deterministic regular wave, at fixed sea state, heading, and speed). Design-space dimensionality reduction is based on a generalized Karhunen-Loève expansion of the shape modification vector combined with low-fidelity-based physical variables. A multi-objective deterministic particle swarm optimization algorithm is applied to a stochastic radial-basis-function metamodel that provides objective predictions. UQ methods include Gaussian quadrature and metamodel-based importance sampling. Numerical simulations are based on unsteady Reynolds-averaged Navier–Stokes and potential flow solvers. The paper shows and discusses the joint effort of computational-cost reduction methods in enabling high-fidelity SBDO, providing guidelines for future research directions in this area.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26


  1. Anderson T, Gerhard K, Sievenpiper B (2013) Operational ship utilization modeling of the DDG-51 class. In: Proceedings of ASNE day 2013 symposia

  2. Bales SL (1983) Designing ships to the natural environment. Naval Eng J 95(2):31–40

    Article  Google Scholar 

  3. Bassanini P, Bulgarelli U, Campana EF, Lalli F (1994) The wave resistance problem in a boundary integral formulation. Surv Math Ind 4:151–194

    MathSciNet  MATH  Google Scholar 

  4. Campana EF, Peri D, Tahara Y, Stern F (2006) Shape optimization in ship hydrodynamics using computational fluid dynamics. Comput Methods Appl Mech Eng 196(1–3):634–651

    MATH  Article  Google Scholar 

  5. Chen X, Diez M, Kandasamy M, Zhang Z, Campana EF, Stern F (2015) High-fidelity global optimization of shape design by dimensionality reduction, metamodels and deterministic particle swarm. Eng Optim 47(4):473–494

    Article  Google Scholar 

  6. Clerc M (2006) Stagnation analysis in particle swarm optimization or what happens when nothing happens. Technical report.

  7. Coello CAC, Pulido GT, Lechuga MS (2004) Handling multiple objectives with particle swarm optimization. IEEE Trans Evol Comput 8(3):256–279

    Article  Google Scholar 

  8. Coppedè A, Gaggero S, Vernengo G, Villa D (2019) Hydrodynamic shape optimization by high fidelity CFD solver and gaussian process based response surface method. Appl Ocean Res 90:101841

    Article  Google Scholar 

  9. Dasgupta D, Michalewicz Z (2013) Evolutionary algorithms in engineering applications. Springer, Berlin

    MATH  Google Scholar 

  10. Dawson CW (1977) A practical computer method for solving ship-wave problems. In: Proceedings of the 2nd international conference on numerical ship hydrodynamics, Berkeley, pp 30–38

  11. Deb K, Jain H (2013) An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part i: solving problems with box constraints. IEEE Trans Evol Comput 18(4):577–601

    Article  Google Scholar 

  12. Deb K, Nain PK (2007) An evolutionary multi-objective adaptive meta-modeling procedure using artificial neural networks. Evolutionary computation in dynamic and uncertain environments. Springer, Berlin, pp 297–322

    Chapter  Google Scholar 

  13. Diez M, Broglia R, Durante D, Olivieri A, Campana EF, Stern F (2018) Statistical assessment and validation of experimental and computational ship response in irregular waves. J Verif Valid Uncertain Quantif 3(2):021004

    Article  Google Scholar 

  14. Diez M, Campana EF, Stern F (2015) Design-space dimensionality reduction in shape optimization by Karhunen-Loève expansion. Comput Methods Appl Mech Eng 283:1525–1544

    MATH  Article  Google Scholar 

  15. Diez M, Campana EF, Stern F (2018) Stochastic optimization methods for ship resistance and operational efficiency via CFD. Struct Multidiscip Optim 57(2):735–758

    MathSciNet  Article  Google Scholar 

  16. Diez M, He W, Campana EF, Stern F (2014) Uncertainty quantification of delft catamaran resistance, sinkage and trim for variable froude number and geometry using metamodels, quadrature and Karhunen-Loève expansion. J Mar Sci Technol 19(2):143–169

    Article  Google Scholar 

  17. Diez M, Serani A, Stern F, Campana EF (2016) Combined geometry and physics based method for design-space dimensionality reduction in hydrodynamic shape optimization. In: Proceedings of the 31st symposium on naval hydrodynamics, Monterey, CA, USA

