Efficiently routing packages during the holiday season is a complex problem for companies like FedEx, a task often tackled with specialized software, known as mixed-integer linear programming (MILP) solvers. Although they break down the problem into smaller parts and use generic algorithms to find solutions, they could still take hours or days to complete.
MIT and ETH Zurich researchers, however, have found a way to speed up this process using machine learning. They pinpointed an intermediate step in MILP solvers consisting of potential solutions that take a long time to cut down. By employing a filtering method to this step and using machine learning to find the optimal solution, they were able to make the process considerably quicker.
This new technique, which focuses on data-driven problem-solving, tailored a general-purpose MILP solver using a company’s unique data. It accelerated the MILP solver by 30 to 70 percent without compromising accuracy, providing optimal solutions more quickly or generating a superior solution in a reasonable timespan for complex issues.
This approach could be valuable in multiple industries that utilize MILP solvers, for instance, ride-hailing services, electric grid operators, vaccination distributors, as well as any organization dealing with resource-allocation problems.
While dividing and conquering is the commonplace procedure of a solver, it often involves an intricate method of branching, which splits the solution space into smaller segments. The solver then employs another technique called cutting to quicken the search in these fragments.
Wu and her team recognized that deciding the ideal blend of separator algorithms to apply is a problem that also has potential solutions in exponential numbers, notoriously hard to solve. This led to the creation of a filtering mechanism that minimized the separator search space from more than 130,000 potential combinations to approximately 20. They then used a machine learning model to select the most effective combination from these remaining options.
The practical application of this research ranged from simple, open-source solvers to more advanced, commercial ones, with similar results. In future, the team plans to tackle more complex problems while delving into understanding the efficiency of different separator algorithms. Among their supporters are MathWorks, National Science Foundation, MIT Amazon Science Hub, and MIT’s Research Support Committee.
