2009
DOI: 10.1016/j.orl.2008.12.002
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Average-case approximation ratio of the 2-opt algorithm for the TSP

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Cited by 29 publications
(13 citation statements)
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“…In practice, it usually converges quite quickly to close-to-optimal solutions [25]. To explain its performance in practice, probabilistic analyses of its running-time on geometric instances [18,28,33] and its approximation performance on geometric instances [18] and with independent, non-metric edge lengths [17] have been conducted. We prove that for random shortest path metrics, the expected number of iterations that 2-opt needs is bounded by a polynomial.…”
Section: Running-time Of 2-opt For the Tspmentioning
confidence: 99%
See 1 more Smart Citation
“…In practice, it usually converges quite quickly to close-to-optimal solutions [25]. To explain its performance in practice, probabilistic analyses of its running-time on geometric instances [18,28,33] and its approximation performance on geometric instances [18] and with independent, non-metric edge lengths [17] have been conducted. We prove that for random shortest path metrics, the expected number of iterations that 2-opt needs is bounded by a polynomial.…”
Section: Running-time Of 2-opt For the Tspmentioning
confidence: 99%
“…In the worst case on metric instances, it is O( √ n) [12]. For independent, non-metric edge lengths drawn uniformly from the interval [0, 1], the expected approximation ratio is O( √ n·log 3/2 n) [17]. For d-dimensional geometric instances, the smoothed approximation ratio is O(φ 1/d ) [18], where φ is the perturbation parameter.…”
Section: Open Problemsmentioning
confidence: 99%
“…Theorem 2.2 is too weak for this. This problem of bounding the expected value of the inverse of the optimal objective value arises frequently in bounding expected approximation ratios [11,12].…”
Section: Smoothed Approximation Ratiomentioning
confidence: 99%
“…Although the 2-opt algorithm (Helsgaun, 2000;Engels and Manthey, 2009) performs well and can be applied to TSP with many cities, it finds only a local minimum. Furthermore, for the general (i.e.…”
Section: Source: Author's Illustrationmentioning
confidence: 99%
“…5. Merge fragments (u i → y) and (x → v j ) into (u i → v j ). 6. If EP C is not empty, go to step 3.…”
Section: Endwhilementioning
confidence: 99%