Using simulated annealing, Schneider's app solves traveling salesman problem for 48 U.S. state capitals. Todd Schneider

What's the shortest route, if you're visiting each city exactly once and then returning to the point of origin?

When he's not designing software for a living, Todd Schneider makes weird and wonderful apps for fun. In his latest effort, if you enter any list of cities—in the U.S. or anywhere in the world—the app will solve the famous "traveling salesman problem", which you may remember from your college math courses. It asks: what's the shortest route, if you're visiting each city exactly once and then returning to the point of origin?

"I don't think there is any practical application (for the app)," Schneider says. It's just something cool for people, especially math students, to play around and have some fun with, he says.

The app uses "simulated annealing," a method that finds answers to problems that have a really, really large number of possible solutions—so many, that it would take forever to try every single possibility on your own.

The first phase of calculations (called "high temperature") tries only a few solutions. In this phase, the app is trying possibilities randomly. Sometimes, it accepts a solution that may take it further from the right answer. As more and more tries go by, or "temperature" gets lower, the simulation starts choosing only those possible solutions that help it find the shortest route.

It sounds counter-intuitive and confusing. But picture a marble rolling down a hilly landscape, Schneider explains. To get to the lowest point in the valley, it may have to climb up a hill first. Similarly, to get to the shortest route, it has to try the longer routes first.

"Simulated annealing" accepts worse solutions in the first phase, and then only those that help it reach the correct answer.

Invoking the wisdom of Chief Wiggum, Schneider explains that behind the complicated math is a very simple idea: sometimes things have to get worse before they get better.

About the Author

Most Popular

  1. Charts

    The Evolution of Urban Planning in 10 Diagrams

    A new exhibit from the San Francisco Planning and Urban Research Association showcases the simple visualizations of complex ideas that have changed how we live.

  2. POV

    Why the Future Looks Like Pittsburgh

    The city’s rise as a global innovation city reflects decades of investment in emerging technology, a new Brookings report says.

  3. A Juggalo standing in front of Buffalo City Hall.
    Equity

    The Juggalo March Is Not a Joke

    Facepainted fans of the Insane Clown Posse are gathering on the National Mall this weekend. And they have something important to say.

  4. Equity

    What the New Urban Anchors Owe Their Cities

    Corporations like Google and Amazon reap the spoils of winner-take-all urbanism. Here’s how they can also bear greater responsibility.

  5. Design

    Octopuses Are Urbanists, Too

    Scientists were surprised to find that this smart and solitary species had built a cephalopod city. Why?