Effective implementation of nonlinear constraints in optimization of three-dimensional transonic wings

A new approach to effective implementation of non-linear constraints for optimization problems solving using genetic algorithms (GA) is proposed. The feature of the approach is to change the traditional strategy in which the search path can only pass through permissible (satisfying the constraints) point by admitting routes passing through both valid and invalid points. The basic idea of this approach is that the information from the "forbidden" (i.e., not satisfying the constraints) areas can be very important, and the path to the optimal point that runs through these areas can appear to be much shorter. The method was applied to the problem of multiobjective optimization of aerodynamic shapes depending on different geometrical and aerodynamic constraints. The results showed that the method maintains high reliability with preservation of the traditional GA computational costs (in the calculation of the objective function on the basis of the full Navier–Stokes equations) at an acceptable level.