Running time vs. tour quality for the traveling salesman problem
Suppose you need to find good tours for Traveling Salesman Problem (TSP) instances of around N cities, and will have about t seconds available for solving each instance. Which TSP heuristic should you choose? As a result of an extensive experimental study of TSP heuristics, we can given some preliminary advice. In particular, this talk will examine the tradeoffs between running time and tour quality for a wide variety of efficiently-implemented tour construction and local optimization heuristics for the TSP, for instances ranging in size from a hundred to a million cities. Our first conclusion if N {<=} 100, running time is no longer much of an object. On a modern workstation, even a sophisticated heuristic like Lin-Kernighan, which typically gets within 1% of the optimal tour length for instances of this size, takes less than 0.1 seconds of user time. Time does make a difference when N = 1,000,000, but good solutions are still feasible to obtain. lin-Kernighan takes less than 50 minutes, and one can get within 35% of optimal in just 22 seconds using the Spacefilling Curve heuristic. In between there are only a few undominated possibilities (algorithms for which no faster competitor produces better tours), including Nearest Neighbor, the Clarke-Wright Savings Heuristic 2-Opt, and 3-Opt. The above results are for random Euclidean instances, but correlation well with results for more-structure instances from TSPLIB.
- OSTI ID:
- 36171
- Report Number(s):
- CONF-9408161--
- Country of Publication:
- United States
- Language:
- English
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