Kanellakis, P.C., Papadimitriou, C.H.: Local search for the asymmetric traveling salesman problem. Oper. Res. 28 (1980) 1086--1099  Home/Search   Document Not in Database   Summary   Related Articles   Check

....branching factor and edge cost distribution. These estimates are then used to calculate a value for . As the search proceeds, the estimates of the branching factor and edge cost distribution can be refined and used to update the value of . We compared DFBnB with local search for the ATSP [16]. The average running time of local search is longer than that of DFBnB on four different problem structures we considered. Figure 5 shows the results on the ATSP with (c i;j ) uniformly selected from f0; 1; Delta Delta Delta ; i Theta jg, which are known to be very difficult for BnB using ....

P. C. Kanellakis and C. H. Papadimitriou. Local search for the asymmetric traveling salesman problem. Operations Research, 28:1086--1099, 1980.

....have one on all four of their sides. This class is thus generated by letting k grow with N , in particular as the nearest integer to 10 p N . No Wait Flowshop Instances (shop) The no wait flowship was the application that inspired the local search heuristic of Kanellakis and Papadimitriou [20]. In a k processor no wait flowshop, a job u consists of a sequence of tasks (u 1 ; u 2 ; u k ) that must be performed by a fixed sequence of machines. The processing of u i 1 must start on machine i 1 as soon as processing of u i is complete on machine i. This models the processing of ....

....implementation of 3 Opt that generates its starting tours using NN and employs many of the speedup tricks exploited by their implementation of symmetric 3opt. For details on these, see Chapter 9 and [18] Kanellakis Papadimitriou (KP) This heuristic, invented by Kanellakis and Papadimitriou in [20], attempts to mimic the Lin Kernighan heuristic for the STSP [24] subject to the constraint that it does not reverse any tour segments. The symmetric version of Lin Kernighan is discussed in more detail in Chapters 8 and 9. KP consists of two alternating search processes. The first process is a ....

P. C. Kanellakis and C. H. Papadimitriou. Local search for the asymmetric traveling salesman problem. Oper. Res., 28(5):1066-- 1099, 1980.

....algorithms [ 7; 8 ] DFBnB has not been studied as an approximation or anytime algorithm so far. We study DFBnB as an approximation and anytime algorithm in this paper. We compare it against the Kanellakis Papadimitriou local search algorithm on the asymmetric Traveling Salesman Problem (ATSP) [ 12 ] . This local search algorithm is an adaptation and extension of the well known Lin Kernighan local search algorithm [ 17 ] and the only local search algorithm for the ATSP which we found in the literature. We choose the ATSP due to the following two reasons. First, the ATSP is an important ....

....Within a neighborhood, a tour is a local optimum if it is the best among its neighbors. Given a neighborhood structure, a local search moves from a tour to a neighboring tour that has a smaller cost until a local optimum is reached. The Kanellakis Papadimitriou local search algorithm for the ATSP [ 12 ] follows the Lin Kernighan local search algorithm for the symmetric TSP [ 17 ] and uses primary changes, which change an odd number of edges in a tour. Figure 1 shows a primary 3 change. Primary changes are found by the following sequential process. To construct a primary change of a tour , we ....

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P. C. Kanellakis and C. H. Papadimitriou. Local search for the asymmetric traveling salesman problem. Operations Research, 28:1086--1099, 1980.

....be formulated as ATSPs, such as vehicle routing, workshop scheduling, computer wiring, etc [14] Although we present the approximation method on the ATSP, our algorithm can be simply applied to other problems as well. We empirically compare our approximation method to a local search algorithm of [9], the best existing approximation algorithm for the ATSP we found in the literature. Given a non optimal complete tour, a local search algorithm repeatedly improves the tour by local perturbations [16, 9, 8] In our experiments, we considered many ATSPs with different cost matrix structures. The ....

....problems as well. We empirically compare our approximation method to a local search algorithm of [9] the best existing approximation algorithm for the ATSP we found in the literature. Given a non optimal complete tour, a local search algorithm repeatedly improves the tour by local perturbations [16, 9, 8]. In our experiments, we considered many ATSPs with different cost matrix structures. The cost matrices we used include random matrices, matrices with the triangle inequality, random matrices with c i;j from f0; 1; i Theta jg, matrices converted from no wait workshop scheduling for 4 ....

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Kanellakis, P.C., and C.H. Papadimitriou, "Local search for the asymmetric traveling salesman problem, " Operations Research, 28 (1980) 1086-99.

