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We consider the problem of constrained multi-objective optimization over black-box objectives, with user-defined preferences, with a largely infeasible input space. Our goal is to approximate the optimal Pareto set from the small fraction of feasible inputs. The main challenges include huge design space, multiple objectives, numerous constraints, and rare feasible inputs identified only through expensive experiments. We present PAC-MOO, a novel preference-aware multi-objective Bayesian optimization algorithm to solve this problem. It leverages surrogate models for objectives and constraints to intelligently select the sequence of inputs for evaluation to achieve the target goal.