Johnson, D.S., McGeoch, L.A.: The travelling salesman problem: A case study. In: Aarts, E.H.L. and Lenstra, J.K. (eds.): Local Search in Combinatorial Optimization. John Wiley & Sons, New York (1997) 215--310  Home/Search   Document Not in Database   Summary   Related Articles   Check

....which make it stand out amongst combinatorial optimisation problems. Firstly, and perhaps because of the fact that the problem is so intuitive and easy to state, it has almost certainly been more widely studied than any other combinatorial optimisation problem. For example Johnson McGeoch, [26], survey a wide range of approaches which run the gamut from local search, through simulated annealing, tabu search genetic algorithms to neural nets. Remarkably, and despite all this interest, the local search algorithm proposed by Lin Kernighan in 1973, 38] still remains at the heart of ....

....TSP from 1973 to 1989. Further, this was only conclusively superseded by chained or iterated versions of LK (CLK ILK) originally proposed by Martin, Otto Felten, 40] in 1991. Even today, in spite of all the work on exotic and complex combinatorial optimisation techniques, Johnson McGeoch, [26], conclude that an iterated or chained Lin Kernighan (ILK CLK) scheme provides the highest quality tours for a reasonable cost. In fact it is usually possible to improve on the quality of (suboptimal) CLK ILK tours, for example by sophisticated tour merging techniques similar to genetic algorithm ....

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D. S. Johnson and L. A. McGeoch. The travelling salesman problem: a case study. In E. Aarts and J. K. Lenstra, editors, Local Search in Combinatorial Optimization, pages 215--310. John Wiley & Sons, Chichester, 1997.

....which make it stand out amongst combinatorial optimisation problems. Firstly, and perhaps because of the fact that the problem is so intuitive and easy to state, it has almost certainly been more widely studied than any other combinatorial optimisation problem. For example Johnson McGeoch, [17], survey a wide range of approaches which run the gamut from local search, through simulated annealing, tabu search genetic algorithms to neural nets. Remarkably, and despite all this interest, the local search algorithm proposed by Lin Kernighan in 1973, 24] still remains at the heart of ....

....heuristic for the TSP from 1973 to 1989. Further, this was only conclusively superseded by chained or iterated versions of LK originally proposed by Martin, Otto Felten, 25] Even until recently, in spite of all the work on exotic and complex combinatorial techniques, Johnson McGeoch, [17], concluded in 1997 that an iterated Lin Kernighan scheme provides the highest quality tours for a reasonable cost and that variants of this algorithm are the most cost effective way to improve on Lin Kernighan, at least until one reaches stratospheric running times . Note that it is often ....

[Article contains additional citation context not shown here]

D. S. Johnson and L. A. McGeoch. The Travelling Salesman Problem: A Case Study. In E. Aarts and J. K. Lenstra, editors, Local Search in Combinatorial Optimization, pages 215--310. John Wiley & Sons, Chichester, 1997.

....the algorithm over the HKLB for each instance. Another unusual feature of the TSP, perhaps due to the fact that the problem is so intuitive and easy to state, is that it has almost certainly been more widely studied than any other combinatorial optimisation problem. For example Johnson McGeoch, [6], survey a wide range of approaches which run the gamut from local search, through simulated annealing, tabu search genetic algorithms to neural nets. Remarkably, and despite all this interest, the local search algorithm proposed by Lin Kernighan in 1973, 9] still remains at the heart of the ....

....for the TSP from 1973 to 1989. Further, this was only conclusively superseded by chained or iterated versions of LK originally proposed by Martin, Otto Felten, 10] in 1991. Even as recently as 1997, and despite all the work on exotic and complex optimisation techniques, Johnson McGeoch, [6], concluded that an iterated or chained Lin Kernighan (ILK CLK) 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 ....

[Article contains additional citation context not shown here]

D. S. Johnson and L. A. McGeoch. The travelling salesman problem: a case study. In E. Aarts and J. K. Lenstra, editors, Local Search in Combinatorial Optimization, pages 215--310. John Wiley & Sons, Chichester, 1997.

....not have this luxury in practical applications, like the TSP. 4.2 TSP MTSP: decomposition via multi objectivization The travelling salesperson problem (TSP) is the most well known of all NP hard optimization problems. For a comprehensive review and comparison of methods used to solve it see [6], where the problem is stated as follows: We are given a set C = fc 1 ; c 2 ; c N g of cities and for each pair fc i ; c j g of distinct cities there is a distance d(c i ; c j ) Our goal is to find an ordering of the cities that minimizes the quantity N Gamma1 X i=1 d(c (i) c ....

