A General Hybrid Optimization Strategy for Curve Fitting in the Non-uniform Rational Basis Spline Framework
TypeArticles dans des revues avec comité de lecture
In this paper, a general methodology to approximate sets of data points through Non-Uniform Rational Basis Spline 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 Non-Uniform Rational Basis Spline curve. To this purpose, a new formulation of the curve fitting problem is required: it is stated in the form of a Constrained Non-Linear 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 Non-Linear 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.
Fichier(s) constituant cette publication
Cette publication figure dans le(s) laboratoire(s) suivant(s)
Visualiser des documents liés par titre, auteur, créateur et sujet.
On the integration of additive manufacturing constraints in the framework of a NURBS-based topology optimisation method COSTA, Giulio; MONTEMURRO, Marco; PAILHES, Jérôme (2017)This work focuses on the topology optimization (TO) of 2D structures: the Solid Isotropic Material with Penalisation (SIMP) method is revisited and reformulated within the mathematical framework of Non-Uniform Rational ...
COSTA, Giulio; MONTEMURRO, Marco; PAILHES, Jérôme (J.F. Silva Gomes and Shaker A. Meguid editors, 2017)In this work, the Solid Isotropic Material with Penalization (SIMP) topology optimization (TO) method is revisited and reformulated within the mathematical framework of NURBS functions. This implies several advantages: ...
COSTA, Giulio; MONTEMURRO, Marco; PAILHÈS, Jérôme; PERRY, Nicolas (Elsevier BV, 2019)This paper deals with a new method for handling manufacturing and geometrical requirements in the framework of a general Topology Optimisation (TO) strategy. In particular, the maximum length scale constraint (MLSC) ...
COSTA, Giulio; MONTEMURRO, Marco; PAILHES, Jérôme (Springer Nature, 2017)In this paper, the Solid Isotropic Material with Penalisation (SIMP) method for Topology Optimisation (TO) of 2D problems is reformulated in the Non-Uniform Rational BSpline (NURBS) framework. This choice implies several ...
BERTOLINO, Giulia; COSTA, Giulio; MONTEMURRO, Marco; PERRY, Nicolas; POURROY, Franck (2019)In this work, a new semi-automatic surface reconstruction procedure is proposed. The main goal of the method is to reconstruct the boundary surface of a triangulation obtained as a result of a topology optimisation ...