The logistics of delivering holiday packages by companies such as FedEx requires specialized software for efficient routing, given the immense complexity of the optimization problem. The software currently in use, known as a mixed-integer linear programming (MILP) solver, often takes days to arrive at a solution, and even then, the companies have to accept solutions that are not entirely ideal due to the time constraint. To speed up this process, researchers from Massachusetts Institute of Technology (MIT) and ETH Zurich leveraged machine learning.
The researchers pinpointed a critical intermediate step in the MILP solvers that contains countless potential solutions, taking an excessively long time to unwind and thereby slowing down the entire process. To simplify this step, they employed a filtering technique. They then used machine learning to find the most optimal solution to a specific type of problem. This data-driven approach allowed companies to tailor a general-purpose MILP solver to their specific problem using their data.
This technique increased the speed of the MILP solvers by 30-70% without compromising their accuracy. It could be used to obtain optimal solutions more quickly or to find better solutions to particularly complex problems within a reasonable timeframe. The method is applicable in various settings where MILP solvers are utilized, ranging from ride-hailing companies and electric grid operators to vaccination distributors and other entities dealing with resource allocation issues.
The large number of potential solutions for MILP problems makes them notoriously hard to solve and time-consuming. A standard solver employs techniques such as branching (which entails splitting the potential solution space into smaller chunks) and cutting (which tightens these smaller pieces for quicker searching). The current MILP solver uses several rules to tighten the search space while ensuring that no feasible solutions are eliminated.
The researchers uncovered that the process of identifying the best combination of separator algorithms to use is in and of itself a problem with an exponential number of solutions, a task well-suited to machine learning. Consequently, they developed a filtering mechanism that decreases the separator search space from over 130,000 possible combinations to about 20 options. They then used a machine learning model to select the best algorithm combination from these 20 finalists. This model is trained with a dataset specific to the user’s optimization problem, so it keeps learning to choose algorithms that best suit the user’s task.
This data-guided approach accelerated MILP solvers between 30 and 70% without affecting precision. Furthermore, this acceleration was consistent when the method was applied to both a simpler open-source solver and a commercial solver. Looking ahead, the researchers intend to leverage this approach for more intricate MILP problems, where amassing labeled data to train the model could pose considerable challenges. They plan to train the model on a smaller dataset and then adjust it to handle a larger optimization problem. Additionally, the researchers aim to interpret the learned model to better comprehend the effectiveness of distinctive separator algorithms.
