Deep generative model for non-convex constraint handling

In this study, we consider black-box minimization problems with non-convex constraints, where the constraints are significantly cheaper to evaluate than the objective. Non-convex constraints generally make it difficult to solve problems using evolutionary approaches. In this paper, we revisit a conventional technique called decoder constraint handling, which transforms a feasible non-convex domain into an easy-to-control convex set. This approach is promising because it transforms a constrained problem into an almost unconstrained one. However, its application has been considerably limited, because designing or training such a nonlinear decoder requires domain knowledge or manually prepared training data. To fully automate the decoder design, we use deep generative models. We propose a novel scheme to train a deep generative model without using manually prepared training data. For this purpose, we first train feasible solution samplers, which are deep neural networks, using the constraint functions. Subsequently, we train another deep generative model using the data generated from the trained samplers as the training data. The proposed framework is applied to tasks inspired by topology optimization problems. The empirical study demonstrates that the proposed approach can locate better solutions with fewer objective function evaluations than the existing approach.