Explicitly Constrained Black-Box Optimization With Disconnected Feasible Domains Using Deep Generative Models

We tackle explicitly constrained black-box continuous optimization problems in which the feasible domain forms a union of disconnected feasible subdomains. The decoder-based constraint-handling technique is a promising approach when the feasible domain is disconnected. However, the design of a reasonable decoder requires deep prior knowledge of the optimization problem to be solved and, hence, human effort. In this study, we investigated the usefulness of a deep neural network as a decoder and developed a training scheme for a deep neural network without prior information, such as a training dataset consisting of feasible and infeasible solutions required by existing decoder approaches. To stabilize the training of the deep generative model as the decoder, we propose decomposing the decoder into sub-models, introducing skip connections to each sub-model, and training the sub-models sequentially with separate loss functions. Numerical experiments using a test problem and a topology optimization problem show that the proposed method can find feasible domains with better objective function values and higher probability than both conventional decoder-based constraint-handling methods and non-decoder-based constraint-handling methods.