S. Lin. Computer Solutions of the Traveling Salesman Problem. Bell System Technical Journal, 44:2245--2269, 1965. 149  Home/Search   Document Not in Database   Summary   Related Articles   Check

....iteration of the algorithm, once all the ants have built a solution, pheromone trail is added to the arcs used by the ant that found the best tour from the beginning of the trial. In ACS 3 opt the daemon rst activates a local search procedure based on a variant of the 3 opt local search procedure [71] to improve the solutions generated by the ants and then performs o ine pheromone trail update. The o ine pheromone trail update rule is: ij (t) 1 ) ij (t) ij (t) 7) where 2 (0; 1] is a parameter governing pheromone decay, ij (t) 1=L , and L is the length of T , the ....

S. Lin. Computer solutions of the traveling salesman problem. Bell Systems Journal, 44:2245-2269, 1965.

.... that local optimization algorithms seem to be the best t for our application ( 10] compares various algorithms) Thereby, in order to improve a feasible tour it is modi ed by deleting some edges, thus breaking the tour into paths, and then reconnection those paths in an other possible way [12]. Neural nets are too slow, and genetic algorithms are too complex and, therefore, also not fast enough. The migration optimization module calculates a suitable migration strategy i.e. how migration is done in Tracy (pull code, push code, etc. see [4] For this task mainly the line data on the ....

S. Lin. Computer Solutions of the Traveling Salesman Problem. Bell System Technical Journal, 44:2245-2269, 1965.

....available. The next chapter of this book presents an overview of the available ACO algorithms for the QAP. Results obtained by the application of ACO algorithms to the TSP are very encouraging (see [20] results obtained using a rather unsophisticated local search procedure based on the 3 opt [38] allow to obtain results which are very close to those obtainable by much more sophisticated methods. More research will be necessary to assess whether ACO algorithms can reach the performance of state of the art algorithms like Iterated Lin Kernighan [35] An ACO algorithm called AntNet [13, ....

S. Lin. Computer solutions of the traveling salesman problem. Bell Systems Journal, 44:2245-2269, 1965.

.... move of local search is the 2 opt [4] move which consists in removing two edges from a tour and reconstruct a new di#erent tour (there is always one and only one way to reconstruct a new valid tour that is di#erent from the original) The 3 opt proposed by Bock in 1958 exchanges up to 3 edges [21]. We can go on and define the k opt which exchanges k edges. In practice, values of k 4 are seldomly used. The LK move, defined by Lin and Kernighan in 1973 [22] is based on the exchange of edges, the number of edges to exchange being evaluated to get the best possible improvement. Since 1973, ....

S. Lin, Computer Solutions Of The Traveling Salesman Problem, Bell System Technical Journal, 44, 2245--2269, 1965

....path between N cities. This path should start and end in the same city, and 3 should pass only once through each city. An analogy can be made for the JSP where cities become tasks and paths become setup times. The TSP is a practical problem that has been studied widely in the OR literature [4, 8, 12, 10]. However this model imposes that we know at the start the duration of each task, but in our problem this is one of the questions. Therefore, we need a new model that can represent the problem correctly. 3 The Job Sequencing model for CLP In order to find a solution, we first need to formulate ....

S. Lin. Computer solutions of the traveling salesman problem. Bell Syst. Tech. J., 44:2245--2269, 1965.

....for the travelling salesman problem A multilevel TSP algorithm is perhaps not so intuitive as that for the GPP. Clearly the LK or CLK ILK algorithms should make a good refinement method although in principle any iterative refinement procedure including the well known 2 opt, 9] and 3 opt, [37], algorithms could be used. However, with no graph as such, how can the problem be coarsened In fact from [58] it seems that the crucial point in devising a coarsening algorithm is the requirement that the solution to each coarsened problem must contain a solution of the original problem (even ....

....the basis of the 2 opt algorithm due to Croes, 9] which is a steepest descent approach, repeatedly flipping pairs of edges if they improve the tour quality until it reaches a local minimum of the objective function and no more such flips exist. In a similar vein, the 3 opt algorithm of Lin, [37], 13 exchanges 3 edges at a time. The Lin Kernighan (LK) algorithm, 38] also referred to as variable opt, however incorporates a limited amount of hill climbing by searching for a sequence of exchanges, some of which may individually increase the tour length, but which combine to form a shorter ....

S. Lin. Computer solutions of the traveling salesman problem. Bell Syst. Tech. J., 44:2245--2269, 1965.

....the basis of the 2 opt algorithm due to Croes, 8] which is a steepest descent approach, repeatedly flipping pairs of edges if they improve the tour quality until it reaches a local minimum of the objective function and no more such flips exist. In a similar vein, the 3 opt algorithm of Lin, [23], exchanges 3 edges at a time. The Lin Kernighan (LK) algorithm, 24] also referred to as variable opt, however incorporates a limited amount of hill climbing by searching for a sequence of exchanges, some of which may individually increase the tour length, but which combine to form a shorter ....

