FINDING CUTS IN THE TSP ( A preliminary report

TSPLIB is Gerhard Reinelt's library of some hundred instances of the traveling salesman problem. Some of these instances arise from drilling holes in printed circuit boards; others arise from X-ray crystallography; yet others have been constructed articially. None of them (with a single exception) is contrived to be hard and none of them is contrived to be easy; their sizes range from 17 to 85,900 cities; some of them have been solved and others have not. We have solved twenty previously unsolved problems from the TSPLIB. One of them is the problem with 225 cities that was contrived to be hard; the sizes of the remaining nineteen range from 1,000 to 7,397 cities. Like all the successful computer programs for solving the TSP, our computer program follows the scheme designed by George Dantzig, Ray Fulkerson, and Selmer Johnson in the early nineteen-fties. The purpose of this preliminary report is to describe some of our innovations in implementing the Dantzig-Fulkerson-Johnson scheme; we are planning to write up a more comprehensive account of our work soon.