Skip to main content
SpringerLink
Log in

A multi-objective DIRECT algorithm for ship hull optimization

  • Published:
Computational Optimization and Applications Aims and scope Submit manuscript

Abstract

The paper is concerned with black-box nonlinear constrained multi-objective optimization problems. Our interest is the definition of a multi-objective deterministic partition-based algorithm. The main target of the proposed algorithm is the solution of a real ship hull optimization problem. To this purpose and in pursuit of an efficient method, we develop an hybrid algorithm by coupling a multi-objective DIRECT-type algorithm with an efficient derivative-free local algorithm. The results obtained on a set of “hard” nonlinear constrained multi-objective test problems show viability of the proposed approach. Results on a hull-form optimization of a high-speed catamaran (sailing in head waves in the North Pacific Ocean) are also presented. In order to consider a real ocean environment, stochastic sea state and speed are taken into account. The problem is formulated as a multi-objective optimization aimed at (i) the reduction of the expected value of the mean total resistance in irregular head waves, at variable speed and (ii) the increase of the ship operability, with respect to a set of motion-related constraints. We show that the hybrid method performs well also on this industrial problem.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Bandyopadhyay, S., Pal, S.K., Aruna, B.: Multiobjective GAs, quantitative indices, and pattern classification. Syst. Man Cybern. B IEEE Trans. Cybern. 34(5), 2088–2099 (2004)

    Article  Google Scholar 

  2. Campana, E.F., Diez, M., Iemma, U., Liuzzi, G., Lucidi, S., Rinaldi, F., Serani, A.: Derivative-free global ship design optimization using global/local hybridization of the DIRECT algorithm. Optim. Eng. 17(1), 127–156 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  3. Chen, X., Diez, M., Kandasamy, M., Campana, E.F., Stern, F.: Design optimization of the waterjet-propelled delft catamaran in calm water using urans, design of experiments, metamodels and swarm intelligence. In: Proceedings of the 12th International Conference on Fast Sea Transportation (FAST2013), Amsterdam, The Netherlands, pp. 1–12 (2013)

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

    Article  Google Scholar 

  5. Conn, A., Scheinberg, K., Vicente, L.N.: Introduction to Derivative-Free Optimization, vol. 8. SIAM, New Delhi (2009)

    Book  MATH  Google Scholar 

  6. Custódio, A.L., Madeira, J.F.A., Vaz, A.I.F., Vicente, L.N.: Direct multisearch for multiobjective optimization. SIAM J. Optim. 21(3), 1109–1140 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  7. Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)

    Article  Google Scholar 

  8. Di Pillo, G., Liuzzi, G., Lucidi, S., Piccialli, V., Rinaldi, F.: A direct-type approach for derivative-free constrained global optimization. Comput. Optim. Appl. 65(2), 361–397 (2016)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  10. Diez, M., Chen, X., Campana, E.F., Stern, F.: Reliability-based robust design optimization for ships in real ocean environment. In: Proceedings of the 12th International Conference on Fast Sea Transportation (FAST2013), Amsterdam, The Netherlands, pp. 1–17 (2013)

  11. Dolan, E.D., Moré, J.J.: Benchmarking optimization software with performance profiles. Math. Program. 91(2), 201–213 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  12. Ehrgott, M.: Multicriteria Optimization, 2nd edn. Springer, Berlin (2005)

    MATH  Google Scholar 

  13. Evtushenko, Y.G., Posypkin, M.A.: Nonuniform covering method as applied to multicriteria optimization problems with guaranteed accuracy. Comput. Math. Math. Phys. 53(2), 144–157 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  14. Evtushenko, Y.G., Posypkin, M.A.: A deterministic algorithm for global multi-objective optimization. Optim. Methods Softw. 29(5), 1005–1019 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  15. Gablonsky, J.M., Kelley, C.T.: A locally-biased form of the DIRECT algorithm. J. Global Optim. 21(1), 27–37 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  16. Gen, M., Cheng, R., Lin, L.: Multiobjective Genetic Algorithms, pp. 1–47. Springer, Berlin (2008)

    Google Scholar 

  17. He, J., Verstak, A., Watson, L.T., Sosonkina, M.: Design and implementation of a massively parallel version of DIRECT. Comput. Optim. Appl. 40, 217–245 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  18. He, W., Diez, M., Zou, Z., Campana, E.F., Stern, F.: 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 (2013)

    Article  Google Scholar 

  19. Jones, D.R., Perttunen, C.D., Stuckman, B.E.: Lipschitzian optimization without the Lipschitz constant. J. Optim. Theory Appl. 79(1), 157–181 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  20. Kvasov, D.E., Sergeyev, Y.D.: Deterministic approaches for solving practical black-box global optimization problems. Adv. Eng. Softw. 80, 58–66 (2015)

