Escaping Unknown Discontinuous Regions in Blackbox Optimization

The design of key nonlinear systems often requires the use expensive blackbox simulations presenting inherent discontinuities whose positions in variable space cannot be analytically predicted. Without further precautions, solution related optimization problems leads to configurations which may close output functions. These betray unsafe regions space, such as resonance regions. To account for possible changes operating conditions, an acceptable must away from variables. objective this work is solve a constrained problem with additional constraint that should outside unknown zones or strong variations function constraints. proposed approach extension mesh adaptive direct search (\sf Mads) algorithm and aims at building series inner approximations these zones. algorithm, called \sf DiscoMADS, relies on two main mechanisms: revealing progressively escaping surrounding A convergence analysis supports preserves optimality conditions Mads. Numerical tests are conducted analytical three engineering illustrating following applications algorithm: simplified truss, synthesis chemical component, turbomachine blade. DiscoMADS successfully solves by providing feasible discontinuous