We introduce AutODEx, an automated machine learning platform for optimal design of experiments to expedite solution discovery with optimal objective trade-offs. We implement state-of-the-art multi-objective Bayesian optimization (MOBO) algorithms in a unified and flexible framework for optimal design of experiments, along with efficient asynchronous batch strategies extended to MOBO to harness experiment parallelization. For users with little or no experience with coding or machine learning, we provide an intuitive graphical user interface (GUI) to help quickly visualize and guide the experiment design. For experienced researchers, our modular code structure serves as a testbed to quickly customize, develop, and evaluate their own MOBO algorithms. Extensive benchmark experiments against other MOBO packages demonstrate \platname's competitive and stable performance. Furthermore, we showcase \platname's real-world utility by autonomously guiding hardware experiments with minimal human involvement.