Reduction techniques providing initial groupings for Euclidean traveling salesman patching algorithms

Abstract

Patching algorithms are accepted methods for dealing with large traveling salesman problems. These techniques involve finding an initial set of groupings of the cities and combining them in such a way as to form an approximation to the optimum tour. The solution to the corresponding assignment problem does not provide subtours in the Euclidean case which are as effective as in the general case. An improvement is then suggested to the usual dissection method involving the step-by-step reduction of the number of cities.