Objective. Online adaptive radiation therapy requires fast and automated contouring of daily scans for treatment plan re-optimization. However, automated contouring is imperfect and introduces contour uncertainties. This work aims at developing and comparing robust optimization strategies accounting for such uncertainties. Approach. A deep-learning method was used to predict the uncertainty of deformable image registration, and to generate a finite set of daily contour samples. Ten optimization strategies were compared: two baseline methods, five methods that convert contour samples into voxel-wise probabilities, and three methods accounting explicitly for contour samples as scenarios in robust optimization. Target coverage and organ-at-risk (OAR) sparing were evaluated robustly for simplified proton therapy plans for five head-and-neck cancer patients. Results. We found that explicitly including target contour uncertainty in robust optimization provides robust target coverage with better OAR sparing than the baseline methods, without increasing the optimization time. Although OAR doses first increased when increasing target robustness, this effect could be prevented by additionally including robustness to OAR contour uncertainty. Compared to the probability-based methods, the scenario-based methods spared the OARs more, but increased integral dose and required more computation time. Significance. This work proposed efficient and beneficial strategies to mitigate contour uncertainty in treatment plan optimization. This facilitates the adoption of automatic contouring in online adaptive radiation therapy and, more generally, enables mitigation also of other sources of contour uncertainty in treatment planning.