J. L. Bentley. Experiments on traveling salesman heuristics. In Proc. 1st ACM-SIAM Sympos. Discrete Algorithms, pages 91--99, 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....better tness or to terminate the local search without actually checking all neighboring solutions: With the concept of don t look bits, only a small, dynamically changing subset of the candidates in the neighborhood is considered. This concept has been used in local search algorithms for the TSP [2, 8] and the QAP [13, 16] Furthermore, sophisticated data structures to perform the most time consuming tasks during the local search have been proposed. The use of these data structures can improve the performance of a local search drastically for large instances without in uencing the solution ....

J. L. Bentley, \Experiments on Traveling Salesman Heuristics," in Proc. of the First Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 91-99, 1990.

....the chained or iterated Lin Kernighan algorithm is the most successful local search technique for iteratively optimising a TSP tour. It is usually combined with a tour construction heuristic which builds an legitimate initial tour. One such construction technique is Bentley s greedy algorithm, [4, 5], which proceeds by sorting all the inter city distances by length and repeatedly adding in the shortest edge which is not already in the tour and which will not create a subcycle (a tour with fewer than N edges) In this way it progressively builds a series of tour fragments and in many ways ....

J. L. Bentley. Experiments on Traveling Salesman Heuristics. In D. S. Johnson, editor, Proc. 1st Annual ACM-SIAM Symp. Discrete Alg. (SODA '90), pages 91--99, San Francisco, 1990. SIAM.

....cities i = 1; N , separated by distances d ij the (euclidean) Traveling Salesman Problem TSP from now consists of finding the shortest closed path visiting each city exactly once. The solution of very large instances of the TSP has challenged several authors over the last few years [1, 2, 5, 7, 10]. The results have been quite satisfactory. In fact, by using, e.g. the Lin Kernighan method LK from now it is possible to face TSP instances with thousands of cities and obtain, within a reasonable time, tours which are very close to the optimal one. On the other hand we are still far ....

J. L. Bentley. Experiments on traveling salesman heuristics. Proc. 1st Symp. on Discrete Algorithms, 91--99, 1990.

....memory. Very recently, a new data structure called buffer tree and its applications are given in [2, 3] and an external memory version of the directed topology tree ( 18] called topology B tree is given in [9] For excellent examples of experimental work in computational geometry, see Bentley [5, 6, 7, 8]. As for experimental work on I O efficient computation, very recently Vengroff has built an environment called TPIE for programming external memory algorithms as he proposed earlier in [29] and also Vengroff and Vitter [30] have reported some benchmarks of TPIE on sorting and matrix ....

J. L. Bentley. Experiments on traveling salesman heuristics. In Proc. 1st ACM-SIAM Sympos. Discrete Algorithms, pages 91--99, 1990.

....the total cost C( Furthermore, we included another mechanism to speed up the local search: To reduce the time to search for an improving swap in the neighborhood of the current solution, a don t look bit for each location is maintained. The don t look bit technique has been proposed by Bentley [7] to speed up the 2 opt and 3 opt local search algorithm for the traveling salesman problem. However, it can also be used in a local search for the QAP. If the don t look bit for location i is set to one, the facility at location i will not be considered for an improvement swap in the current local ....

J. L. Bentley, \Experiments on Traveling Salesman Heuristics," in Proceedings of the First Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 91-99, 1990.

....bound holds even in the Euclidean Plane. Another interesting insertion method is random insertion: the order in which the vertices are inserted is chosen uniformly at random. This method is of special interest since it performs better than nearest insertion and cheapest insertion in practice (see [Be], GBDS] LLRS] Moreover, it is easier to implement and has lower running time. However, no better bounds on the performance of random insertion were known 1 ( RSL] LLRS] It was tempting to think that random insertion may have a constant approximation factor. Surprisingly, we prove a ....

J.L. Bentley, Experiments on Traveling Salesman Heuristics, in Proc. 1st Annual ACM-SIAM SODA San-Francisco, California, 1990 pp. 91-99.

