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We study the random link traveling salesman problem, where lengths l_ijbetween city i and city j are taken to be independent, identically distributedrandom variables. We discuss a theoretical approach, the cavity method, thathas been proposed for finding the optimal tour length over this randomensemble, given the assumption of replica symmetry. Using finite size scalingand a renormalized model, we test the cavity predictions against the results ofsimulations, and find excellent agreement over a range of distributions. Wethus provide numerical evidence that the replica symmetric solution to thisproblem is the correct one. Finally, we note a surprising result concerning thedistribution of kth-nearest neighbor links in optimal tours, and invite atheoretical understanding of this phenomenon.Comment: 21 pages, 7 figures; to appear in Journal of Statistical Physics  (March 1999); this revision contains final version incorporating some change

The stochastic traveling salesman problem: Finite size scaling and the cavity prediction