by M. Held, A. J. Hoffman, E. L. Johnson, P. Wolfe
For fifty years the traveling salesman problem has fascinated mathematicians, computer scientists, and laymen. It is easily stated, but hard to solve; it has become the prototypical hard problem in theoretical computer science. A large part of the extensive research conducted by IBM in the broad area of optimization, or mathematical programming, contributed to or was inspired by aspects of this challenging problem. This article reviews some of that work as well as recent developments in techniques that were used on the largest traveling salesman problem ever solved.