Mo Willem's children's book Dont Let the Pigeon Drive the Bus! features a pigeon as the main character. She uses every trick in the book to convince the reader that the pigeon should be allowed to drive the bus when the human driver has to go. In 2012, Willems' book was unintentionally influenced scientifically by Human Cognition publishing a respectable paper by three highly respected researchers, Matthew Wilkinson and Debbie Kelly. They demonstrated experimentally that pigeons could find solutions to simple cases of a well-known mathematical curiosity, the Travelling Salesman Problem. Their title was "Let the pigeon drive a bus: Pigeons can plan future routes within a room."
The bus driver may have worried that the pigeon wouldn't be able safely drive the bus. The driver might have been more concerned about the pigeon's ability to safely drive the bus.
Scientists are not supposed to lack humor. Or that clever titles don't help generate publicity.
The Traveling Salesman problem is more than a curiosity. Combinatorial optimization is a class of extremely important problems that has enormous practical importance. Mathematicians are known for asking deep, significant questions using apparent trivia.
This piece of trivia was inspired by a book that was written foryou guessed right, traveling salesmen. Door-to-door sellers. As any smart businessperson, the German traveling salesman (1832) valued efficiency and cost cutting. A manual was available to help the traveling salesman to know what he needed to do to get orders and ensure a successful business.
An elderly peripatetic vendor stated that:
Traveling salesmen are often brought to business. It is impossible to indicate travel routes that are appropriate for every case. However, we believe that it is possible to make the most of your time by choosing the right tour.
Although the manual did not propose any mathematical solutions to this problem, it did include examples of five supposedly optimal tours.
TSP (Traveling Salesman Problem), or TSP as it was later known, was a foundation example of the mathematical area known as combinatorial optimization. This means that you have to find the best option from a wide range of options.
Adapted from "What's the Use", by Ian Stewart. Courtesy: Basic Books. Buy this book at Amazon
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Curiously, however, the TSP name has not been explicitly used in any publication about this problem since 1984. However, it was common usage in informal discussions among mathematicians much earlier.
Companies rarely sell their products by sending someone with a suitcase filled of samples from one town to another. They upload everything to the internet. Despite its unreasonable effectiveness, this cultural shift has not rendered the TSP obsolete. Online shopping is growing exponentially and so does the need for efficient methods to determine routes or schedules for everything, from parcels to orders at supermarkets to pizza.
It is also important to consider the portability of mathematics. The TSP's applications aren't limited to traveling between cities or along streets. Once upon a while, prominent astronomers owned their telescopes or shared them with a few others. It was simple to redirect the telescopes to point at new heavenly bodies. It is no longer possible to reorient the telescopes to point at new heavenly bodies, especially when they are large and expensive and can be accessed online. It takes time to point the telescope at a new object. The telescope cannot be used for observations while it is being moved. If you visit targets in an incorrect order, it can take a lot of time to move the telescope long distances and back again to the original location.
To avoid computer time being wasted, DNA sequencing requires that fragmentary sequences of DNA bases be correctly joined. Other uses include efficient routing of aircraft and the design and manufacturing of computer microchips or printed circuit boards. The approximate solutions to TSPs were used to optimize the delivery of blood to hospitals and find efficient routes for Meals on Wheels. One version of the TSP was even used in Star Wars' hypothetical Strategic Defense Initiative by President Ronald Reagan. A powerful laser orbiting Earth would have been targeted at several incoming nuclear missiles.
Merrill Flood, an operations researcher and pioneer in 1956, argued that the TSP was likely to be difficult. In 1979, Michael Garey, David Johnson and David Johnson proved him right. There is no efficient algorithm that can solve the problem in the worst case. However, worst-case scenarios are often very contrived and not common in the real world. Operation research mathematicians set out to find out how many cities they could solve for real-world problems.
