Solution of a Large-Scale Traveling-Salesman Problem

The RAND Corporation in the early 1950s contained “what may have been the most remarkable group of mathematicians working on optimization ever assembled” [6]: Arrow, Bellman, Dantzig, Flood, Ford, Fulkerson, Gale, Johnson, Nash, Orchard-Hays, Robinson, Shapley, Simon, Wagner, and other household names. Groups like this need their challenges. One of them appears to have been the traveling salesman problem (TSP) and particularly its instance of finding a shortest route through Washington, DC, and the 48 states [4, 7]. Dantzig’s work on the assignment problem [1] revealed a paradigm for minimizing a linear function f : Rn → R over a finite subset S of Rn: first describe the convex hull of S by a system Ax ≤ b of linear constraints and then solve the linear programming problem