### 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: 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: 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 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 1. Comparison of results between grids with and without diagonals. New results

1994

"... In PAGE 2: ... For two-dimensional n n meshes without diagonals 1-1 problems have been studied for more than twenty years. The so far fastest solutions for 1-1 problems and for h-h problems with small h 9 are summarized in Table1 . In that table we also present our new results on grids with diagonals and compare them with those for grids without diagonals.... ..."

Cited by 11

### Table 2: Performance of exact algorithm

"... In PAGE 16: ...ore on this in section 5.4.1. A nal issue to consider is whether the problems in Table 3 are somehow \easy. quot; We would argue that the numbers in Table2 show otherwise. In any case, consider problem MS5.... ..."

### Table 2 Travel distance D and time T obtained by two approaches for the four-obstacle problem

in A Genetic-Fuzzy Approach for Optimal Path-planning of a Robotic Manipulator among Static Obstacles

"... In PAGE 6: ... The results of the two approaches are com- pared. The travelling distance and travelling time are presented for approaches 1 and 2 in Table2 where three out of 10 scenarios used during the optimization process are shown in the first three rows. The subsequent three rows show three new and different test scenarios which are not used during the optimization process.... ..."

### Table 7 Exact values of MIPLIB problems

2007

"... In PAGE 6: ...approximate dual solutions to prune the branch- and-bound search tree when possible. In Table7 we report the optimal values for six instances from the MIPLIB 2003 collection. Other problems from MIPLIB can also be solved with this code, but, in general, running times are larger than commercial branch and bound implementations by two or three orders of magnitude.... In PAGE 6: ... Other problems from MIPLIB can also be solved with this code, but, in general, running times are larger than commercial branch and bound implementations by two or three orders of magnitude. The running times for the six instances in Table7 ranged from 58 sec- onds for mann81 to 23 hours for gesa2 o. 5.... ..."

Cited by 1

### Table 7 Exact values of MIPLIB problems

"... In PAGE 6: ...approximate dual solutions to prune the branch- and-bound search tree when possible. In Table7 we report the optimal values for six instances from the MIPLIB 2003 collection. Other problems from MIPLIB can also be solved with this code, but, in general, running times are larger than commercial branch and bound implementations by two or three orders of magnitude.... In PAGE 6: ... Other problems from MIPLIB can also be solved with this code, but, in general, running times are larger than commercial branch and bound implementations by two or three orders of magnitude. The running times for the six instances in Table7 ranged from 58 sec- onds for mann81 to 23 hours for gesa2 o. References [1] D.... ..."

### Table 2. Service Pool for the Example Travel Guide Service.

"... In PAGE 4: ... function of the specified vehicle (e.g. car, train, boat, bi- cycle), and a Location Service (LS) that returns the exact ad- dress given an approximate location. The service pool and interaction table for this example are shown in Table2 and Table 3 respectively. In this scenario, if a service request has exact endpoint addresses, the service DDS is directly invoked.... In PAGE 5: ... For the dis- cussion below consider a request for a service that provides driving directions between two addresses. Possible compo- sition scenarios for the service pool in Table2 are presented in Table 4. The autonomic service composition process is presented below.... ..."