### Table 8: Computational results for the traveling salesman problem.

1996

"... In PAGE 36: ...2 The Traveling Salesman Problem The literature on computational results for the traveling salesman problem is vast, and some of the results have already been shown in Section 3. To make the progress visual, we give in Table8 a list of \world records quot; with respect to the size of the instances. It should be noted that there are still some small instances unsolved, which indicates that small does not necessarily imply easy, and that large is not synonymous with di cult.... In PAGE 36: ... The instances can be found in the library TSPLIB, see Reinelt (1991). Table8 contains information on the number of \cities quot; n of the instances. For all instances a complete graph is assumed which means that the number of variables is equal to 1 2n(n ? 1).... In PAGE 36: ... To give an idea of the solution times, the 2392-city problem was solved in approximately 6 hours on a CYBER. As can be seen from Table8 , the lower bounds in the root node are very close to the optimal value which partly explains the success of cutting plane algorithms for the symmetric traveling salesman problem. When solving large instances a very advanced implementation is necessary, see Applegate et al.... ..."

Cited by 4

### Table 8: Results for the traveling salesman problem.

1996

"... In PAGE 32: ... To give an idea of the solution times, the 2392-city problem was solved in approximately 6 hours on a CYBER. As can be seen from Table8 , the lower bounds in the root node are very close to the optimal value which partly explains the success of cutting plane algorithms for the symmetric traveling salesman problem. When solving large instances a very... ..."

Cited by 4

### Table 1. Simulation Results on Traveling Salesman Problems

2007

"... In PAGE 4: ... To qualify how much better our proposed algorithm is making shorter routes than the traditional approaches, we have tested all of the algorithms with a large number of Traveling Salesman Problems up to 532 cities and all the simulations are run 10 times, and then compared to several known algorithms: Kohonen Networks [6] [7], a conventional genetic algorithm using a greedy crossover operator [8] [9]. The results of these simulations are summarized in Table1 . The first three columns indicate the problem ... In PAGE 5: ... And the symbol - means no convergence. From Table1 , we can see that the proposed algorithm has superior ability to search the shortest routes and cost less computation times. 5.... ..."

### Table 8. Table of results for the Traveling Salesman Problem.

1994

"... In PAGE 22: ... Ten runs were made for each problem. Table8... ..."

Cited by 10

### Table 1: Computational results for the traveling salesman problem.

1996

"... In PAGE 15: ...perform well in general. To illustrate the progress made by using the polyhedral approach to solve the TSP,we present, in Table1 , the sizes of the largest instances that have been solved to optimality since 1954. Note that the values given in the column z root LP have been rounded to the nearest integer.... ..."

Cited by 4

### Table 1: Symmetric travelling salesman problems

2000

"... In PAGE 1: ... After each 100st generation the best elements are exchanged between the PNs. The results obtained are given in Table1 in the last column. The second column de- scribes the results obtained by a reimplementation of the same algorithm on a Sun UltraSparc1.... ..."

Cited by 1

### Table 1: 50 Cities Traveling Salesman problem, Initial Energy = 28.56

"... In PAGE 36: ... This is because quasi-equilibrium is not reached at every temperature in this case. Table1 compares the serial method with the replication approach. The replication approach turned out to be the best approach as far as quality of the result goes.... In PAGE 47: ...6 22 22 27.8 Energy Table1 0: Graph Partitioning Problem, 120 vertices, 316 edges graph Figure 41: Graph Partition Problem, Input Graph trial state is generated by choosing at random one non-empty set, extracting at random one element from this set, and placing it in the other set. For the distributed versions only the vertex location array and the counter of edges with vertices in the two sets are passed between processors, the linked lists are reconstructed from this information.... In PAGE 49: ...0 -2328.4 Energy Table1 1: Graph Coloring Problem, 10x10 dense mesh graph Figure 43: Graph Coloring Problem, Input Graph... ..."

### Table III. Travelling-salesman problem (execution time in seconds)

1992

Cited by 27

### Table 2. Simulation Results for the Traveling Salesman Problem Number of

1999

Cited by 2