Autoencoder enabled global optimization

Abstract

High-dimensional optimization problems with expensive and non-convex cost functions pose a significant challenge, as the non-convexity limits the viability of local optimization, where the results are sensitive to initial guesses and often only represent local minima. But as the number of expensive cost function evaluations required for a full exploration of the search space grows exponentially with the increasing number of dimensions, the use of standard global optimization algorithms is also not practical. To overcome this obstacle and to lower the dimensionality of the problem, the use of an autoencoder for model order reduction is proposed. In the resulting lower dimensional space, standard global optimization methods can then be utilized, as fewer cost functions evaluations are necessary. For problems with comparatively more expensive cost functions, this optimization includes the employment of a surrogate model, which reduces the necessary number of these computationally expensive evaluations further. This proposed method is then tested firstly on a number of benchmark functions, where it shows the ability to find global optima under certain conditions. Secondly, the proposed method is used to solve a compliance minimization problem, where it shows the ability to improve upon a large number of designs generated by local optimization.