....formula above for calculating DeltaC in our algorithm. In contrast to the original 2 opt heuristic, our variant is based on performing the first swap found that reduces the total cost C( Furthermore, don t look bits are incorporated to reduce computation time for checking the neighborhood [4]. This reduces the running time without a loss in quality of the solutions. Our experiments have shown that similar to the 2opt for the TSP, it is not worth spending time to search for the best 2 opt move in our local search procedure, as it is done, for example, in tabu search. Compared to the ....

J. L. Bentley, "Experiments on Traveling Salesman Heuristics," in Proceedings of the First Annual ACMSIAM Symposium on Discrete Algorithms, pp. 91--99, 1990.

.... is bound by a constant, it is possible to identify an improving k opt move associated with a given starting node in constant time, and hence the time for checking an improving move is O(n) Further reductions result from performing a fixed radius nearest neighbor search, as proposed by Bentley [1], 3] Another mechanism to speed up local search algorithms is to incorporate a don t look bit for each node, in order to reduce the time for checking the interesting neighbors [1] With the don t look bit set to 1, the node is not considered as a starting point for finding an improving move. ....

.... is O(n) Further reductions result from performing a fixed radius nearest neighbor search, as proposed by Bentley [1] 3] Another mechanism to speed up local search algorithms is to incorporate a don t look bit for each node, in order to reduce the time for checking the interesting neighbors [1]. With the don t look bit set to 1, the node is not considered as a starting point for finding an improving move. Initially, all bits are set to 0. If an improving move could not be found starting at node i, the don t look bit for that node is set. On the other hand, the don t look bit will be ....

J. L. Bentley, "Experiments on Traveling Salesman Heuristics," in Proceedings of the First Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 91--99, 1990.

....Lutton gave an experimentally derived value of K = 0:749 for Beardwood s formula in the limit N Gamma 1 [9] For uniform point sets of size 10 4 inside a unit square D.S. Johnson has observed a lower bound on K of 0:715 and conjectures that for a set of that cardinality K has the value 0:725 [10]. The divergence of results may be connected with finite size effects associated with the different calculations. The Relationship Between the TSP and Fractals We can consider a TSP tour as a fractal curve. In the case of the optimal tour of an infinite number of cities uniformly distributed in ....

....implying there is something special about sets of cities defined by MPeano. Frustration We proved the optimality of the MPeano tour by showing that all cities are connected to both of their two nearest neighbours. This implies that the MPeano TSP can be solved exactly by the NNStart heuristic [10]. In general instances of the TSP, a tour can be optimal without this property. Given a set C of cities, it is useful to define a quantity we shall refer to as frustration, f , such that given a city c 2 C whose nearest neighbours are n c and m c and a tour T , with edges fc; a c g and fc; b c ....

[Article contains additional citation context not shown here]

J.L. Bentley. Experiments on traveling salesman heuristics. In First Annual ACM-SIAM Symposium on Discrete Algorithms, pages 91--90, San Francisco, CA, January 1990.

....an account of those attempts) For uniform point sets of size 10 4 inside a unit square D.S. Johnson has observed a lower bound on L opt of 71:5 (which implies an effective lower bound of K eff = 0:715 for that size) and he conjectures that for a set of that cardinality L opt has the value 72:5 [5]. Recently, a self avoiding space filling curve was shown to be an optimal tour through a corresponding set of an arbitrarily large number of cities contained in the unit square. This curve was called MNPeano to honour Giuseppe Peano s construction of the first space filling curve (1890) In ....

J.L. Bentley. Experiments on traveling salesman heuristics. In First Annual ACM-SIAM Symposium on Discrete Algorithms, pages 91--90, San Francisco, CA, January 1990.

