Parametric optimization of pulsating jets in unsteady flow by Multiple-Gradient Descent Algorithm (MGDA)

International audienceTwo numerical methodologies are combined to optimize six design characteristics of a system of pulsating jets acting on a laminar boundary layer governed by the compressible Navier-Stokes equations in a time-periodic regime. The flow is simulated by second-order in time and space finite-volumes, and the simulation provides the drag as a function of time. Simultaneously, the sensitivity equations, obtained by differentiating the governing equations w.r.t. the six parametersare also marched in time, and this provides the six-component parametric gradient of drag. When the periodic regime is reached numerically, one thus disposes of an objective-function, drag, to be minimized, and its parametric gradient, at all times of a period. Second, the parametric optimization is conducted as a multi-point problem by the Multiple-Gradient Descent Algorithm (MGDA) which permits to reduce the objective-function at all times simultaneously, and not simply in the sense of a weighted average

Jeux dynamiques en optimisation couplée fluide-structure

International audienceMultidisciplinary optimisation (MDO) adresses the design process of materials and structures that must comply with several criteria, sometimes antagonistic. Moreover, different criteria may be derived from different models, coupled or not. Due to the competing nature of the criteria, rational non-arbitrary methods should be used to drive the MDO, and clearly game theory paradigm offers such a framework. In this paper, we present a case study of MDO in aeronautics, where aerodynamics designer interacts with structural designer in a Nash and Stackelberg games. The developped algorithms as well as numerical results of optimization are presented.L'optimisation multidisciplinaire (MDO) adresse le processus de conception des matériaux et des structures qui doivent être conformes à plusieurs critères, parfois antagonique. D'ailleurs, dif-férents critères qui peuvent résulter de différents modèles, couplés ou pas. En raison de la nature de la concurrence des critères, des méthodes raisonnables non-arbitraires devraient être employées pour conduire le MDO, et clairement le paradigme de la théorie des jeux offre un tel cadre. Dans ce papier, nous présentons un cas d'étude de MDO en aéronautique, où le concepteur aérodynamique intéragit avec le concepteur structural dans le cas du jeu de Nash et de Stackelberg. Les algorithmes développés ainsi que les résultats numériques de l'optimisation seront présentés

Multiobjective Design Optimization using Nash Games

International audienceIn the area of pure numerical simulation of multidisciplinary coupled systems, the computational cost to evaluate a configuration may be very high. A fortiori, in multi- disciplinary optimization, one is led to evaluate a number of different configurations to iterate on the design parameters. This observation motivates the search for the most in- novative and computationally efficient approaches in all the sectors of the computational chain : at the level of the solvers (using a hierarchy of physical models), the meshes and geometrical parameterizations for shape, or shape deformation, the implementation (on a sequential or parallel architecture; grid computing), and the optimizers (deterministic or semi-stochastic, or hybrid; synchronous, or asynchronous). In the present approach, we concentrate on situations typically involving a small number of disciplines assumed to be strongly antagonistic, and a relatively moderate number of related objective functions. However, our objective functions are functionals, that is, PDE-constrained, and thus costly to evaluate. The aerodynamic and structural optimization of an aircraft configuration is a prototype of such a context, when these disciplines have been reduced to a few major objectives. This is the case when, implicitly, many subsystems are taken into account by local optimizations. Our developments are focused on the question of approximating the Pareto set in cases of strongly-conflicting disciplines. For this purpose, a general computational technique is proposed, guided by a form of sensitivity analysis, with the additional objective to be more economical than standard evolutionary approaches

Descent algorithm for nonsmooth stochastic multiobjective optimization

International audienceAn algorithm for solving the expectation formulation of stochastic nonsmooth multiobjective optimization problems is proposed. The proposed method is an extension of the classical stochastic gradient algorithm to multi-objective optimization using the properties of a common descent vector defined 10 in the deterministic context. The mean square and the almost sure convergence of the algorithm are proven. The algorithm efficiency is illustrated and assessed on an academic example

Cooperation and Competition Strategies in Multi-objective Shape Optimization - Application to Low-boom/Low-drag Supersonic Business Jet

International audienceCooperation and competition are natural laws that regulate the interactions between agents in numerous physical, or social phenomena. By analogy, we transpose these laws to devise e cient multi-objective algorithms applied to shape optimization problems involving two or more disciplines. Two e cient strategies are presented in this paper: a multiple gradient descent algorithm (MGDA) and a Nash game strategy based on an original split of territories between disciplines. MGDA is a multi-objective extension of the steepest descent method. The use of a gradient-based algorithm that exploits the cooperation principle aims at reducing the number of iterations required for classical multi-objective evolutionary algorithms to converge to a Pareto optimal design. On the other hand side, the Nash game strategy is well adapted to typical aeronautical optimization problems, when, after having optimized a preponderant or fragile discipline (e.g. aerodynamics), by the minimization of a primary objective-function, one then wishes to reduce a secondary objective-function, representative of another discipline, in a process that avoids degrading excessively the original optimum. Presently, the combination of the two approaches is exploited, in a method that explores the entire Pareto front. Both algorithms are rst analyzed on analytical test cases to demonstrate their main features and then applied to the optimum-shape design of a low-boom/low-drag supersonic business jet design problem. Indeed, sonic boom is one of the main limiting factors to the development of civil supersonic transportation. As the driving design for low-boom is not compliant with the low-drag one, our goal is to provide a trade-o between aerodynamics and acoustics. Thus Nash games are adopted to de ne a low-boom con guration close to aerodynamic optimality w.r.t. wave drag