The traveling salesman problem might be described as follows: Find the shortest route for a salesman starting from a given city, visiting each of a specified group of cities, and then returning to the original point of departure. More generally, given an n by n symmetric matrix D = (dij), where dij represents the "distance" from i to j, arrange the points in a cyclic order in such a way that the sum of the dij between consecutive points is minimal. Since there are only a finite number of possibilities to consider, the problem is to devise a method of picking out the optimal arrangement which is reasonably efficient for fairly large values of n. Although algorithms have been devised for problems of similar nature, e.g., the optimal assignment problem, little is known about the traveling salesman problem. We do not claim that this note alters the situation very much; what we shall do is outline a way of approaching the problem that sometimes, at least, enables one to find an optimal path and prove it so.
This report is part of the RAND Corporation Paper series. The paper was a product of the RAND Corporation from 1948 to 2003 that captured speeches, memorials, and derivative research, usually prepared on authors' own time and meant to be the scholarly or scientific contribution of individual authors to their professional fields. Papers were less formal than reports and did not require rigorous peer review.
This document and trademark(s) contained herein are protected by law. This representation of RAND intellectual property is provided for noncommercial use only. Unauthorized posting of this publication online is prohibited; linking directly to this product page is encouraged. Permission is required from RAND to reproduce, or reuse in another form, any of its research documents for commercial purposes. For information on reprint and reuse permissions, please visit www.rand.org/pubs/permissions.
The RAND Corporation is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.