Awaiting delivery of a vacation package? There is a tricky math problem that needs to be solved before the delivery truck arrives at your door, and MIT researchers have a strategy that could speed up the solution.
The approach applies to vehicle routing issues such as last mile delivery, where the goal is to deliver goods from a central depot to multiple cities while reducing travel costs. While there are algorithms designed to solve this problem for a few hundred cities, these solutions become too slow when applied to more cities.
To remedy this, Cathy Wu, Gilbert W. Winslow Career Development Assistant Professor in Civil and Environmental Engineering and at the Institute of Data, Systems and Society, and her students devised a learning strategy automatic which speeds up some of the strongest algorithmic solvers 10 to 100 times.
Solving algorithms work by dividing the delivery problem into smaller subproblems to be solved, for example 200 subproblems for moving vehicles between 2000 cities. Wu and his colleagues augment this process with a new machine learning algorithm that identifies the most useful subproblems to solve, instead of solving all the subproblems, to increase the quality of the solution while using orders from magnitude less calculated.
Their approach, which they call “learning to delegate,” can be used for a variety of solvers and a variety of similar problems, including planning and path finding for warehouse robots, the researchers said.
The work pushes the boundaries of quickly solving large-scale vehicle routing issues, says Marc Kuo, founder and CEO of Routific, a smart logistics platform for delivery route optimization. Some of Routific’s recent algorithmic advances were inspired by Wu’s work, he notes.
âMost university researchers tend to focus on specialized algorithms for small problems, trying to find better solutions at the expense of processing times. But in the real world, companies don’t care about finding better solutions, especially if they’re taking too long to calculate, âsays Kuo. âIn the world of last mile logistics, time is money, and you can’t let your entire warehouse operations wait for a slow algorithm to return routes. An algorithm has to be super fast to be practical.
Wu, social systems and engineering doctoral student Sirui Li, and electrical and computer engineering doctoral student Zhongxia Yan presented their research this week at the NeurIPS 2021 conference.
Selection of good problems
Routing problems are a class of combinatorial problems, which involve the use of heuristic algorithms to find “good enough solutions” to the problem. It is usually not possible to find the “best” answer to these problems because there are too many possible solutions.
âThe name of the game for these types of problems is to design efficient algorithmsâ¦ that are optimal in some factor,â Wu explains. âBut the point is not to find optimal solutions. It’s too hard. On the contrary, we want to find the best possible solutions. Even a 0.5% improvement in solutions can translate into a huge increase in a company’s revenue. “
Over the past decades, researchers have developed a variety of heuristics to provide rapid solutions to combinatorial problems. They usually do this by starting with a poor but valid initial solution and then gradually improving the solution – trying small tweaks to improve routing between neighboring towns, for example. However, for a big problem like a routing challenge of more than 2000 cities, this approach takes too long.
More recently, machine learning methods have been developed to solve the problem, but although faster, they tend to be more inaccurate, even at the scale of a few dozen cities. Wu and his colleagues decided to see if there was a beneficial way to combine the two methods to find quick but high-quality solutions.
âFor us, that’s where machine learning comes in,â Wu says. âCan we predict which of these subproblems, which, if we were to solve them, would lead to a greater improvement in the solution, by saving computing time and expense? “
Traditionally, a large scale vehicle routing problem heuristic can choose which subproblems to solve in which order, either at random or by applying yet another carefully designed heuristic. In this case, the MIT researchers ran sets of subproblems through a neural network they created to automatically find the subproblems that, when solved, would lead to the greatest gain in quality of the solutions. This process sped up the process of selecting subproblems 1.5 to 2 times, Wu and colleagues found.
âWe don’t know why these subproblems are better than other subproblems,â Wu notes. âThis is actually an interesting line of future work. If we had any ideas here, they might lead to the design of even better algorithms. “
Wu and his colleagues were surprised by the effectiveness of the approach. In machine learning, the idea of ââgarbage entry and exit applies, that is, the quality of a machine learning approach is highly dependent on the quality of the data. A combinatorial problem is so difficult that even its subproblems cannot be solved optimally. A neural network trained on the “medium quality” subproblem solutions available as input data “would generally yield medium quality results,” Wu says. In this case, however, the researchers were able to take advantage of medium quality solutions to achieve high quality results much faster than advanced methods.
For vehicle tours and similar issues, users often have to design very specialized algorithms to solve their specific problem. Some of these heuristics have been in development for decades.
The learning-to-delegate method provides an automatic way to speed up these heuristics for big problems, regardless of the heuristic or, potentially, the problem.
Since the method can work with a variety of solvers, it can be useful for a variety of resource allocation issues, Wu explains. âWe can unlock new applications which will now be possible because of the cost of solving the problem. is 10 to 100 times lower. “
The research was supported by the MIT Indonesia Seed Fund, the US Department of Transportation’s Dwight David Eisenhower Transportation Fellowship Program, and the MIT-IBM Watson AI Lab.