Multi-objective Optimization in CFD by Genetic Algorithm

Abstract

{T}his report approaches the question of multi-objective optimizationfor optimum shape design in aerodynamics. {T}he employed optimizeris a semi-stochas- tic method, more precisely a {G}enetic {A}lgorithm({GA}). {GA}s are very robust optimization algorithms particularlywell suited for problems in which (1) the initialization is not intuitive,(2) the parameters to be optimized are not all of the same type (boolean,integer, real, functionnal), (3) the cost functional may presentseveral local minima, (4) several criteria should be accounted forsimultaneously (multiphysics, efficiency, cost, quality, ...). {I}na multi-objective optimization problem, there is no unique optimalsolution but a whole set of potential solutions since in generalno solution is optimal w.r.t. all criteria simultaneously�; instead,one identifies a set of non-dominated solutions, referred to as the{P}areto optimal front. {A}fter making these concepts precise, geneticalgorithms are implemented and first tested on academic examples�;then a numerical experimentation is conducted to solve a multi-objectiveshape optimization problem for the design of an airfoil in {E}ulerianflow.