  18. Durante D, Broglia R, Diez M, Olivieri A, Campana E, Stern F (2020) Accurate experimental benchmark study of a catamaran in regular and irregular head waves including uncertainty quantification. Ocean Eng 195:106685

    Article  Google Scholar 

  19. D’Agostino D, Serani A, Diez M (2020) Design-space assessment and dimensionality reduction: an off-line method for shape reparameterization in simulation-based optimization. Ocean Eng 197:106852

    Article  Google Scholar 

  20. Giannakoglou K (2002) Design of optimal aerodynamic shapes using stochastic optimization methods and computational intelligence. Prog Aerosp Sci 38(1):43–76

    Article  Google Scholar 

  21. Grigoropoulos G, Campana E, Diez M, Serani A, Goren O, Sariöz K, Danişman D, Visonneau M, Queutey P, Abdel-Maksoud M, et al. (2017) Mission-based hull-form and propeller optimization of a transom stern destroyer for best performance in the sea environment. In: VII International conference on computational methods in marine engineering MARINE2017

  22. Harries S, Abt C (2019) Faster turn-around times for the design and optimization of functional surfaces. Ocean Eng 193:106470

    Article  Google Scholar 

  23. He W, Diez M, Zou Z, Campana EF, Stern F (2013) URANS study of delft catamaran total/added resistance, motions and slamming loads in head sea including irregular wave and uncertainty quantification for variable regular wave and geometry. Ocean Eng 74:189–217

    Article  Google Scholar 

  24. Huang J, Carrica PM, Stern F (2008) Semi-coupled air/water immersed boundary approach for curvilinear dynamic overset grids with application to ship hydrodynamics. Int J Numer Methods Fluids 58(6):591–624

    MATH  Article  Google Scholar 

  25. Iuliano E, Pérez EA (2016) Application of surrogate-based global optimization to aerodynamic design. Springer, Berlin

    Book  Google Scholar 

  26. Jin R, Chen W, Sudjianto A (2002) On sequential sampling for global metamodeling in engineering design. In: International design engineering technical conferences and computers and information in engineering conference 36223, pp 539–548

  27. Kennedy J, Eberhart RC (1995) Particle swarm optimization. In: Proceedings of the fourth IEEE conference on neural networks, Piscataway, NJ, pp 1942–1948.

  28. Kennell CG, White BL, Comstock EN (1985) Innovative naval designs for north atlantic opeartions. SNAME Trans 93:261–281

    Google Scholar 

  29. Larson J, Menickelly M, Wild SM (2019) Derivative-free optimization methods. Acta Numer 28:287–404

    MathSciNet  MATH  Article  Google Scholar 

  30. Larsson L, Stern F, Visonneau M, Hirata N, Hino T, Kim J (2015) Proceedings, Tokyo 2015 workshop on cfd in ship hydrodynamics. In: Tokyo CFD workshop

  31. Lin Y, He J, Li K (2018) Hull form design optimization of twin-skeg fishing vessel for minimum resistance based on surrogate model. Adv Eng Softw 123:38–50

    Article  Google Scholar 

  32. Longo J, Stern F (2005) Uncertainty assessment for towing tank tests with example for surface combatant DTMB model 5415. J Ship Res 49(1):55–68

    Article  Google Scholar 

  33. Lukaczyk T, Palacios F, Alonso JJ, Constantine P (2014) Active subspaces for shape optimization. In: Proceedings of the 10th AIAA multidisciplinary design optimization specialist conference, National Harbor, Maryland, USA, 13–17 January

  34. Meyers WG, Baitis AE (1985) SMP84: improvements to capability and prediction accuracy of the standard ship motion program SMP81. In: Technical report. SPD-0936-04, David Taylor naval ship research and development center

  35. Miao A, Zhao M, Wan D (2020) CFD-based multi-objective optimisation of S60 catamaran considering demihull shape and separation. Appl Ocean Res 97:102071

    Article  Google Scholar 

  36. Michel WH (1999) Sea spectra revisited. Mar Technol 36(4):211–227

    Google Scholar 

  37. Mirjalili S (2016) Dragonfly algorithm: a new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems. Neural Comput Appl 27(4):1053–1073

    MathSciNet  Article  Google Scholar 

  38. Mirjalili S, Gandomi AH, Mirjalili SZ, Saremi S, Faris H, Mirjalili SM (2017) Salp swarm algorithm: a bio-inspired optimizer for engineering design problems. Adv Eng Softw 114:163–191

    Article  Google Scholar 

  39. Mousaviraad SM (2010) CFD prediction of ship response to extreme winds and/or waves. Ph.D. thesis, University of Iowa, Iowa City, Iowa, USA.

