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A General Hybrid Optimization Strategy for Curve Fitting in the Non-uniform Rational Basis Spline Framework

Author

Listed:
  • Giulio Costa

    (Arts et Métiers ParisTech)

  • Marco Montemurro

    (Arts et Métiers ParisTech)

  • Jérôme Pailhès

    (Arts et Métiers ParisTech)

Abstract

In this paper, a general methodology to approximate sets of data points through Non-uniform Rational Basis Spline (NURBS) curves is provided. The proposed approach aims at integrating and optimizing the full set of design variables (both integer and continuous) defining the shape of the NURBS curve. To this purpose, a new formulation of the curve fitting problem is required: it is stated in the form of a constrained nonlinear programming problem by introducing a suitable constraint on the curvature of the curve. In addition, the resulting optimization problem is defined over a domain having variable dimension, wherein both the number and the value of the design variables are optimized. To deal with this class of constrained nonlinear programming problems, a global optimization hybrid tool has been employed. The optimization procedure is split in two steps: firstly, an improved genetic algorithm optimizes both the value and the number of design variables by means of a two-level Darwinian strategy allowing the simultaneous evolution of individuals and species; secondly, the optimum solution provided by the genetic algorithm constitutes the initial guess for the subsequent gradient-based optimization, which aims at improving the accuracy of the fitting curve. The effectiveness of the proposed methodology is proven through some mathematical benchmarks as well as a real-world engineering problem.

Suggested Citation

  • Giulio Costa & Marco Montemurro & Jérôme Pailhès, 2018. "A General Hybrid Optimization Strategy for Curve Fitting in the Non-uniform Rational Basis Spline Framework," Journal of Optimization Theory and Applications, Springer, vol. 176(1), pages 225-251, January.
    • Handle: RePEc:spr:joptap:v:176:y:2018:i:1:d:10.1007_s10957-017-1192-2
    DOI: 10.1007/s10957-017-1192-2
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    References listed on IDEAS

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    1. Marco Montemurro & Anita Catapano, 2016. "A New Paradigm for the Optimum Design of Variable Angle Tow Laminates," Springer Optimization and Its Applications, in: Aldo Frediani & Bijan Mohammadi & Olivier Pironneau & Vittorio Cipolla (ed.), Variational Analysis and Aerospace Engineering, pages 375-400, Springer.
    2. Marco Montemurro & Angela Vincenti & Paolo Vannucci, 2012. "A Two-Level Procedure for the Global Optimum Design of Composite Modular Structures—Application to the Design of an Aircraft Wing," Journal of Optimization Theory and Applications, Springer, vol. 155(1), pages 24-53, October.
    3. Marco Montemurro & Angela Vincenti & Paolo Vannucci, 2012. "A Two-Level Procedure for the Global Optimum Design of Composite Modular Structures—Application to the Design of an Aircraft Wing," Journal of Optimization Theory and Applications, Springer, vol. 155(1), pages 1-23, October.
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    Cited by:

    1. Enrico Panettieri & Marco Montemurro & Daniele Fanteria & Francesco Coccia, 2020. "Multi-scale Least-Weight Design of a Wing-Box Through a Global/Local Modelling Approach," Journal of Optimization Theory and Applications, Springer, vol. 187(3), pages 776-799, December.

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