Santa Claus delivers presents with the help of magic, but delivering holiday packages isn’t quite as simple for companies like FedEx. These businesses often rely on advanced software called mixed-integer linear programming (MILP) solvers to route their deliveries. Yet, while these solvers break down complex problems into smaller, more manageable segments, it can still take days for the system to find an optimal solution.
Looking to speed up the process, researchers from MIT and ETH Zurich introduced machine learning into the equation. They applied a filtering technique to simplify a complex step in the routing process that took considerable time to unravel, used machine learning to determine optimal solutions, and designed software to tailor the general-purpose MILP solver to the specific problem.
Using this hybrid approach, the researchers increased the speed of MILP solvers between 30 and 70%, without compromising accuracy. Complex optimization problems could either be solved faster or be given a more suitable solution within a reasonable timeframe.
This technique could be applied wherever MILP solvers are used, in ride-hailing services, power grid operators, vaccination distributors, or for any business faced with complicated resource-allocation problems.
Researchers found that finding the best combination of algorithms to apply, known as ‘separator management’, was itself a problem with countless potential solutions. To overcome this challenge, they created a filtering mechanism that cut the search space from over 130,000 possibilities to around 20 options. A machine-learning model then trained with the user’s specific problem data selected the best algorithm combination from the remaining options.
The model used a data-driven approach, known as contextual bandits, to improve its accuracy over time. This involved selecting a potential solution, receiving feedback on its effectiveness, and then using this feedback to seek a better solution.
Results showed that introducing this process could hasten MILP solvers by 30 to 70%, all while maintaining accuracy. Also, the method was equally effective when applied to both a less complex, open-source solver and a more complex, commercial solver.
The researchers hope to apply this solution to more complex MILP problems in challenging environments that may limit data availability. They are exploring options to train the model on smaller data sets then adapt it to deal with larger optimization problems, and also understand the effectiveness of different separator algorithms better. The research received support from organizations like Mathworks, the National Science Foundation, the MIT Amazon Science Hub, and MIT’s Research Support Committee.
