Numerous companies like FedEx grapple with the sophisticated problem of optimising the routing of holiday packages. Specialised software known as a mixed-integer linear programming (MILP) solver is often used to split this massive optimisation issue into smaller pieces, allowing generic algorithms to locate the most suitable solution. This time-consuming process sometimes forces companies to settle for less than ideal solutions due to time constraints.
Researchers from MIT and ETH Zurich used machine learning to streamline this process. They focused on a key step in the MILP solver that generates many potential solutions, causing a slowdown because of the time taken decipher them. The researchers created a filtering method to simplify this step and combined it with machine learning to find the most optimal solution for a given type of problem. This customised a general-purpose MILP solver to the precise problem, using a company’s own data.
This novel technique boosted the speed of MILP solvers by 30-70% without diminishing accuracy. It could be employed in various sectors where MILP solvers are used, such as ride-hailing companies, electric grid operators, and vaccine distributors, among others facing complex resource-allocation challenges.
The researchers used a filtering mechanism that reduced the separator search space from over 130,000 possible combinations to around 20. A machine-learning model then selected the best combination of algorithms from these 20 alternatives.
The model was trained using a dataset specific to the user’s optimisation problem. This enabled it to select algorithms that were best suited to the user’s specific task. The approach saw MILP solvers accelerate by 30-70% without any decrease in precision.
In future, the researchers aim to apply this strategy to increasingly complex MILP problems, particularly those where collecting labelled data for model training could pose significant challenges. They aspire to train the model on a smaller dataset and gradually tweak it to handle a significantly larger optimisation problem. Furthermore, they are keen to interpret the learned model to gain a deeper comprehension of the efficacy of different separator algorithms. The research was supported by various organisations including Mathworks, the National Science Foundation (NSF), the MIT Amazon Science Hub, and MIT’s Research Support Committee.
