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

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