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We consider the problem of multi-objective optimization (MOO) of expensive black-box functions with the goal of discovering high-quality and diverse Pareto fronts where we are allowed to evaluate a batch of inputs. This problem arises in many real-world applications including penicillin production where diversity of solutions is critical. We solve this problem in the framework of Bayesian optimization (BO) and propose a novel approach referred to as Pareto front-Diverse Batch Multi-Objective BO (PDBO). PDBO tackles two important challenges: 1) How to automatically select the best acquisition function in each BO iteration, and 2) How to select a diverse batch of inputs by considering multiple objectives. We propose principled solutions to address these two challenges. First, PDBO employs a multi-armed bandit approach to select one acquisition function from a given library. We solve a cheap MOO problem by assigning the selected acquisition function for each expensive objective function to obtain a candidate set of inputs for evaluation. Second, it utilizes Determinantal Point Processes (DPPs) to choose a Pareto-front-diverse batch of inputs for evaluation from the candidate set obtained from the first step. The key parameters for the methods behind these two steps are updated after each round of function evaluations. Experiments on multiple MOO benchmarks demonstrate that PDBO outperforms prior methods in terms of both the quality and diversity of Pareto solutions. 

Abstract The development of a general‐purpose machine learning algorithm capable of quickly identifying optimal 3D‐printing settings can save manufacturing time and cost, reduce labor intensity, and improve the quality of 3D‐printed objects. Existing methods have limitations which focus on overall performance or one specific aspect of 3D‐printing quality. Here, for addressing the limitations, a multi‐objective Bayesian Optimization (BO) approach which uses a general‐purpose algorithm to optimize the black‐box functions is demonstrated and identifies the optimal input parameters of direct ink writing for 3D‐printing different presurgical organ models with intricate geometry. The BO approach enhances the 3D‐printing efficiency to achieve the best possible printed object quality while simultaneously addressing the inherent trade‐offs from the process of pursuing ideal outcomes relevant to requirements from practitioners. The BO approach also enables us to effectively explore 3D‐printing inputs inclusive of layer height, nozzle travel speed, and dispensing pressure, as well as visualize the trade‐offs between each set of 3D‐printing inputs in terms of the output objectives which consist of time, porosity, and geometry precisions through the Pareto front.