    Article  Google Scholar 

  21. Lera, D., Sergeyev, Y.D.: Deterministic global optimization using space-filling curves and multiple estimates of Lipschitz and Hölder constants. Commun. Nonlinear Sci. Numer. Simul. 23(1–3), 328–342 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  22. Liu, Q., Zeng, J.: Global optimization by multilevel partition. J. Global Optim. 61(1), 47–69 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  23. Liuzzi, G., Lucidi, S., Piccialli, V.: A DIRECT-based approach exploiting local minimizations for the solution of large-scale global optimization problems. Comput. Optim. Appl. 45, 353–375 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  24. Liuzzi, G., Lucidi, S., Piccialli, V.: A partition-based global optimization algorithm. J. Global Optim. 48, 113–128 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  25. Liuzzi, G., Lucidi, S., Piccialli, V.: Exploiting derivative-free local searches in direct-type algorithms for global optimization. Comput. Optim. Appl. 65(2), 449–475 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  26. Liuzzi, G., Lucidi, S., Rinaldi, F.: A derivative-free approach to constrained multiobjective nonsmooth optimization. SIAM J. Optim. 26(4), 2744–2774 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  27. Miettinen, K.: Nonlinear Multiobjective Optimization. International Series in Operations Research and Management Science. Springer, Berlin (1998)

    Book  Google Scholar 

  28. Paulavičius, R., Sergeyev, Y.D., Kvasov, D.E., Žilinskas, J.: Globally-biased disimpl algorithm for expensive global optimization. J. Global Optim. 59(2–3), 545–567 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  29. Sergeyev, Y.D.: On convergence of “Divide the Best” global optimization algorithms. Optimization 44(3), 303–325 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  30. Sergeyev, Y.D., Kvasov, D.E.: Global search based on efficient diagonal partitions and a set of Lipschitz constants. SIAM J. Optim. 16(3), 910–937 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  31. Strongin, R.G., Sergeyev, Y.D.: Global Optimization with Non-Convex Constraints: Sequential and Parallel Algorithms. Kluwer, Dordrecht (2000)

    Book  MATH  Google Scholar 

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

    Article  Google Scholar 

  33. Žilinskas, A., Gimbutienė, G.: On one-step worst-case optimal trisection in univariate bi-objective lipschitz optimization. Commun. Nonlinear Sci. Numer. Simul. 35, 123–136 (2016)

    Article  MathSciNet  Google Scholar 

  34. Žilinskas, A., Žilinskas, J.: Adaptation of a one-step worst-case optimal univariate algorithm of bi-objective lipschitz optimization to multidimensional problems. Commun. Nonlinear Sci. Numer. Simul. 21(1), 89–98 (2015). Numerical Computations: Theory and Algorithms (NUMTA 2013), International Conference and Summer School

  35. Zhou, A., Qu, B.-Y., Li, H., Zhao, S.-Z., Suganthan, P.N., Zhang, Q.: Multiobjective evolutionary algorithms: a survey of the state of the art. Swarm Evolut. Comput. 1(1), 32–49 (2011)

    Article  Google Scholar 

Download references

Acknowledgements

We thank two anonymous reviewers whose comments helped us improve the paper.

Author information

Authors and Affiliations

  1. Istituto Nazionale per Studi ed Esperienze di Architettura Navale, Consiglio Nazionale delle Ricerche, Via di Vallerano 139, 00128, Rome, Italy

    E. F. Campana, M. Diez, R. Pellegrini & A. Serani

  2. Istituto di Analisi dei Sistemi ed Informatica, Consiglio Nazionale delle Ricerche, Via dei Taurini 19, 00185, Rome, Italy

    G. Liuzzi

  3. Dipartimento di Ingegneria Informatica, Automatica e Gestionale, Sapienza Università di Roma, Via Ariosto 25, 00185, Rome, Italy

    S. Lucidi

  4. Dipartimento di Ingegneria Civile e Ingegneria Informatica, Università degli Studi di Roma “Tor Vergata”, Via del Politecnico 1, 00133, Rome, Italy

    V. Piccialli

  5. Dipartimento di Matematica, Università di Padova, Via Trieste 63, 35121, Padua, Italy

    F. Rinaldi

Authors
  1. E. F. Campana
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Diez
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. G. Liuzzi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. S. Lucidi
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. R. Pellegrini
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. V. Piccialli
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. F. Rinaldi
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. A. Serani
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. Liuzzi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Campana, E.F., Diez, M., Liuzzi, G. et al. A multi-objective DIRECT algorithm for ship hull optimization. Comput Optim Appl 71, 53–72 (2018). https://doi.org/10.1007/s10589-017-9955-0

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10589-017-9955-0

Keywords

Mathematics Subject Classification

Search

Navigation