Enhanced hybrid algorithm based on Bayesian optimization and Interior Point OPTimizer for constrained optimization

Kurzfassung

Optimization methods are essential for solving problems in fields like engineering, operations research, machine learning, and data science. In real-world applications, most optimization problems involve numerous constraints and nonlinear relationships, such as nonlinear balance equations. As a result, solving these constrained nonlinear optimization problems is challenging, with the global optimum often hidden behind multiple local ones. To address these challenges, recent work introduced the BO-IPOPT method, which combines Bayesian Optimization (BO) with the Interior Point OPTimizer (IPOPT) to leverage the global search of BO and the local search of IPOPT. To enhance the performance of the optimizer, this work explores aspects of the BO component, such as candidate selection for the Gaussian process model and constraint handling. First, we propose an effective strategy to provide IPOPT with good starting points without significantly increasing the computational costs of BO-IPOPT. Second, we introduce a novel approach using a single surrogate model for handling equality and inequality constraints in the BO part through the augmented Lagrangian framework with slack variables. This approach supports the global role of BO while reducing computational time and minimizing the number of hyperparameters defined by users. Third, a parameter study is conducted to optimize the hyperparameters in BO-IPOPT, minimizing user-defined inputs. This enhances the global guidance provided by the BO component and reduces the computational resources required by the hybrid method, improving its performance especially in problems of higher dimensions. Last, we evaluate BO-IPOPT against state-of-the-art methods using test and real-world problems with varying sizes, multimodality, and nonlinearity. Results show that BO-IPOPT achieves high accuracy, robustness, and efficiency, especially in high-dimensional, complex cases where other methods struggle.