Generative deep learning for decision making in gas networks

Mixed-Integer Linear Programming (MILP) is concerned with the modelling and solving of problems from discrete optimisation. These problems can represent real-world scenarios, where discrete decisions can be appropriately captured and modelled by the integer variables. In real-world scenarios a MILP model is rarely solved only once. More frequently, the same model is used with varying data to describe different instances of the same problem which are solved on a regular basis. This holds true in particular for decision support systems, which can utilise MILP to provide real-time optimal decisions on a continual basis, see [4] and [40] for examples in nurse scheduling and vehicle routing. The MILPs that these decision support systems solve have identical structure due to both their underlying application and cyclical nature, and thus often have similar optimal solutions. Our aim is to exploit this repetitive structure, and create generative neural networks that generate binary decision encodings for subsets of important variables. These encodings can then be used in a primal heuristic by solving the induced sub-problem following variable fixations. Additionally, the then result of the primal heuristic can be used in a warm-start context to help improve solver performance in a globally optimal context.