A comparison of mixed-variables Bayesian optimization approaches

Abstract Most real optimization problems are defined over a mixed search space where the variables both discrete and continuous. In engineering applications, objective function is typically calculated with numerically costly black-box simulation. General therefore of great practical interest, yet their resolution remains in large part an open scientific question. this article, approached through Gaussian processes relaxed into continuous latent variables. The more easily harvested by classical Bayesian techniques than would. Discrete recovered either subsequently to optimization, or simultaneously additional continuous-discrete compatibility constraint that handled augmented Lagrangians. Several possible implementations such optimizers compared. particular, reformulation problem put competition searches working directly space. Among algorithms involving Lagrangian, particular attention devoted Lagrange multipliers for which local global estimation studied. comparisons based on repeated three analytical functions beam design problem.