With liquefied natural gas becoming increasingly prevalent as a flexible source of energy, the design and optimization of industrial refrigeration cycles becomes even more important. In this article, we propose an integrated surrogate modeling and optimization framework to model and optimize the complex CryoMan Cascade refrigeration cycle. Dimensionality reduction techniques are used to reduce the large number of process decision variables which are subsequently supplied to an array of Gaussian processes, modeling both the process objective as well as feasibility constraints. Through iterative resampling of the rigorous model, this data-driven surrogate is continually refined and subsequently optimized. This approach was not only able to improve on the results of directly optimizing the process flow sheet but also located the set of optimal operating conditions in only 2 h as opposed to the original 3 weeks, facilitating its use in the operational optimization and enhanced process design of large-scale industrial chemical systems.