  40. Olivieri A, Pistani F, Avanzini A, Stern F, Penna R (2001) Towing tank, sinkage and trim, boundary layer, wake, and free surface flow around a naval combatant INSEAN 2340 model. In: Technical report, DTIC

  41. Pellegrini R, Serani A, Leotardi C, Iemma U, Campana EF, Diez M (2017) Formulation and parameter selection of multi-objective deterministic particle swarm for simulation-based optimization. Appl Soft Comput 58:714–731

    Article  Google Scholar 

  42. Pellegrini R, Serani A, Liuzzi G, Rinaldi F, Lucidi S, Diez M (2020) Hybridization of multi-objective deterministic particle swarm with derivative-free local searches. Mathematics 8(4):546

    Article  Google Scholar 

  43. Piazzola C, Tamellini L, Pellegrini R, Broglia R, Serani A, Diez M (2020) Uncertainty quantification of ship resistance via multi-index stochastic collocation and radial basis function surrogates: a comparison. In: AIAA AVIATION 2020 FORUM, p 3160

  44. Pinto A, Peri D, Campana EF (2004) Global optimization algorithms in naval hydrodynamics. Ship Technol Res 51(3):123–133

    Article  Google Scholar 

  45. Pinto A, Peri D, Campana EF (2007) Multiobjective optimization of a containership using deterministic particle swarm optimization. J Ship Res 51(3):217–228

    Article  Google Scholar 

  46. Quagliarella D, Serani A, Diez M, Pisaroni M, Leyland P, Montagliani L, Iemma U, Gaul NJ, Shin J, Wunsch D, et al. (2019) Benchmarking uncertainty quantification methods using the NACA 2412 airfoil with geometrical and operational uncertainties. In: AIAA Aviation 2019 Forum, p 3555

  47. Raghavan B, Breitkopf P, Tourbier Y, Villon P (2013) Towards a space reduction approach for efficient structural shape optimization. Struct Multidiscip Optim 48:987–1000

    Article  Google Scholar 

  48. Sahinidis NV (2004) Optimization under uncertainty: state-of-the-art and opportunities. Comput Chem Eng 28(6–7):971–983

    Article  Google Scholar 

  49. Schlichting H, Gersten K (2000) Boundary-layer theory. Springer, Berlin

    MATH  Book  Google Scholar 

  50. Serani A, Campana EF, Diez M, Stern F (2017) Towards augmented design-space exploration via combined geometry and physics based Karhunen-Loève expansion. In: 18th AIAA/ISSMO multidisciplinary analysis and optimization conference (MA&O), AVIATION 2017. Denver, USA, June 5–9

  51. Serani A, D’Agostino D, Campana EF, Diez M (2019) Assessing the interplay of shape and physical parameters by unsupervised nonlinear dimensionality reduction methods. J Ship Res 64(4):313–327

    Article  Google Scholar 

  52. Serani A, Diez M (2017) Are random coefficients needed in particle swarm optimization for simulation-based ship design? In: Proceedings of the 7th international conference on computational methods in marine engineering (Marine 2017)

  53. Serani A, Diez M (2018) Shape optimization under stochastic conditions by design-space augmented dimensionality reduction. In: 19th AIAA/ISSMO multidisciplinary analysis and optimization conference (MA&O), AVIATION 2018. Atlanta, USA, June 25–29

  54. Serani A, Diez M, Wackers J, Visonneau M, Stern F (2019) Stochastic shape optimization via design-space augmented dimensionality reduction and RANS computations. In: AIAA Scitech 2019 Forum. San Diego, Californa, USA, January 7–11

  55. Serani A, Leotardi C, Iemma U, Campana EF, Fasano G, Diez M (2016) Parameter selection in synchronous and asynchronous deterministic particle swarm optimization for ship hydrodynamics problems. Appl Soft Comput 49:313–334

