A branch and bound algorithm for robust binary optimization with budget uncertainty

Abstract Since its introduction in the early 2000s, robust optimization with budget uncertainty has received a lot of attention. This is due to intuitive construction sets and existence compact reformulation for (mixed-integer) linear programs. However, despite compactness, performs poorly when solving integer problems weak relaxation. To overcome arising from formulation, we propose bilinear formulation binary programming, which as strong theoretically possible. From this derive formulations well structural properties problems, use within tailored branch bound algorithm. We test our algorithm’s performance together other approaches literature on diverse set “robustified” real-world instances MIPLIB 2017. Our computational study, first compare many sophisticated broad instances, shows that algorithm outperforms existing by far. Furthermore, show fundamental proven paper can be used substantially improve literature. highlights relevance findings, not only tested algorithms, but also future research optimization. encourage algorithms benchmarking, make all materials freely available online.