This paper presents the first multi-objective transformer model for constructing open cloze tests that exploits generation and discrimination capabilities to improve performance. Our model is further enhanced by tweaking its loss function and applying a post-processing re-ranking algorithm that improves overall test structure. Experiments using automatic and human evaluation show that our approach can achieve up to 82% accuracy according to experts, outperforming previous work and baselines. We also release a collection of high-quality open cloze tests along with sample system output and human annotations that can serve as a future benchmark.