We present an approach for highly accurate bottom-up object segmentation. Given an image, the approach rapidly generates a set of regions that delineate candidate objects in the image. The key idea is to train an ensemble of figure-ground segmentation models. The ensemble is trained jointly, enabling individual models to specialize and complement each other. We reduce ensemble training to a sequence of uncapacitated facility location problems and show that highly accurate segmentation ensembles can be trained by combinatorial optimization. The training procedure jointly optimizes the size of the ensemble, its composition, and the parameters of incorporated models, all for the same objective. The ensembles operate on elementary image features, enabling rapid image analysis. Extensive experiments demonstrate that the presented approach outperforms prior object proposal algorithms by a significant margin, while having the lowest running time. The trained ensembles generalize across datasets, indicating that the presented approach is capable of learning a generally applicable model of bottom-up segmentation.