We investigate the finite size scaling of the mean optimal tour length as a function of density of obstacles in a constrained variant of the traveling salesman problem (TSP). The computational experience pointed out a critical transition (at ${\rho }_c\approx 85\%)$ in the dependence between the excess of the mean optimal tour length over the Held-Karp lower bound and the density of obstacles.

• Received 12 October 2000

DOI:https://doi.org/10.1103/PhysRevE.63.047103