Blackbox optimization and surrogate models for machining free-form surfaces

This paper introduces an optimization model for machining free-form surfaces. It involves one categorical decision variable and continuous decision variables. Its objective function is partially separable. It is composed of two blackboxes: a clustering blackbox that outputs a partition of the surface into K zones, and K independent blackboxes, each of which outputs a machining time for a zone. This blackbox optimization problem is solved with the state-of-the-art software NOMAD. In order to improve the performance of the optimization process, we propose several surrogates of the machining-time blackboxes. Some of these surrogates are simple numerical approximations of the machining time, while one proposed surrogate is analytical, cheap to evaluate and exact for zones that are rectangles. Numerical experiments on two benchmark test surfaces show that our methodology outperforms other approaches from the literature. Although performances are strongly dependent on the topology of the test surfaces, the gains in machining time can go up to 40%.