    Article  Google Scholar 

  56. Serani A, Pellegrini R, Wackers J, Jeanson CE, Queutey P, Visonneau M, Diez M (2019) Adaptive multi-fidelity sampling for CFD-based optimisation via radial basis function metamodels. Int J Comput Fluid Dyn 33(6–7):237–255

    Article  Google Scholar 

  57. Stern F, Volpi S, Gaul NJ, Choi K, Diez M, Broglia R, Durante D, Campana E, Iemma U (2017) Development and assessment of uncertainty quantification methods for ship hydrodynamics. In: 55th AIAA aerospace sciences meeting, p 1654

  58. Tezdogan T, Shenglong Z, Demirel YK, Liu W, Leping X, Yuyang L, Kurt RE, Djatmiko EB, Incecik A (2018) An investigation into fishing boat optimisation using a hybrid algorithm. Ocean Eng 167:204–220

    Article  Google Scholar 

  59. Tezzele M, Salmoiraghi F, Mola A, Rozza G (2018) Dimension reduction in heterogeneous parametric spaces with application to naval engineering shape design problems. Adv Model Simul Eng Sci 5(1):25

    Article  Google Scholar 

  60. Theodoridis S (2015) Machine learning: a Bayesian and optimization perspective. Academic Press, New York

    Google Scholar 

  61. Uryasev S, Pardalos PM (2013) Stochastic optimization: algorithms and applications, vol 54. Springer, Berlin

    Google Scholar 

  62. Viana FAC, Simpson TW, Balabanov V, Vasilli T (2014) Special section on multidisciplinary design optimization: metamodeling in multidisciplinary design optimization: How far have we really come? AIAA J 52(4):670–690

    Article  Google Scholar 

  63. Volpi S, Diez M, Gaul N, Song H, Iemma U, Choi KK, Campana EF, Stern F (2015) Development and validation of a dynamic metamodel based on stochastic radial basis functions and uncertainty quantification. Struct Multidiscip Optim 51(2):347–368

    Article  Google Scholar 

  64. Xing T, Stern F (2010) Factors of safety for Richardson extrapolation. J Fluids Eng 132(6):061403

    Article  Google Scholar 

  65. Yang C, Huang F (2016) An overview of simulation-based hydrodynamic design of ship hull forms. J Hydrodyn Ser B 28(6):947–960

    MathSciNet  Article  Google Scholar 

  66. Yang XS (2011) Metaheuristic optimization: algorithm analysis and open problems. In: International symposium on experimental algorithms, Springer, pp 21–32

  67. Zhang S, Tezdogan T, Zhang B, Xu L, Lai Y (2018) Hull form optimisation in waves based on CFD technique. Ships Offshore Struct 13(2):149–164

    Article  Google Scholar 

  68. Zhang S, Zhang B, Tezdogan T, Xu L, Lai Y (2018) Computational fluid dynamics-based hull form optimization using approximation method. Eng Appl Comput Fluid Mech 12(1):74–88

    Google Scholar 

  69. Zhao L, Choi K, Lee I (2011) Metamodeling method using dynamic kriging for design optimization. AIAA J 49(9):2034–2046

    Article  Google Scholar 

Download references


The work is supported by the US Department of the Navy Office of Naval Research Global, NICOP grant N62909-15-1-2016, administered by Dr. Salahuddin Ahmed, Dr. Elena McCarthy, and Dr. Woei-Min Lin, and by the Italian Flagship Project RITMARE, funded by the Italian Ministry of Education. The research is performed within NATO STO Task Group AVT-252 ”Stochastic Design Optimization for Naval and Aero Military Vehicles”.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Andrea Serani.

Ethics declarations

Conflict of Interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Serani, A., Stern, F., Campana, E.F. et al. Hull-form stochastic optimization via computational-cost reduction methods. Engineering with Computers (2021).

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI:


  • Simulation-based design optimization
  • Stochastic optimization
  • Reliability-based robust design optimization
  • Physics-informed design-space dimensionality reduction
  • Adaptive metamodeling
  • Uncertainty quantification
  • Global multi-objective optimization
  • Computational fluid dynamics