....other figures are estimates. For the RAN 20 problem, the optimum is an estimate based on the fact that SA reached this value on 30 consecutive runs, and given the small size of the problem. For the RAN 50 problem, the estimated figure is based on the expected limiting value of an optimal tour [6], and similarly for EUC 50 and EUC 100, the estimates are based on the formula for expected tour length = K p NA with N the number of cities, A = 1:0 the area in which the cities are placed, and K 0:7124 [6] Algorithm Problem num evals Optimum Best Mean oe SHC RAN 20 500000 2.547394 2.550811 ....

[Article contains additional citation context not shown here]

D. S. Johnson and L. A. McGeoch. The travelling salesman problem: a case study. In E. Aarts and J. K. Lenstra, editors, Local Search in Combinatorial Optimization, pages 215--310. John Wiley and Sons, 1997.

....number of features which make it stand out amongst such problems. Firstly, and perhaps because of the fact that the problem is so intuitive and easy to state, it has almost certainly been more widely studied than any other NP hard combinatorial optimisation problem. For example Johnson McGeoch, [20], survey a wide range of approaches which run the gamut from local search, through simulated annealing, tabu search genetic algorithms to neural nets. Remarkably, and despite all this interest, the local search algorithm proposed by Lin Kernighan in 1973, 25] still remains at the heart of ....

....Further, this was only conclusively superseded by chained or iterated versions of LK (see x2.3 for clarification) originally proposed by Martin, Otto Felten, 26, 27] in 1991. Even today, in spite of all the work on exotic and complex combinatorial optimisation techniques, Johnson McGeoch, [20], conclude that an iterated Lin Kernighan (ILK) scheme provides the highest quality Email: C.Walshaw gre.ac.uk; URL: www.gre.ac.uk c.walshaw 1 tours for a reasonable cost. This conclusion has been backed up very recently by Applegate, Cook Rohe, 2] who also illustrate the scalability of ....

[Article contains additional citation context not shown here]

D. S. Johnson and L. A. McGeoch. The travelling salesman problem: a case study. In E. Aarts and J. K. Lenstra, editors, Local Search in Combinatorial Optimization, pages 215--310. Wiley, Chichester, 1997.

....Heuristics In this section we are going to propose some heuristics to tackle the minimum weight hypertour problem, as described in the previous section, arising for multi headed placement machines. Many efficient heuristics have been proposed for the Travelling Salesman Problem in the literature [8], 11] However, these heuristics are not suitable for the model we are confronted with. The heuristics we have developed take their inspiration from two well known heuristics for the Travelling Salesman Problem which have been modified to be suitable for the hypertour problem. These heuristics ....

....n 2 ) more expensive than the approach outlined before. However, it gives access to a larger neighborhood which may improve the quality of the tour constructed. We will now consider a local improvement algorithms for the hypertour problem based on the local search algorithm k opt for the TSP [8], 11] One possibility is to directly apply k opt as defined for the TSP. This algorithm works for the hypertour problem subject to the restriction that each hyperedge has maximal length of h 1. The algorithm consists of applying simple tour modifications to a feasible tour. This process is ....

[Article contains additional citation context not shown here]

D. Johnson and L. McGeoch. The Travelling Salesman Problem: A case study. In Local Search in Combinatorical Optimization. Wiley, 1997.

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Johnson, D.S., McGeoch, L.A.: The travelling salesman problem: A case study. In: Aarts, E.H.L. and Lenstra, J.K. (eds.): Local Search in Combinatorial Optimization. John Wiley & Sons, New York (1997) 215--310

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D. S. Johnson and L. A. McGeoch. The travelling salesman problem: a case study. In E. Aarts and J. K. Lenstra, editors, Local Search in Combinatorial Optimization, pages 215--310. John Wiley & Sons, Chichester, 1997.

No context found.

D. S. Johnson and L. A. McGeoch. The travelling salesman problem: a case study. In E. Aarts and J. K. Lenstra, editors, Local Search in Combinatorial Optimization, pages 215--310. John Wiley & Sons, Chichester, 1997.

No context found.

D. S. Johnson and L. A. McGeoch. The travelling salesman problem: a case study. In E. Aarts and J. K. Lenstra, editors, Local Search in Combinatorial Optimization, pages 215--310. Wiley, Chichester, 1997.

No context found.

D. S. Johnson and L. A. McGeoch. The Travelling Salesman Problem: A Case Study. In E. Aarts and J. K. Lenstra, editors, Local Search in Combinatorial Optimization, pages 215--310. John Wiley & Sons, Chichester, 1997.

No context found.

D. S. Johnson and L. A. McGeoch. The travelling salesman problem: a case study. In E. Aarts and J. K. Lenstra, editors, Local Search in Combinatorial Optimization, pages 215--310. John Wiley & Sons, Chichester, 1997.

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