S. Lin. Computer Solutions of the Traveling Salesman Problem. Bell Syst. Tech. J., 44:2245--2269, 1965.

....the approaches with respect to all the surveyed work is that our main goal at this level of abstraction is to develop a technique for creation of IP property at the higher level of abstraction. It appears that the first paper that introduced heuristic search is by Newell and Ernst [New65] and Lin [Lin65]. The first comprehensive experimental study of the heuristic procedure was done by Doran and Michie [Dor66] In 1968, Hart, Nilsson, and Raphael [Har68] introduced a generic heuristic search technique named A . Pohl [Poh77] and Pearl [Pea84] theoretically analyzed the procedure. Simultaneously, ....

S. Lin. Computer solutions of the traveling salesman problem. Bell Systems Journal, Vol. 44, pp. 2245-2269, 1965.

....called simply k Opt, and in this section we study various pure and restricted heuristics of this kind. Currently, 2 Opt and 3 Opt are the main k Opt heuristics used in practice, introduced respectively by Flood and Croes [27, 24] and by Bock [15] In Shen Lin s influential 1965 study of 3 Opt [49], he concluded that the extra time required for 4 Opt was not worth the small improvement in tour quality it yielded, and no results have appeared since then to contradict this conclusion. In contrast, there have been several attempts to trade tour quality for improved running time in 3Opt by ....

S. Lin. Computer solutions of the traveling salesman problem. Bell System Technical Journal, 44:2245--2269, 1965. REFERENCES 79

....to minimize the total motor cost required to reproduce the reference text. Our optimization scheme is based on earlier work done by our research team for the optimization of ambiguous keypads (like on a telephone) 2] which in turn was inspired by research in the field of operations research [3]. In this approach, characters are initially assigned to random keys. The total motor cost of this arrangement is computed as described above. We then try to decrease the motor cost by systematically re arranging the characters. This is accomplished by repeatedly selecting pairs of characters and ....

.... T U M Y R A S P B L O F X J Q A E Space Space Z K Y Q G N D B C I L U H T R M V S O P X W F J Optimization of Single Finger Keyboards Our character swapping algorithm is a specific instance of a more general methodology known as n optimization (or n opt) [3]. In this paradigm, one considers the effect of rearranging n characters at a time, rather than just swapping 2 characters at a time (a 2 opt approach) The larger the value of n, the more likely the final result is the true optimum the single best possible arrangement. We have subjected the ....

Lin, S. (1965). Computer solutions of the traveling salesman problem. Bell Systems Technical Journal, 44, 2245--2269.

....k 0 (h k 0 1 ) k 0 (h k 0 2 ) k 0 (h k 0 2 1) Figure 4. A cross exchange operation The 2 opt neighborhood was proposed in [21] which is a variant of the 2 opt neighborhood for the traveling salesman problem (TSP, a special case of VRP in which the number of vehicles is one) [15]. A 2 opt operation removes two edges from two di erent routes (one from each) to divide each route into two parts and exchanges the second parts of the two routes (see Fig. 5) Let N 2opt ( k; k 0 ) be the set of all solutions obtainable by 2 opt operations on two routes k and ....

....always 20 correspond to the valid cycles found during the above repeated calls to FVC, since k u 6= k v holds for any two vertices u and v in these valid cycles. 6 Metaheuristic algorithms In this section, we describe three metaheuristic algorithms, the multi start local search (MLS) [15, 16, 22], the iterated local search (ILS) 12, 17, 18] and the adaptive multi start local search (AMLS) 5, 26] All of these algorithms are based on the LS described so far. We describe how to generate initial solutions within their frameworks. 6.1 The multi start local search and iterated local ....

S. Lin, \Computer solutions of the traveling salesman problem," Bell System Technical Journal, 44 (1965) 2245-2269.

....achieved in much less time by their domainspecific local search counterparts. Domain specific heuristics such as 2 Opt [4] E.J.W. Boers et al. Eds. EvoWorkshop 2001, LNCS 2037, pp. 193 202, 2001. c # Springer Verlag Berlin Heidelberg 2001 194 R. Baraglia, J.I. Hidalgo, and R. Perego 3 Opt [5], and Lin Kernighan (LK) 6] are e#ective. In particular LK is considered to be the heuristic that leads to the best solutions. E#cient implementations have been devised for LK which take just a few seconds to compute a high quality solution for problems with hundreds of cities [7,8] Several ....

