### Table 1: Number of Function Evaluations of selected problems using DE, DE-QN, SA and TS

"... In PAGE 11: ... By trial and error, incorporating QN into DE at 500 iterations was found to be the most computationally efficient. As seen from Table1 , the number of function evaluations required for solving the benchmark problems by DE-QN is considerably reduced compared to just using DE alone, indicating the local optimizer (QN) is able to locate the global minimum efficiently when DE has done the hard work at the beginning. Thus, DE is successfully combined with QN to reduce the computational time while maintaining the reliability.... ..."

### Table 8: Comparison with Lin and Kernighan apos;s heuristic on the traveling salesman problem for cities on a lattice.

1988

"... In PAGE 17: ... The speedups, defined as the ratio of the CPU time used by Lin and Kernighan apos;s heuristic, t apos;, to the CPU time used by simulated annealing, t , are shown in Table 6 to Table 9. In Table 6 and Table 9, where the optimal costs are not known, 6 apos; and 6 are the percentages above the estimated best costs respectively for Lin and Kernighan apos;s heuristic and for simulated annealing while in Table 7 and Table8 , where the optimal costs are known, 6 apos; and 6 are the percentages above the optimal costs. From these tables, we observe that Lin and Kernighan apos;s heuristic performs very poorly on super-clustered cities and does a very good job on cities on a lattice.... ..."

Cited by 7

### Table 1 An optional schedule for N = 10, S = 5 and T =10 Period Venue 12345 1 (8,9) (1,2) (3,6) (4,5) (7,10)

2003

"... In PAGE 2: ... 2. Solution approaches Beam Search (BS) and Simulated Annealing (SA) are applied to the multi-venue problem where the following are used to facilitate implementing schedule given in Table1 is an optimal solution with Z = 0 for N =10,S = 5 and T =10. In this work, we apply a construction heuristic and a meta-heuristic method to the problem in Section 2.... ..."

### Table 2 Cooperative versus independent methods

"... In PAGE 11: ... There is no clear winner, although the uniFFed tabu search slightly outperforms our version of Taburoute and the evolutionary algorithms. Table2 displays results for the cooperative (LC02 and LC03) and independent (LCIND) parallel methods. In the independent runs, there is no communication between the individual searches and the solution warehouse serves only to report the best solution of all the four methods (UT1, TS1, ER, OX).... In PAGE 17: ...ig. 2. Evolution of solutions for RC204 by independent search. ( Table2 ), these solutions are important in order for the performance of the cooperative method in terms of solution quality. This insight is also supported by the evolution of the cooperative meta-heuristic, as illustrated by the evolution of the best solution kept in the solution warehouse, and its comparison to the evolution of the independent search method.... ..."

### 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 11: Comparison with Karp apos;s heuristic coupled with Lin and Kernighan apos;s heuristic on the traveling salesman problem with 10,000 uniformly distributed cities. In this table, M is the number of sub-problems in the partition, t apos; and t represent the CPU time for Karp apos;s heuristic and simulated annealing, respectively, while 6 apos; and 6 represent the percentages above the best cost estimated from formula (20). These are the average results of four executions.

1988

"... In PAGE 19: ... As a result, we compute the distances as the need arises and store the distances of only 250 nearest neighbors. The result of the comparison between simulated annealing and Karp apos;s heuristic is shown in Table11 while the pictures of tours obtained via both methods are shown in Fig. 3.... In PAGE 20: ...Table11 is constructed by varying the number of partitions used in Karp apos;s heuristic and comparing the resulting solutions with simulated annealing for different values of A. Figure 3a Figure 3b Figure 3: Tours of a 10,000-city traveling salesman problem.... ..."

Cited by 7

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

1999

Cited by 2

### Table 8: Comparison between different search heuristics

"... In PAGE 31: ... However, a new covering design is always found. Table8 compares simulated annealing, our one level tabu search and multilevel cooperative search. Tests have been conducted on problems for which multilevel cooperative search found new upper bounds.... In PAGE 31: ... Tests have been conducted on problems for which multilevel cooperative search found new upper bounds. Tabu search and simulated annealing procedures are given the same amount of CPU time (in seconds in Table8 ) as multilevel cooperative search using computers with same clock rates. We report the number of iterations2 performed by each procedure as well as the number of t-subsets that have not been covered.... In PAGE 31: ... We report the number of iterations2 performed by each procedure as well as the number of t-subsets that have not been covered. Results in Table8 show that the tabu search procedure is very competitive. These results also confirm that multilevel cooperation substantially improves the performance of tabu search.... ..."

### Table 4 Comparison of results between Tabu search and SA Circuits C2 C5 C7 SA

"... In PAGE 3: ...2. Results The experimental results are shown in Table 3, Table4 , and Table 5, respectively. Table 2 shows the needed notations.... In PAGE 4: ...Table4 , we can find that Tabu search obtains similar results in routing area compared with simulated annealing method [3, 7]. The shielding number only increases a little.... ..."

### Table 2. Comparison of tabu search with different tabusize

"... In PAGE 11: ... The stopping rule Nmax represents the number of consecutive iterations allowed for the search to continue without cost improvement. The experimental results are illustrated in Table2 and 3. The RCBA algorithm was employed as an initial heuristic for all experiments.... In PAGE 11: ... In particular, a fixed or variable tabusize including its scale should be determined through various experimental simulations. In Table2 , fixed tabusize n/4, n/2 and a uniformly distributed tabusize ranged from n/4 to n/2 are compared with the initial solution for each problem. From the table, we conclude that tabusize n/4 is appropriate for the problem structure considered in this paper.... In PAGE 11: ... Based on the experiments by various Nmax, we see that the stopping criteria Nmax with 2n is appropriate for all the problems. Table2 . Comparison of tabu search with different tabusize Table 3.... ..."