A set‐based approach for hierarchical optimization problem using Bayesian active learning

Abstract

AbstractIn the development of complex engineering systems, many engineers from different disciplines collaborate to identify feasible designs that satisfy all system requirements. Analytical target cascading (ATC) is a method for the design optimization of hierarchical, multilevel systems and has been successfully employed in the design of complex engineering systems. In this paper, we propose a novel data‐driven set‐based ATC (SBATC) method for hierarchical design optimization problems using machine learning techniques. The proposed SBATC offers two advantages in engineering processes. First, it decomposes hierarchical design optimization problems into sets of suboptimization problems. The feasible regions of the suboptimization problems are explored and cascaded to lower‐level optimization problems. Using the set‐based approach, couplings between two adjacent levels in the optimization process are not required. Second, an efficient strategy is employed to determine feasible regions based on Bayesian active learning (BAL). In BAL, the Gaussian process (GP) of all cost functions is trained. An acquisition function that combines the probability of feasibility and entropy search is evaluated using posterior distributions of the trained GP. The acquisition function is maximized to generate new sampling points around the feasible regions by balancing the exploitation and exploration of the design space. To verify the effectiveness of the proposed method, numerical examples of hierarchical optimization problems are evaluated.