Metamodels for mixed variables by multiple kernel regression

Abstract This paper is concerned with the development of metamodels specifically tailored for mixed variables, in particular continuous and categorical variables. Practically, we propose a surrogate model based on multiple kernel regression, and apply it to six benchmark test functions and a rigid frame structural analysis. When compared to other metamodels (support vector regression, ordinary least squares), the numerical results show the efficiency of the method, related to the flexible selection of different types of kernel functions. Further work will include the use of these metamodels for mixed-variable surrogate-based optimization involving computationally expensive simulations. 2

Etude expérimentale du comportement géomécanique d'une argile sèche -- Mécanique des sols

info:eu-repo/semantics/nonPublishe

Probabilistic Dominance in Multiobjective Reliability-Based Optimization: Theory and Implementation

This paper is concerned with multiobjective evolutionary optimization under uncertainty modeled through probability distributions, with a focus on reliability-based approaches. The contribution is twofold. First, an in-depth study of the notion of probability of dominance is performed, including state-of-the-art multiobjective reliability-based formulations and their numerical calculation. In particular, the notion of dominance limit state function is defined and its properties are thoroughly investigated. Second, the assessment of the probability of dominance is proposed based on a first-order reliability method tailored for Pareto dominance and incorporated into a multiobjective evolutionary algorithm through a repairing mechanism. The analysis of the numerical results on five biobjective benchmark test cases (from two up to five design variables) by means of two adapted metrics (averaged Hausdorff distance and maximum Pareto front error) demonstrates the potential of the proposed approach to reach reliable nondominated fronts within a limited number of generations.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Optimization based on evolutionary algorithms for aeronautics

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Moteur d'inférence pour l'optimisation de structures (MINOS)

FIRST Doctorat 001/4442, Activity reports 1-8 (2000-2004)info:eu-repo/semantics/publishe

Fiabilité des structures et des matériaux

CNST-H-409info:eu-repo/semantics/published

Optimisation multicritère avec prise en compte des incertitudes (en variables continues et discrètes) appliquée aux constructions

BB2B (Brains Back to Brussels) Project - Activity reports (2009-2013).info:eu-repo/semantics/publishe

Bi-objective hypervolume-based Pareto optimization: A gradient-based approach as an alternative to evolutionary algorithms

The search for the best trade-off solutions with respect to several criteria (also called the Pareto set) is the main approach pursued in multi-objective optimization when no additional preferences are associated to the objectives. This problem is known to be compliant with the maximization of the hypervolume (or S-metric), consisting in the Lebesgue measure of the dominated region covered by a set of solutions in the objective space, and bounded by a reference point. While several variants of population-based metaheuristics like evolutionary algorithms address formulations maximizing the hypervolume, the use of gradient-based algorithms for this task has been largely neglected in the literature. Therefore, this paper proposes to solve bi-objective problems by hypervolume maximization through a sequential quadratic programming algorithm. After theoretical developments including the analytical expression of the sensitivities of the hypervolume expressed as functions of the gradient of the objectives, the method is applied to six benchmark test cases, demonstrating the efficiency of the proposed method in comparison with a scalarization of the objectives, and with a state-of-the-art multi-objective genetic algorithm. This method is believed to provide an interesting alternative to metaheuristics when the gradients of the objective functions are available at a limited additional cost, a situation which is encountered in versatile applications, for instance with adjoint methods implemented in computational solid mechanics or fluid dynamics.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Reliability of Structures and Materials

info:eu-repo/semantics/published

Extending moving least squares to mixed variables for metamodel-assisted optimization

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