....heuristic to ACS could make it competitive with the best algorithms. We have therefore added a tour improvement heuristic to ACS. In order to maintain ACS ability to solve both TSP and ATSP problems we have decided to base the local optimization heuristic on a restricted 3 opt procedure [25] [27] that, while inserting removing three edges on the path, considers only 3 opt moves that do not revert the order in which the cities are visited. The resulting algorithm, called ACS 3 opt, is shown in Fig. 10. In this way the same procedure can be applied to symmetric and asymmetric TSPs, avoiding ....

P-C. Kanellakis and C.H. Papadimitriou, "Local search for the asymmetric traveling salesman problem," Operations Research, vol. 28, no. 5, pp. 1087--1099, 1980.

....rule in their ACO for the solution of the TSP. The idea is to apply local improvement rules to various solutions to find a local optimum for each of them. The authors suggest use of successive edge exchange methods and in particular the restricted 3 opt method [Johnson McGeoch, 1997] [Kanellakis Papadimitriou, 1980]. This method removes three edges from a tour and reconnects them in the unique way that does not reverse the direction of the entire tour. For example if edges (a,b) e,f) and (i,j) are removed, the tour will be reconnected as (a,f) e,j) and (i,b) thus preserving the direction of the ....

Kanellakis P.-C., Papadimitriou C.H., [1980], Local search for the asymmetric traveling salesman problem, Operations Research, 28, 5, 1087-1099.

.... problem (ATSP) There are currently three general classes of such heuristics: classical tour construction heuristics such as Nearest Neighbor and the Greedy algorithm, local search algorithms based on re arranging segments of the tour, as exemplified by the Kanellakis Papadimitriou algorithm [KP80], and algorithms based on patching together the cycles in a minimum cycle cover, the best of which are variants on an algorithm proposed by Zhang [Zha93] We test implementations of the main contenders from each class on a variety of instance types, introducing a variety of new random ....

....that we cover. Current ATSP heuristics can be divided into three classes: 1) classical tour construction heuristics such as Nearest Neighbor and the Greedy algorithm, 2) local search algorithms based on re arranging segments of the tour, as exemplified by the Kanellakis Papadimitriou algorithm [KP80], and (3) algorithms based on patching together the cycles in a minimum cycle cover (which can be computed as the solution to an Assignment Problem, i.e. by constructing a minimum weight perfect bipartite matching) Examples of this last class include the algorithms proposed in [Kar79,KS85] and ....

[Article contains additional citation context not shown here]

P. C. Kanellakis and C. H. Papadimitriou. Local search for the asymmetric traveling salesman problem. Oper. Res., 28(5):1066--1099, 1980.

.... problem (ATSP) There are currently three general classes of such heuristics: classical tour construction heuristics such as Nearest Neighbor and the Greedy algorithm, local search algorithms based on re arranging segments of the tour, as exemplified by the Kanellakis Papadimitriou algorithm [KP80], and algorithms based on patching together the cycles in a minimum cycle cover, the best of which are variants on an algorithm proposed by Zhang [Zha93] We test implementations of the main contenders from each class on a variety of instance types, introducing a variety of new random instance ....

....that we cover. Current ATSP heuristics can be divided into three classes: 1) classical tour construction heuristics such as Nearest Neighbor and the Greedy algorithm, 2) local search algorithms based on re arranging segments of the tour, as exemplified by the Kanellakis Papadimitriou algorithm [KP80], and (3) algorithms based on patching together the cycles in a minimum cycle cover, which can be computed as the solution to an Assignment Problem, i.e. by constructing a minimum weight perfect bipartite matching) Examples of this last class include the algorithms proposed in [Kar79, KS85] and ....

[Article contains additional citation context not shown here]

P. C. Kanellakis and C. H. Papadimitriou. Local search for the asymmetric traveling salesman problem. Oper. Res., 28(5):1066--1099, 1980.

....Manufacturing Systems, University of Kentucky, and in part by the National Science Foundation under the Grant NSF ECS 9409712. 1 instance can be obtained from the corresponding STSP instance. This represents an improvement over earlier such transformations which triple the size of the problem [7, 3]. Our interest in ATSP is because of its application in automated printed circuit board assembly (PCB) machines [4, 5] A pick and place robot is used to pick components from their pickup locations and place them at their placement locations on the PCB being assembled. Thus if the placement of ....

....1(a) all five real nodes are of odd degree, whereas only three virtual nodes [1] 2] and [5] are of odd degree. Say there are more number of real odd degree nodes. Then during the matching phase, a real node will be matched to another real node which will add an edge of infinite 8 [1] 1 2 [3] 3 [2] 5] b) MST with extraneous edge 4 [4] 4] 5 1 2 5 [1] 2] 4] 5] 3 (a) Minimal spanning tree [1] 1 2 [3] 3 [5] 2] 4] 5 4 4 [1] 1 2 [3] 3 [5] 2] 4] 5 4 (d) Eulerian tour (c) Minimal matching Figure 1: Tour construction in ATSP setting 9 cost. Recall that d ij = 1 for any i; j n. ....

