In line with the growing trend of using machine learning to improve solving of combinatorial optimisation problems, one promising idea is to improve node selection within a mixed integer programming branch-and-bound tree by using a learned policy. In contrast to previous work using imitation learning, our policy is focused on learning which of a node's children to select. We present an offline method to learn such a policy in two settings: one that is approximate by committing to pruning of nodes; one that is exact and backtracks from a leaf to use a different strategy. We apply the policy within the popular open-source solver SCIP. Empirical results on four MIP datasets indicate that our node selection policy leads to solutions more quickly than the state-of-the-art in the literature, but not as quickly as the state-of-practice SCIP node selector. While we do not beat the highly-optimised SCIP baseline in terms of solving time on exact solutions, our approximation-based policies have a consistently better optimality gap than all baselines if the accuracy of the predictive model adds value to prediction. Further, the results also indicate that, when a time limit is applied, our approximation method finds better solutions than all baselines in the majority of problems tested.

The focus of this project is to develop a web application that automates the process of drawing schematic networks from geographical networks. It allows users to upload geographical networks and inspect the schematic representation in the browser. During the two week research phase we found a Master's Thesis which explains a method for modelling railway tracks and junctions and attempts to draw schematics. We improve upon the findings of this thesis. We wrote a transformer that can transform real-world GeoJSON data of railway networks to abstract input usable by our algorithms. If our application is to be extended to other infrastructure networks, a different transformer can be implemented while using the same underlying algorithm. We performed weekly sprints. At the end of each, we presented the improvements to our client to receive feedback. With this feedback we created a sprint plan to assign and prioritise the tasks and responsibilities of the next sprint. The testing of our application is based on extensive unit tests and end-to-end tests. We evaluated the results of our application and documented recommendations for improving the algorithm. Our application serves as a proof-of-concept to our client.