S. Lin. Computer solution of the traveling salesman problem. Bell System Technical Journal, 44:2245--2269, 1965.

....CSP problems show very encouraging performances. 1 Introduction Heuristic (i.e. non complete) methods have been used in Combinatorial Optimization for nding optimal or near optimal solutions since a few decades, originating with the pioneering work of Lin on the Traveling Salesman Problem [10]. In the last few years, the interest for the family of Local Search methods for solving large combinatorial problems has been revived, and they have attracted much attention from both the Operations Research and the Arti cial Intelligence communities, see for instance the collected papers in [1] ....

S. Lin. Computer solutions of the traveling salesman problem. Bell System Technical Journal, vol. 44 (1965), pp 2245-2269.

.... from a given tour and attempt to reduce its length by exchanging edges chosen according to some heuristic rule until a local optimum is found (i.e. until no further improvement is possible using the heuristic rule) The most used and well known tour improvement heuristics are 2 opt and 3 opt [30], and Lin Kernighan [31] in which respectively two, three, and a variable number of edges are exchanged. It has been experimentally shown [35] that, in general, tour improvement heuristics produce better quality results than tour constructive heuristics. A general approach is to use tour ....

S. Lin., "Computer solutions of the traveling salesman problem," Bell Systems Journal, vol. 44, pp. 2245--2269, 1965.

....CSP problems show very encouraging performances. Introduction Heuristic (i.e. non complete) methods have been used in Combinatorial Optimization for finding optimal or near optimal solutions since a few decades, originating with the pioneering work of Lin on the Traveling Salesman Problem [10]. In the last few years, the interest for the family of Local Search methods for solving large combinatorial problems has been revived, and they have attracted much attention from both the Operations Research and the Artificial Intelligence communities, see for instance the collected papers in [1] ....

S. Lin. Computer solutions of the traveling salesman problem. Bell System Technical Journal, vol. 44 (1965), pp 2245-2269.

....have shown to be a very illustrative tool for the graphical presentation of the cost distance relationship [3,24,34] Here, we exemplify results on the FDC analysis using some instances which are larger than previously studied ones. For our investigation we use a 3 opt local search algorithm [27]. This local search algorithm proceeds by systematically testing whether the current tour can be improved by replacing at most three arcs. Straightforward 3 opt implementations require O(n 3 ) exchanges to be examined. Since this is too time consuming in practice, we use a number of standard ....

S. Lin. Computer solutions for the traveling salesman problem. Bell Systems Technology Journal, 44:2245--2269, 1965.

....(s; V; H(p) C) 13) 8q 2 P (V; V ) and 8y 2 P (V; V ) These Lemmas tell us that we can get the solution set of KMCSP by expanding the trivial path p(s; s) and all its extended feasible head paths step by step. This gives the basic ideas of the A Prune Algorithm. III. A PRUNE ALGORITHM A search[15][16] 17] 18] as well as uniform search, breadth first search and depth first search are well known searching strategies in Artificial Intelligence [19] We combine the A search with a proper pruning technique to get the A Prune algorithm, which can be used to solve the KMCSP problem. Using the ....

S. Lin. Computer solutions of the traveling salesman problem. Bell Systems Technical Journal, 44(10):2245-2269, 1965.

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S. Lin. Computer solutions of the traveling salesman problem. Bell Syst. Tech. J., 44:2245--2269, 1965.

....the basis of the 2 opt algorithm due to Croes, 1] which is a steepest descent approach, repeatedly flipping pairs of edges if they improve the tour quality until it reaches a local minimum of the objective function and no more such flips exist. In a similar vein, the 3 opt algorithm of Lin, [8], exchanges 3 edges at a time. The Lin Kernighan (LK) algorithm, 9] also referred to as variable opt, however incorporates a limited amount of hill climbing by searching for a sequence of exchanges, some of which may individually increase the tour length, but which combine to form a shorter ....

S. Lin. Computer solutions of the traveling salesman problem. Bell Syst. Tech. J., 44:2245--2269, 1965.

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S. Lin. Computer Solutions of the Traveling Salesman Problem. Bell System Technical Journal, 44:2245--2269, 1965. 149

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S. Lin. Computer solutions of the traveling salesman problem. Bell Syst. Tech. J., 44:2245--2269, 1965.

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S. Lin. Computer Solutions of the Traveling Salesman Problem. Bell Syst. Tech. J., 44:2245--2269, 1965.

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S. Lin. Computer solutions of the traveling salesman problem. Bell Syst. Tech. J., 44:2245--2269, 1965.

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S. Lin, Computer Solutions of the Traveling Salesman problems, BSTJ 44(10) (1965) 2245-- 69.

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S. Lin. Computer solutions for the traveling salesman problem. Bell System Tech. J., 44:2245--2269, 1965.

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