While delivering holiday presents may seem straightforward for fictional characters like Santa Claus, for companies like FedEx, the task represents a complex optimization problem. To solve it, these companies usually utilize specialized software known as mixed-integer linear programming (MILP) solvers. These solvers break down large optimization problems into smaller pieces, utilizing generic algorithms to identify the most efficient solution. However, this process is often time-consuming and occasionally has to be halted, accepting a non-ideal solution due to time constraints.
Recognizing these challenges, researchers from the Massachusetts Institute of Technology (MIT) and ETH Zurich have turned to machine learning to streamline the process. They identified a step in the MILP solver, inundated with potential solutions, that consumed significant time, slowing the entire process.
To overcome this, the researchers developed a filtering technique to simplify this step and then applied machine learning to find the best solution for a particular type of problem. Using the company’s own data, this data-driven method lets them adapt a general-purpose MILP solver to the problem at hand.
The new technique has increased the speed of MILP solvers by 30-70% without affecting accuracy. It enables quick attainment of ideal solutions or, for especially complex problems, better solutions within a manageable timeframe. This approach is applicable in areas where MILP solvers are used, such as ride-hailing services, electric grid operators, and vaccination distributors.
“This is a really strong instantiation of [a] hybrid approach,” says Cathy Wu, one of the study’s authors. She believes that this approach beautifully combines machine learning and classical methods for optimization problems.
MILP problems have immense volumes of potential solutions. An example is the classic traveling salesman problem, where the shortest path to visit several cities and then return to the starting city needs to be found. With numerous cities that could be visited in any order, the potential solutions might be greater than the number of atoms in the universe.
However, Wu and her team identified that determining the right combination of separator algorithms used in an MILP solver is in itself a problem with an astronomical number of potential solutions. The researchers devised a filtering mechanism that shrinks this separator-search space from over 130,000 potential combinations to about 20 options. After filtering, they use a machine-learning model to select the best algorithm combination from the 20 remaining options.
This innovative, data-driven approach accelerates MILP solvers between 30-70% without any drop in accuracy. The researchers want to utilize this strategy for more complex MILP problems in future, which could be challenging due to the need for large labeled datasets for model training.
This research is partially supported by Mathworks, the National Science Foundation (NSF), the MIT Amazon Science Hub, and MIT’s Research Support Committee.