....of those attempts) For uniform point sets of size 10 4 inside a unit square, D.S. Johnson has observed a lower bound on L opt of 71:5 (which implies an effective lower bound of K eff = 0:715 for that size) and he conjectures that, for a set of that cardinality, L opt has the value 72:5 [19]. Steve Finch maintains an essay, which is frequently updated, about the Traveling Salesman Constants as part of his Web essays on famous mathematical constants 7 . Recently, a self avoiding space filling curve was shown to be an optimal tour through a corresponding set of an arbitrarily large ....

J.L. Bentley. Experiments on traveling salesman heuristics. In First Annual ACM-SIAM Symposium on Discrete Algorithms, pages 91--99, San Francisco, CA, January 1990.

....as a function of problem instance size. 0 200 400 600 800 1000 0 1000 2000 3000 4000 5000 Problem size Flower Lin Kernighan 3 Change Figure 4.12: Time to opt. using the considerbit, as a function of problem instance size. when used in an implementation of a Lin Kernighan like transition type. Bentley, 1990a] presents some investigation on how descents, based on 2 and 3 Changes, behave when the problem instances are large ( 10; 000 cities) The paper reports an hidden factor of O(n 1:74 ) caused by the subpath inversion. This factor is significant at n = 10; 000 and is dominating when n = 1; ....

....The pseudo code is shown in Algorithms C.5 and C.6. As a note it should be mentioned that special care has to be taken when y k :t r hits a neighbour to the root or basis (this is not shown) The check out time in local minima can be reduced by associating a consider bit with every city [Bentley, 1990a] This bit is initiated to TRUE for all cities at the beginning of a descent. If no improving transition can be found with t 1 as anchor, the bit for t 1 is set to FALSE. Every time a transition is executed, the consider bit for all involved cities is set to TRUE, and only cities with ....

Bentley, J.L. "Experiments on Traveling Salesman Heuristics ", Computer Science Technical Report No. 151, 1990, AT& T Bell Laboratories.

....the edges added by the insertion method and the edges in a minimum spanning tree. Note that the cost of the minimum spanning tree is at most the cost of the optimal tour, which in turn, has cost at most twice the cost of the minimum spanning tree [7] In empirical trials conducted by Bentley [4] and Rosenkrantz et al., the orderings that yielded the best tours of points uniformly distributed in the unit square were farthest insertion and random insertion. In farthest insertion the point v i 1 is the point not in T i that is farthest from T i , and in random insertion v i 1 is chosen ....

J. Bentley, "Experiments on Traveling Salesman Heuristics", Proceedings of 1st ACM/SIAM Conference on Discrete Algorithms, pp. 91--99, 1990.

....(empirical) bounds on the constant K 0:765 K 0:765 4 N : This, however, did not settle the argument. In 1984 Bonomi and Lutton gave a value of K = 0:749 for Beardwood s formula in the limit N Gamma 1 [6] For uniform point sets of size 10 4 inside a unit square Johnson (cited in Bentley [7]) has observed a lower bound of K = 0:715 and conjectures that the optimal tour has a length of K = 0:725. The results do not agree since there are, doubtless, finite size effects associated with the different calculations, specially in the two first cases. 1.2 TSPLIB Another approach for ....

....that in the limit, the three TSPs have very different properties. Koch simply looks like a more detailed version of the tour at order 2, where each of the lines has turned into a furry line. It is entirely contained within, say, a torus in the same way as one of Bentley s pathological examples [7]. There are various measures of fractal dimension which can be used to characterise these curves. We shall use the box counting dimension, which for the Koch Tour is log 4= log 3 = 1:2619. The coastline of Britain appears to have a fractal dimension of 1.31 [9] On the other hand the two Peano ....

[Article contains additional citation context not shown here]

J.L. Bentley. Experiments on traveling salesman heuristics. In First Annual ACMSIAM Symposium on Discrete Algorithms, pages 91--90, San Francisco, CA, January 1990.

