K. Helsgaun. An Effective Implementation of the Lin-Kernighan Traveling Salesman Heuristic. Eur. J. Oper. Res., 126:106--130, 2000.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....searched efficiently using appropriate data structures even when using a best improvement pivoting rule. However, a recent trend in the design of local search algorithms is to look for large neighbourhoods that can be explored efficiently. For many problems like the traveling salesperson problem [24, 30], the generalized assignment problem [38] and many others [11, 3] local search algorithms exploiting large neighbourhoods are currently at the core of new state of the art algorithms. In this paper, we investigate a new neighbourhood search method that uses a very large scale neighbourhood, and ....

K. Helsgaun. An effective implementation of the lin-kernighan traveling salesman heuristic. European Journal of Operational Research, 126:106--130, 2000.

....minutes, and the longest any such instance took was just a little over two hours. Second, if one is only willing to spend seconds rather than minutes, the best of the current heuristics are hard to beat. For instance, the N=10 iteration version of the publicly available LKH code of Keld Helsgaun [40] can get within 0.2 of optimum in no more than 20 seconds (normalized) for each of our 1,000 city random instances and for the six TSPLIB 3 instances with between 1,000 and 1,200 cities. Thus it is not clear that heuristics are needed at all for instances with fewer than 1,000 cities, and even ....

.... such as the unanchored path of Mak and Morton [52] or the stem and cycle of Glover [33, 34] In addition, alternative ways of extending an LK search Experimental Analysis of Heuristics for the STSP 49 (besides the standard 2 Opt move) have been considered, as in the variant due to Helsgaun [40] that augments via 5 Opt moves. We do not have space to go into full detail on how all the tested implementations differ. Indeed, many implementers written descriptions of their implementations do not provide all the answers. So we concentrate in what follows on key differences (and ....

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K. Helsgaun. An effective implementation of the Lin-Kernighan traveling salesman heuristic. European Journal of Operations Research, 12:106--130, 2000. Source code currently available from the author's http://www.dat.ruc.dk/keld/.

....All the real world instances with 100 cities or less from [10] and all the 100 city randomly generated instances in our testbed can be solved to optimality in reasonable time using the technique described in Section 2.1. Moreover, the publicly available implementation of Helsgaun s heuristic [17] should suffice for most practical situations when instances are this small. It gets within 0.3 of optimal within a (normalized) second for all the real world instances with less than 100 cities from [10] and as we shall see it averages two seconds or less to get within 0.1 of optimal for the ....

.... applies the same sort of trick we used to compute Held Karp bounds and optimal tour lengths for ATSP instances using Concorde: the ATSP instance is transformed into an equivalent STSP instances and then an STSP code is applied, in this case the repeated search version of Helsgaun s heuristic [17] as described in Chapter 9. The transformation used Experimental Analysis of Heuristics for the ATSP 19 is somewhat simpler than the one used for Concorde. Here we replace each city c i by a pair of cities c i and c Gamma i , and set d(c i ; c Gamma j ) d(c i ; c j ) and d(c j ....

K. Helsgaun. An effective implementation of the Lin-Kernighan traveling salesman heuristic. European Journal of Operations Research, 12:106--130, 2000. Source code currently available from the author's http://www.dat.ruc.dk/keld/.

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K. Helsgaun. An Effective Implementation of the Lin-Kernighan Traveling Salesman Heuristic. Eur. J. Oper. Res., 126:106--130, 2000.

....scheme provides the highest quality tours for reasonable costs and that CLK ILK variants are the most cost effective way to improve on Lin Kernighan, at least until one reaches stratospheric running times . However in 2000 an interesting and highly effective LK variant was introduced by Helsgaun, [4]. This Lin Kernighan Helsgaun (LKH) algorithm, at least in its multi trial version, can significantly improve on CLK ILK results although it suffers from runtimes which are quadratic, in fact O(N 2:2 ) for problems of size N . In a further recent development, a general solution strategy known ....

....tour. A vast amount has been written about the LK algorithm, including much on its efficient implementation, and for an excellent overview of techniques see the surveys of Johnson McGeoch, 6, 7] Recently a new and highly effective variant of the LK algorithm has been developed by Helsgaun, [4]. This scheme employs a number of important innovations including sequential 5 opt moves and the use of sensitivity analysis to direct the search. It has been shown to compute solutions extremely close to the optimal (where known) but suffers from the drawback of runtimes which are quadratic in N ....

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K. Helsgaun. An Effective Implementation of the Lin-Kernighan Traveling Salesman Heuristic. Eur. J. Oper. Res., 126:106--130, 2000.

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