Ph. Bouillard

Element-Free Galerkin solutions for Helmholtz problems: fomulation and numerical assessment of the pollution effect

Abstract The Element-Free Galerkin Method (EFGM), a particular case of the meshless methods, is examined in its application to acoustic wave propagation addressed by the Helmholtz equation. Dispersion and pollution effects, two problems encountered by the classical numerical methods, are reviewed. Numerical tests on two-dimensional problems focus on the parameters governing the formulation of the EFGM. They also demonstrate that the EFGM is affected by dispersion and pollution effects as well as FEM, but these effects are rather low, showing that the EFGM is a promising method.

Parametrical mechanical design with constraints and preferences: application to a purge valve

Abstract In the design of mechanical structures, the evolutionary algorithms have taken a more and more important place, mostly because of their ability to explore widely the design space. Furthermore, as several objectives are often pursued simultaneously in industrial applications, multiobjective optimization has become a wide area of research in recent years. However, only a few methods integrate a multicriteria decision aid approach to reflect the user’s preferences since the beginning of the search process. In this paper, PROMETHEE II, an outranking method developed in the operational research field, has been implemented in an evolutionary algorithm. Furthermore, as the handling of the constraints is very critical, an original technique called PAMUC ( Preferences Applied to MUltiobjectivity and Constraints ) is proposed to tackle simultaneously the constrained and multiobjective aspects. It has been validated on standard test cases, and applied to the design optimization of two valves of the Vinci engine (from launcher Ariane 5). Results analyzed thanks to the R1 norm introduced by Hansen and Jaszkiewicz show that PAMUC outperforms the classical weighted-sum method (combined with a dynamic penalty-based technique to handle the constraints), and therefore seem to be more appropriate to reflect the user’s preferences.

PAMUC: A New Method to Handle With Constraints and Multiobjectivity in Evolutionary Algorithms

Multiobjective optimization using evolutionary algorithms (EA) has become a wide area of research during these last years. However, only a few papers deal with the handling of preferences. To take them into account, a method based on multi-criteria decision aid, PROMETHEE II, has been implemented. Further-more, as the handling of the constraints is very critical in EA, an original approach (PAMUC Pr eferences Applied to MUltiobjectivity and Constraints) has been proposed, which considers the satisfaction of the constraints as another objective.