1. On the Potential of Molecular Computing
2. Kirpatrick S., Gelatt C. D., Vecchi M. P., ibid. 220, 671 (1983).
3. As for the traveling salesperson problem (TSP) (2 4) for the HCP we took a tour as a permutation of the numbers 1 2 3 … N . We took the distance between two cities to be 0 if there exists a road between the cities and 1 if not. A tour of length 0 thus corresponds to a Hamiltonian cycle. Instead of the Lin-Kernighan reversal move we substituted a “swap” move in which two randomly chosen cities switch places on the tour. We tried to minimize the length of the tour. As we expected numerous tours to have the same length we augmented the length of a trial tour by a small additive constant δ > 0 to bias the algorithm to seek shorter paths. We annealed according to the schedule T = T 0 (T 1 ) M with T 0 = 0.5 and T 1 = 0.9 ( M an Integer). We used δ = 0.2. We used 125 N 2 tours at each temperature lowering the temperature if 12.5 N 2 successful moves had been accepted at a given temperature. Most of the tours appeared to be needed for the HCP near T = 0 to find the last few roads. N 2 paths are needed at each temperature for the HCP but only N paths at each temperature for the TSP. A 100-city HCP was beginning to be difficult for SA while a 100-city TSP was easy. These may reflect the increased complexity introduced by the “distance” function for the HCP over the 2-D Euclidean distance function of the TSP.
4. Press W. H., Teukolsky S. A., Vetterling W. T., Flannery B. P., Numerical Recipes (Cambridge Univ. Press, Cambridge, UK, 1992).
5. Work at Lawrence Livermore National Laboratory was performed under U.S. Department of Energy contract W-7405-Eng-48.