Optimisation methods, such as mixed integer linear programming, have been very successful at decision-making for more than 50 years. Optimisation algorithms support basically every industry behind the scenes and the simplex algorithm is one of the top 10 most influential algorithms. Major success stories include rostering nurses in hospitals, managing chains of organ transplants, planning production levels for manufacturing, routing delivery trucks for transport, scheduling power stations and electricity grids, to name just a few. In recent years, deep learning is showing startling ability at prediction and pattern recognition tasks but still fails at very simple planning and decision-making problems. This project will develop predictive and prescriptive analytics algorithms that combine traditional optimisation methods and modern deep learning techniques.
Mixed integer linear programming is a successful discrete optimisation methodology but it is incompatible with deep neural networks, which are based on continuous optimisation. This project will develop continuous approximations of discrete optimisation problems to allow a discrete algorithm to be differentiated. The continuous approximation will then be embedded as a layer in a neural network. This will allow end-to-end predictive and prescriptive analytics, answering questions such as “given these prices of my input products, predict the cost of manufacturing my products and decide how many I need to produce in order to sell for maximum profit”, in one step. This will mitigate inaccuracies in the current practice of separating this question into several independent questions. This project will also contribute to an effort at Monash University in developing neuro-symbolic artificial intelligence methods.
This project would suit a mathematics or computer science student with a background in continuous optimisation (linear and non-linear programming) and discrete optimisation (mixed integer programming). An ability to code, preferably in C, C++ or Rust, is also necessary. Candidates with experience or interest in cutting planes, polyhedral geometry and graph theory are especially invited to apply. A fully-funded scholarship for course fees, living allowance (food, rent, entertainment, etc.) and international conference travel may be available.