Local Optimization and the Traveling Salesman Problem

The Traveling Salesman Problem (TSP) is often cited as the prototypical “hard” combinatorial optimization problem. As such, it would seem to be an ideal candidate for nonstandard algorithmic approaches, such as simulated annealing, and, more recently, genetic algorithms. Both of these approaches can be viewed as variants on the traditional technique called local optimization. This paper surveys the state of the art with respect to the TSP, with emphasis on the performance of traditional local optimization algorithms and their new competitors, and on what insights complexity theory does, or does not, provide.