[Article contains additional citation context not shown here]

P.-C. Kanellakis and C. H. Papadimitriou. Local search for the asymmetric traveling salesman problem. Operations Research, 28:1086--1099, 1980.

....heuristics, while Martin et al. 11] have given an extension to earlier heuristics that improves the quality of the returned tour while increasing running times. The literature for asymmetric TSPs is less extensive than for symmetric TSPs, and includes a heuristic by Kanellakis and Papadimitriou [10] which modifies the Lin Kernighan symmetric TSP heuristic. More recent studies by Miller and Pekny [12] and Zhang [15] have applied branch and bound to obtain optimal solutions to asymmetric TSPs. Although branch and bound has exponential time complexity in the worst case, these two studies have ....

P.-C. Kanellakis and C. H. Papadimitriou, "Local Search for the Asymmetric Traveling Salesman Problem", Operations Res. 28 (1980), pp. 1086-1099.

....heuristic to ACS could make it competitive with the best algorithms. We have therefore added a tour improvement heuristic to ACS. In order to maintain ACS ability to solve both TSP and ATSP problems we have decided to base the local optimization heuristic on a restricted 3 opt procedure [25] [27] that, while inserting removing three edges on the path, considers only 3 opt moves that do not revert the order in which the cities are visited. The resulting algorithm, called ACS 3 opt, is shown in Fig. 10. In this way the same procedure can be applied to symmetric and asymmetric TSPs, avoiding ....

P-C. Kanellakis and C.H. Papadimitriou, "Local search for the asymmetric traveling salesman problem," Operations Research, vol. 28, no. 5, pp. 1087--1099, 1980.

....Martin et al. 15] have given an effective way to improve the quality of the solutions obtained by these heuristics at the expense of increasing their running times. Although a few solution methods have been proposed for the asymmetric TSP, including a heuristic by Kanellakis and Papadimitriou [9] which modifies the Lin Kernighan symmetric TSP heuristic and a branch and bound approach by Miller and Pekny [17] there do not exist enough experimental data to judge their performance, and the heuristics have very high time complexity. 4 Block Scheduling with Independent Blocks In this ....

P.-C. Kanellakis and C. H. Papadimitriou, "Local Search for the Asymmetric Traveling Salesman Problem", Operations Research, Vol. 28, pp. 1086-1099, 1980.

....that point can then be taken as an approximation. The main difference between these two algorithms is that the territory explored by iterative ffl DFBnB is generally smaller than the territory explored by truncated DFBnB, although iterative ffl DFBnB may re expand a node many times. Local search [12, 13, 21] is a well known approximation method for many difficult combinatorial problems. Starting at an initial solution, such as one generated by a polynomial time approximation algorithm, local search continuously improves the current solution by local perturbations, until no further improvement can be ....

....experiments. The five initial tours were generated by the nearest neighbor method [6] nearest insertion farthest insertion, greedy algorithms, and the patching algorithm [6, 14] We used random cost matrices and matrices converted from no wait flowshop scheduling for 4 machines, which is NP hard [13]. No wait flowshop scheduling involves determining a sequence for processing a set of jobs where each job must be handled by a set of machines in the same preset order. The objective is a sequence that minimizes a cost function, i.e. total completion time cost which was used in our experiments. ....

P.C. Kanellakis and C.H. Papadimitriou. Local search for the asymmetric traveling salesman problem. Operations Research, 28:1086--1099, 1980.

....heuristic to ACS could make it competitive with the best algorithms. We have therefore added a tour improvement heuristic to ACS. In order to maintain ACS ability to solve both TSP and ATSP problems we have decided to base the local optimization heuristic on a restricted 3 opt procedure [25] [27] that, while inserting removing three edges on the path, considers only 3 opt moves that do not revert the order in which the cities are visited. In this case it is possible to change three edges on the tour (k , l) p, q) and (r , s) with three other edges (k , q) p, s ) and (r , l) ....

P-C. Kanellakis and C.H. Papadimitriou, "Local search for the asymmetric traveling salesman problem," Operations Research, vol. 28, no. 5, pp. 1087--1099, 1980.

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Kanellakis, P.C., Papadimitriou, C.H.: Local search for the asymmetric traveling salesman problem. Oper. Res. 28 (1980) 1086--1099

No context found.

P. C. Kanellakis and C. H. Papadimitriou, "Local search for the asymmetric traveling salesman problem," Operations Research 28 (1980), 1086--1099.

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