"... In PAGE 7: ...teration is not required. This can be the case with WDM. The tabu search algorithm is quite robust and works well with graph node coloring problems. Table4 lists possible parameters with their default values.... ..."

"... In PAGE 9: ...ilk test for normality at an alpha level of 0.1. The results of the tabu search were compared to the genetic algorithm operating on the new facil- ity locations as described in [11]. The results of these experiments are given in Table3 .The last column of Table 3 indicates the alpha level of significance of not rejecting the hypothesis that the means of the solutions found by both the GA and tabu search are equal.... In PAGE 9: ... The results of these experiments are given in Table 3.The last column of Table3 indicates the alpha level of significance of not rejecting the hypothesis that the means of the solutions found by both the GA and tabu search are equal. The solutions found by both the GA and tabu search were tested for normality using the Shapiro-Wilk test.... In PAGE 9: ...1 are indicated in the table. As Table3 shows, the GA finds significantly better solutions for the larger problems, i.e.... In PAGE 16: ... As indicated in Table 5, the average number of iterations for tabu search to map these basins quickly grows very large. This is consistent with the results presented in Table3 . Tabu search is unable to escape from the large local minima, while the GA, with its strong random search component is able to easily jump between local minima.... ..."

"... In PAGE 9: ...ilk test for normality at an alpha level of 0.1. The results of the tabu search were compared to the genetic algorithm operating on the new facil- ity locations as described in [11]. The results of these experiments are given in Table3 .The last column of Table 3 indicates the alpha level of significance of not rejecting the hypothesis that the means of the solutions found by both the GA and tabu search are equal.... In PAGE 9: ... The results of these experiments are given in Table 3.The last column of Table3 indicates the alpha level of significance of not rejecting the hypothesis that the means of the solutions found by both the GA and tabu search are equal. The solutions found by both the GA and tabu search were tested for normality using the Shapiro-Wilk test.... In PAGE 9: ...1 are indicated in the table. As Table3 shows, the GA finds significantly better solutions for the larger problems, i.e.... In PAGE 16: ... As indicated in Table 5, the average number of iterations for tabu search to map these basins quickly grows very large. This is consistent with the results presented in Table3 . Tabu search is unable to escape from the large local minima, while the GA, with its strong random search component is able to easily jump between local minima.... ..."

"... In PAGE 19: ... It also uses an effective heuristic as the starting point of the tabu search. Table5 reports the experimental results of this tabu-search algorithm as given in [1]. The third and fourth columns describes the quality (percentage compared to the optimum) and the time taken by their heuristics on a 48633Mhz PC.... ..."

"... 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.... ..."

"... In PAGE 21: ...Search heuristic in Table4 , and two versions of the Genetic Algorithms in Tables 5 (simple GA, two point crossover) and 6 (perfect offspring crossover). For each test problem we present the value of the cost function, the following evaluation functions: unfitness, total number of duties, the number of single piece-of-work duties, and the time to find the best solution.... ..."

"... In PAGE 13: ... Now, the new CRCWD3D3D7CT function (Algorithm 9) always takes as input an assignment and returns the position with the best improvement and the best weight. Data: an assignment CG Result: a position begin for all positions CX do Compute AR BP CXD1D4D6D3DACTD1CTD2D8B4CGBN CXB5 for all positions CY such that AR is maximum do Compute AB BP DBCTCXCVCWD8B4CGBN CYB5 Return a position that is randomly selected in those which have the AB maximum end Algorithm 9: Choose function for the tabu search with the RVCF Table1 shows the power of the RVCF mechanism when it is added to the standard tabu search.... In PAGE 14: ...Table 1: Influence of the RVCF mechanism on the Tabu Search The results presented in Table1 show the influence of the RVCF mechanism. On structured instances, good results are observed for the RVCF mechanism but on ran- dom instances, no clear dominance appears.... In PAGE 16: ... Only two instances are presented but others were tested and similar results were obtained. For random instances, the diversification mechanism and the RVCF mechanism improve the results but the combination of both deteriorates them (see Table1 ). TS with the diversification mechanism seems to provide the best results for random instances.... In PAGE 24: ...f 1.54 whereas Walksat obtains 2.00 and UnitWalk 2.46. We observe that GASAT gets results with a very small standard deviation compared with the other solvers. Industrial instances: From Table1 2, we observe that the results of GASAT are not as interesting as for the handmade and random instances. Indeed, the average rank for GASAT is 2.... In PAGE 25: ...00 0.035 Table1 0: SAT2003 competition handmade benchmarks: comparison among GASAT, Walksat and UnitWalk. The running time is limited to 1 hour and the number of autho- rized performed flips is BDBCBD A2 BDBCBH.... In PAGE 27: ...20 0.87 29 Table1 2: SAT2003 competition industrial benchmarks: comparison among GASAT, Walksat and UnitWalk. The running time is limited to 1 hour and the number of autho- rized performed flips is BDBCBD A2 BDBCBH.... In PAGE 27: ...00 0.00 2 Table1 3: Large SAT2003 competition industrial benchmarks where the GASAT search power is restricted by the time. The running time is NOT LIMITED and the number of authorized performed flips is BDBCBD A2 BDBCBH.... ..."

"... In PAGE 7: ... Table 1 shows the performance comparison of the genetic algorithm and our simple tabu search. The right part of Table1 shows the results in terms of DSgap obtained by the simple tabu search; the left part shows results obtained by the genetic algorithm. Each row represents one test group that is formed with a corresponding value of DSrecord.... In PAGE 8: ... The bottom row shows the total number of such test problems. From Table1 , a better performance of the simple tabu search over genetic algorithm can be observed. The total number of the test problems where the DStabu is greater than DSrecord is 795, whereas that of the genetic algorithm is 372.... ..."

"... In PAGE 7: ... Table 1 shows the performance comparison of the genetic algorithm and our simple tabu search. The right part of Table1 shows the results in terms of DSgap obtained by the simple tabu search; the left part shows results obtained by the genetic algorithm. Each row represents one test group that is formed with a corresponding value of DSrecord.... In PAGE 8: ... The bottom row shows the total number of such test problems. From Table1 , a better performance of the simple tabu search over genetic algorithm can be observed. The total number of the test problems where the DStabu is greater than DSrecord is 795, whereas that of the genetic algorithm is 372.... ..."