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The printing outcome of vat photopolymerization (VPP) of thermoplastics largely depends on physicochemical properties of monomers and their compositions in resins, which also greatly determine the material properties, e.g., tensile strength (σT) and toughness (UT)and phase transition temperature (Tg). A methodology for optimizing the resin formulation is of paramount importance in realizing highly printable thermoplastics with balanced σT/UT and target Tg while remaining largely underexplored. Herein, we introduce a multi-objective Bayesian optimization (MOBO) algorithm under two physics informed constraints (printability and Tg) to optimize two conflicting properties: σT and UT. The two constraints are formulated as two machine learning (ML) models, which are trained with weight ratios of the six monomers and physics informed (PI) descriptors derived from their physiochemical parameters. Dimensional reduction analysis reveals that the algorithm avoids recommendation of the monomer ratios that do not pass the two constraints. The printing failure rate is reduced from 16% in the background experiments to 3% in the recommended experiments. Within only 36 iterations (72 samples), the MOBO algorithm successfully identifies five sets of ratios leading to Pareto optimal of σT and UT. Due to the constraint in Tg they show appropriate Tg for shape memory application. The partial dependence analysis indicates that σT and UT depend on both the ratios and physiochemical features of the monomers. These results underscore capability of such a smart decision-making algorithm—with constraints that are not fully understood but can be informed by prior knowledge—in planning the experiments from the vast design space, thus holding a great promise for broader applications in materials design and manufacturing.