A multi-objective DIRECT algorithm for ship hull optimization

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.

[1]  Stefano Lucidi,et al.  Derivative-free global ship design optimization using global/local hybridization of the DIRECT algorithm , 2016 .

[2]  Yaroslav D. Sergeyev,et al.  Global Search Based on Efficient Diagonal Partitions and a Set of Lipschitz Constants , 2006, SIAM J. Optim..

[3]  Antanas Žilinskas,et al.  On one-step worst-case optimal trisection in univariate bi-objective Lipschitz optimization , 2016, Commun. Nonlinear Sci. Numer. Simul..

[4]  C. T. Kelley,et al.  A Locally-Biased form of the DIRECT Algorithm , 2001, J. Glob. Optim..

[5]  Stefano Lucidi,et al.  Exploiting derivative-free local searches in DIRECT-type algorithms for global optimization , 2016, Comput. Optim. Appl..

[6]  M. Diez,et al.  Design-space dimensionality reduction in shape optimization by Karhunen–Loève expansion , 2015 .

[7]  Yaroslav D. Sergeyev,et al.  Deterministic global optimization using space-filling curves and multiple estimates of Lipschitz and Holder constants , 2015, Commun. Nonlinear Sci. Numer. Simul..

[8]  Masha Sosonkina,et al.  Design and implementation of a massively parallel version of DIRECT , 2008, Comput. Optim. Appl..

[9]  Katya Scheinberg,et al.  Introduction to derivative-free optimization , 2010, Math. Comput..

[10]  Julius Zilinskas,et al.  Globally-biased Disimpl algorithm for expensive global optimization , 2014, Journal of Global Optimization.

[11]  Kaisa Miettinen,et al.  Nonlinear multiobjective optimization , 1998, International series in operations research and management science.

[12]  Mikhail Posypkin,et al.  A deterministic algorithm for global multi-objective optimization , 2014, Optim. Methods Softw..

[13]  Qingfu Zhang,et al.  Multiobjective evolutionary algorithms: A survey of the state of the art , 2011, Swarm Evol. Comput..

[14]  Julius Žilinskas,et al.  Adaptation of a one-step worst-case optimal univariate algorithm of bi-objective Lipschitz optimization to multidimensional problems , 2015, Commun. Nonlinear Sci. Numer. Simul..

[15]  Y. Sergeyev.  On convergence of "divide the best" global optimization algorithms , 1998 .

[16]  Sanghamitra Bandyopadhyay,et al.  Multiobjective GAs, quantitative indices, and pattern classification , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[17]  Stefano Lucidi,et al.  A DIRECT-based approach exploiting local minimizations for the solution of large-scale global optimization problems , 2010, Comput. Optim. Appl..

[18]  Yaroslav D. Sergeyev,et al.  Deterministic approaches for solving practical black-box global optimization problems , 2015, Adv. Eng. Softw..

[19]  Mikhail Posypkin,et al.  Nonuniform covering method as applied to multicriteria optimization problems with guaranteed accuracy , 2013 .

[20]  Stefano Lucidi,et al.  A partition-based global optimization algorithm , 2010, J. Glob. Optim..

[21]  Jorge J. Moré,et al.  Digital Object Identifier (DOI) 10.1007/s101070100263 , 2001 .

[22]  X. Chen,et al.  High-fidelity global optimization of shape design by dimensionality reduction, metamodels and deterministic particle swarm , 2015 .

[23]  Carlos M. Fonseca,et al.  Multiobjective genetic algorithms , 1993 .

[24]  Gianni Di Pillo,et al.  A DIRECT-type approach for derivative-free constrained global optimization , 2016, Comput. Optim. Appl..

[25]  C. D. Perttunen,et al.  Lipschitzian optimization without the Lipschitz constant , 1993 .

[26]  Matteo Diez,et al.  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 , 2013 .

[27]  Stefano Lucidi,et al.  A Derivative-Free Approach to Constrained Multiobjective Nonsmooth Optimization , 2016, SIAM J. Optim..

[28]  Y. D. Sergeyev,et al.  Global Optimization with Non-Convex Constraints - Sequential and Parallel Algorithms (Nonconvex Optimization and its Applications Volume 45) (Nonconvex Optimization and Its Applications) , 2000 .

[29]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[30]  Qunfeng Liu,et al.  Global optimization by multilevel partition , 2015, J. Glob. Optim..

[31]  K. K. Choi,et al.  Development and validation of a dynamic metamodel based on stochastic radial basis functions and uncertainty quantification , 2014, Structural and Multidisciplinary Optimization.

[32]  Luís N. Vicente,et al.  Direct Multisearch for Multiobjective Optimization , 2011, SIAM J. Optim..