Meta-model-assisted MGDA for multi-objective functional optimization

Adrien Zerbinati (1) , Andrea Minelli (2) , Imane Ghazlane (2) , Jean-Antoine Desideri (1)

1 OPALE - Optimization and control, numerical algorithms and integration of complex multidiscipline systems governed by PDE
2 ONERA - The French Aerospace Lab [Meudon]

A novel numerical method for multi-objective differentiable optimization, the Multiple-Gradient Descent Algorithmm (MGDA), has been proposed in [8] [11] to identify Pareto fronts. In MGDA, a direction of search for which the directional gradients of the objective functions are all negative, and often equal by construction [12], is identified and used in a steepest-descent-type iteration. The method converges to Pareto-optimal points. MGDA is here briefly reviewed to outline its principal theoretical properties and applied first to a classical mathematical test-case for illustration. The method is then ex-tended encompass cases where the functional gradients are approximated via meta-models, as it is often the case in complex situations, and demonstrated on three optimum-shape design problems in compressible aerodynamics.The first problem is purely related to aerodynamic performance. It is a wing shape optimization exercise w.r.t. lift and drag in typical transonic cruise

Mots clés: Multi objective optimization; MGDA; Nash Game; Aerodynamics; Low Boom; Differentiable optimization; Numerical methods; Pareto optimality; Compressible aerodynamics; Drag reduction; Sonic boom

Domaines: Sciences de l'ingénieur [physics]; Mécanique des fluides [physics.class-ph]

Adrien Zerbinati, Andrea Minelli, Imane Ghazlane, Jean-Antoine Desideri. Meta-model-assisted MGDA for multi-objective functional optimization. Computers and Fluids, 2014, 102 (10), pp.116 - 130. ⟨10.1016/j.compfluid.2014.06.018⟩. ⟨hal-01082595⟩