GANGOLLI@SUSHI.STANFORD.EDU (Anil R. Gangolli) (10/03/87)
Office Phone: (415) 723-3605 Message-ID: <12339367659.44.GANGOLLI@Sushi.Stanford.EDU> ReSent-date: Mon 5 Oct 87 10:39:35-PDT ReSent-from: Ken Laws <LAWS@IU.AI.SRI.COM> ReSent-to: ailist@SRI.COM ReSent-Date: Sun 11 Oct 87 22:37:05-PDT ReSent-From: Ken Laws <Laws@KL.SRI.Com> ReSent-To: post-ailist@UCBVAX.Berkeley.EDU ReSent-Message-ID: <12341800883.16.LAWS@KL.SRI.Com> 15-October-87: David Johnson (AT&T Bell Labs) Near-Optimal Solutions to Very Large Traveling Salesman Problems Most experimental studies of algorithms for the Travel- ing Salesman Problem (TSP) have concentrated on relatively small test cases, instances with 100 cities or less. In practice, however, much larger instances are frequently encountered, both in engineering and scientific applica- tions. This talk begins by surveying complexity results about the TSP and the status of algorithms for finding optimal solutions to small instances. It then goes on to report the results of experiments with standard TSP heuris- tics on large instances, from 500 cities to 100,000, examin- ing the trade-offs obtainable between running time and qual- ity of solution. Most of the standard heuristics will be compared, including such new approaches as ``simulated annealing,'' but particular emphasis will be placed on the acknowledged ``champion,'' the sophisticated Lin-Kernighan algorithm. Using various programming tricks, we have imple- mented a version of this heuristic for the Euclidean case that remains feasible even for 10,000 city instances (8 hours on a minicomputer), and continues to find tours that are within 2% of optimal. For 20,000 or more cities, we could still obtain tours that were within 5% of optimal using Lin-Kernighan as a subroutine in a partitioning scheme suggested by Karp. If one is willing to settle for slightly worse tours, an approximate version of the Christofides heuristic seems to stay within 20% of optimal and has quite acceptable running times even for 100,000 cities.