Unhappy Truckers and Other Algorithmic Problems

[ed. See also: The Trucker and the Professor.]

When Bob Santilli, a senior project manager at UPS, was invited in 2009 to his daughter’s fifth grade class on Career Day, he struggled with how to describe exactly what he did for a living. Eventually, he decided he would show the class a travel optimization problem of the kind he worked on, and impress them with how fun and complex it was. The challenge was to choose the most efficient route among six different stops, in a typical suburban-errands itinerary. The class devised their respective routes, then began picking them over. But one girl thought past the question of efficiency. “She says, my mom would never go to the store and buy perishable things—she didn’t use the word perishable, I did—and leave it in the car the whole day at work,” Santilli tells me.

Her comment reflects a basic truth about the math that runs underneath the surface of nearly every modern transportation system, from bike-share rebalancing to airline crew scheduling to grocery delivery services. Modeling a simplified version of a transportation problem presents one set of challenges (and they can be significant). But modeling the real world, with constraints like melting ice cream and idiosyncratic human behavior, is often where the real challenge lies. As mathematicians, operations research specialists, and corporate executives set out to mathematize and optimize the transportation networks that interconnect our modern world, they are re-discovering some of our most human quirks and capabilities. They are finding that their job is as much to discover the world, as it is to change it. (...)

A mathematician claimed the prize, and a regal $10,000. But the contest organizers could only verify that his solution was the shortest of those submitted, and not that it was the shortestpossible route. That’s because solving a 33-city problem by calculating every route individually would require 28 trillion years—on the Department of Energy’s 129,000-core supercomputer Roadrunner (which is among the world’s fastest clusters). It’s for this reason that William J. Cook, in his book In Pursuit of the Traveling Salesman, calls the traveling salesman problem “the focal point of a larger debate on the nature of complexity and possible limits to human knowledge.” Its defining characteristic is how quickly the complexity scales. A six-city tour has only 720 possible paths, while a 20-city tour has—by Cook’s quick calculations on his Mac—more than 100 quadrillion possible paths. (...)

By now it should be clear that we are not talking just about the routing needs of salesmen, for even the most trenchant of regional reps does not think about hitting 90,000 far-flung burghs on a call. But the Traveling Salesman Problem, and its intellectual cousins, are far from theoretical; indeed, they are at the invisible heart of our transportation networks. Every time you want to go somewhere, or you want something to get to you, the chances are someone is thinking at that very moment how to make that process more efficient. We are all of us traveling salesmen.

by Tom Vanderbilt, Nautilus |  Read more:

Image: Peter and Maria Hoey