  Offline optimization aims to maximize a black-box objective function with a
static dataset and has wide applications. In addition to the objective function
being black-box and expensive to evaluate, numerous complex real-world problems
entail optimizing multiple conflicting objectives, i.e., multi-objective
optimization (MOO). Nevertheless, offline MOO has not progressed as much as
offline single-objective optimization (SOO), mainly due to the lack of
benchmarks like Design-Bench for SOO. To bridge this gap, we propose a first
benchmark for offline MOO, covering a range of problems from synthetic to
real-world tasks. This benchmark provides tasks, datasets, and open-source
examples, which can serve as a foundation for method comparisons and
advancements in offline MOO. Furthermore, we analyze how the current related
methods can be adapted to offline MOO from four fundamental perspectives,
including data, model architecture, learning algorithm, and search algorithm.
Empirical results show improvements over the best value of the training set,
demonstrating the effectiveness of offline MOO methods. As no particular method
stands out significantly, there is still an open challenge in further enhancing
the effectiveness of offline MOO. We finally discuss future challenges for
offline MOO, with the hope of shedding some light on this emerging field. Our
code is available at \url{https://github.com/lamda-bbo/offline-moo}.
