Mixed-Integer Bayesian Optimization Utilizing A-Priori Knowledge on Parameter Dependences

Mixed-integer optimization problems arise in various application fields, such as chemical engineering and the optimization of medical image processing pipelines. Stochastic optimization algorithms, such as evolution strategies and estimation of distribution algorithms, can be used as solution methods for solving these problems approximately. Especially for real-world problems they often prove to be powerful methods due to their flexibility and robustness. This paper introduces a new estimation of distribution algorithm that extends the Bayesian optimization algorithm (with fixed network structure) from binary optimization problems to mixed-integer optimization problems. We show that a-priori knowledge on dependences between decision variables can be exploited by this algorithm in order to improve convergence speed and reliability. In discussing the properties of heterogeneous Bayesian networks, representing multivariate distributions of mixed-variable type, we point out which kind of dependence information can be utilized. We assess the performance of the new approach using mixed-integer Nk-landscape models.