Complexity, heuristics, and the traveling salesman problem

Add this one to your long reads queue, because it’s well worth it: Tom Vanderbilt writes in Nautilus about the traveling salesman problem and how algorithmic optimization helps us understand human behavior more deeply. It’s a thorough and nuanced analysis of the various applications of algorithms to solve the traveling salesman problem — what’s the most efficient way (which you of course have to define, either in time or money or gasoline etc.) to deliver some number n of packages to some number d of destinations, given your number t of trucks/drivers? This is a tough problem for several reasons, and Vanderbilt’s discussion of those reasons is clear and interesting.

We can start with a simple transportation model with small numbers of packages, destinations, and trucks. But as the number of them increases, the problem to solve becomes increasingly complex, increasing at least exponentially if not more. Then think about what happens when the locations of the destinations change every day, as is the case for UPS and FedEx deliveries. Then think about what happens when you add in heterogeneity of the deliveries; Vanderbilt opens with a girl pointing out that her mother would never buy perishables and then leave them in the car all day, so the nature of the item changes the constraints on the definition of the efficient route.

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.

One of the most intriguing aspects of implementing logistics that reflect good solutions to the TSP that Vanderbilt highlights is the humanity of the driver. Does the dispatcher know the driver, know that s/he is reliable or not? That may affect how to define the route, and how many stops or changes to put on that particular person’s schedule. Is the driver prone to fatigue, and how does that fatigue affect the driver’s decision-making? What are the heuristics or rules of thumb that different drivers use to make decisions in the face of uncertainty given the cognitive limitations of humans? How different will the different heuristics of different drivers be, and how to they affect the logistics of the system?

What Vanderbilt finds is that good logistics systems take the organic, emergent system that incorporates those heuristics into account when devising the TSP algorithm. They leave a human component in the logistics, but also use the human component to inform and change the algorithm. Another important element is data, because all such algorithms are going to work in conjunction with such data as location. GIS mapping capabilities improve the data used to establish, test, and monitor TSP algorithms.