.... the work in this paper, a new data structure called buffer tree and its applications are given in [2, 5] and an external memory version of the directed topology tree ( 21] called topology B tree is given in [11] For excellent examples of experimental work in computational geometry, see Bentley [7, 8, 9, 10]. As for experimental work on I O efficient computation, concurrent to our work Vengroff builds an environment called TPIE for programming external memory algorithms as he proposed earlier in [36] and also Vengroff and Vitter [37] report some benchmarks of TPIE on sorting and matrix ....

J. L. Bentley. Experiments on traveling salesman heuristics. In Proc. 1st ACM-SIAM Sympos. Discrete Algorithms, pages 91--99, 1990.

....3 Opt descents. 3 We include Random 2 Opt to provide continuity with our original paper [3] Interestingly, Random 2 Opt returns solutions with significantly higher cost than those obtained by Fast 2 Opt. Heuristics 2 through 4 have been compared to other heuristics by Johnson [7] and Bentley [1] and appear to be among the most effective TSP heuristics. For example, 3 Opt and Lin Kernighan return tours even better than simulated annealing 1 The same result was proved independently by Kececioglu and Sankoff [8] in the context of computing the number of chromosome inversions required to ....

J. L. Bentley, "Experiments on Traveling Salesman Heuristics" in First Annual ACM-SIAM Symposium on Discrete Algorithms (January 1990), pp. 187-197.

....of new techniques for designing and analyzing I Oefficient graph algorithms, and apply these techniques to a wide variety of specific problems. Other related theoretical results are reviewed in Section 4.1.2. For excellent examples of experimental work in computational geometry, see Bentley [11, 12, 13, 14]. As for experimental work on I O efficient computation, very recently Vengroff has built an environment called TPIE for programming external memory algorithms as he proposed earlier in [120] and also Vengroff and Vitter [119] have reported some benchmarks of TPIE on sorting and matrix ....

J. L. Bentley. Experiments on traveling salesman heuristics. In Proc. 1st ACM-SIAM Sympos. Discrete Algorithms, pages 91--99, 1990.

....results [13] 2 opt and 3 opt require shorter execution time and are much easier to implement. 2 opt and 3 opt are preferred methods for large TSP problems. They are capable of producing solutions within a few percent of the optimal solution for problems with million uniformly distributed cities [1, 2]. 2 opt and 3 opt are local optimization methods. 2 opt attempts to replace pairs of edges as follows. If a pair of edges can be replaced by another pair of edges, such that the new pair links the same cities, but produces a shorter tour, then the edges are replaced. Otherwise, a new pair of edges ....

J. L. Bentley. Experiments on traveling salesman heuristics. In Proc. 1st. Ann. ACMSIAM Symp. on Discrete Algorithms, pages 91--99, 1990.

No context found.

J. L. Bentley. Experiments on traveling salesman heuristics. In Proc. 1st ACM-SIAM Sympos. Discrete Algorithms, pages 91--99, 1990.

No context found.

J. L. Bentley, "Experiments on Traveling Salesman Heuristics," in Proceedings of the First Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 91--99, 1990.

No context found.

J. L. Bentley, \Experiments on Traveling Salesman Heuristics," in Proceedings of the First Annual ACM-SIAM Symposium on Discrete Algorithms, 1990).

No context found.

Bentley, J. (1990) Experiments on traveling salesman heuristics. Proc. ACM-SIAM Symp. Discrete Algorithms, 91-99.

No context found.

J. L. Bentley. Experiments on Traveling Salesman Heuristics. In D. S. Johnson, editor, Proc. 1st Annual ACM-SIAM Symp. Discrete Alg. (SODA '90), pages 91--99, San Francisco, 1990. SIAM.

No context found.

J. L. Bentley. Experiments on traveling salesman heuristics. In Proceedings of the First ACM-SIAM Symposium on Discrete Algorithms, pages 91--99. ACM-SIAM, New York, Philadelphia, 1990. Discusses both the algorithmic problem and the experimental methodology.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC