Tropical cyclone induced storm surges are some of the largest environmental risks facing infrastructure and human life in dense urban environments. Hurricane Sandy caused 44 deaths and damage of 19 billion US dollars in New York City alone. Changes to the climate, not least sea level rise, will have difficult to predict, and potentially large, effects on the location, frequency, and character of tropical cyclones. While defenses against storm surges exist, these involve major infrastructure investments and are often designed without analysis of optimality. The task of optimizing storm surge defenses is highly complex, owing primarily to the expensive black-box simulations needed for inundation calculation and the probabilistic nature of tropical cyclones. This thesis aims to enable efficient and robust optimization of storm surge barriers by developing a novel optimization framework based on Gaussian process surrogates. The problem is modelled as an optimization of the surge barrier height with the objective of minimizing the sum of the construction cost and the expected storm surge damage incurred over the modelling period. An idealized topography is used, based on Lower Manhattan, and the high-speed GISSR methodology for inundation estimation is used in conjunction with existing climate models and the Hazus risk assessment tool to explore the solution space. The optimization framework is then developed, based on GeoClaw simulations. In order to increase information gain from each GeoClaw simulation, various augmentation methods are proposed and results from optimization using GISSR are used as priors. Despite the need for further hyperparameter tuning, improvements to input model integration, and general computational improvements being identified as necessary further work, the resulting framework is determined to be feasible and to enable tractable optimization using high-fidelity simulations.