### Table 3: LOOCV accuracy of classifiers for binary class expression data sets. The best prediction rate for each particular data set is highlighted in boldface. Method Leukemia CNS DLBCL Colon Prostate1 Prostate2 Prostate3 Lung GCM Average

in Simple

2005

"... In PAGE 11: ... RESULTS The k-TSP classifier performs comparably to PAM and SVM for the binary classification problems. Table3 summarizes the results of LOOCV using the 7 different classifiers on the 9 binary classification problems. In this case, the estimated classification rate is (TP+TN)/N, where TP denotes the number of correctly classified C1 samples, TN denotes the number of correctly classified C2 samples, and N is the total sample size.... In PAGE 12: ...achieve accuracies in the vicinity of 90% and the second-tier classifiers (k-NN, NB and DT) in vicinity of 80%. In this study ( Table3 ), k-TSP outperforms PAM in 4 cases (CNS, DLBCL, Colon and GCM), PAM outperforms k-TSP in 4 cases (Leukemia, Prostate2, Prostate3 and Lung) and they perform the same in one case (Prostate1). SVM is superior to k-TSP in classifying 5 data sets (Leukemia, Prostate2, Prostate3, Lung and GCM), inferior in two cases (CNS, Colon) and the same in two cases (DLBCL, Prostate1).... ..."

### Table 1: Binary class gene expression data sets. # samples (N)

in Simple

2005

"... In PAGE 12: ... Recall that DT, NB, k-NN and PAM directly handle multiple classes. In order to simplify the presentation of the results for TSP, k-TSP and SVM, in Table 4 we only present the multi-class scheme which performs best for each of these methods, 1-vs-1 for SVMs and HC for TSP and k-TSP; the full results for all multi-class schemes are available in the Supplementary Table1 . One general observation from the multi-class experiments ... ..."

### TABLE IV MMAS with additional 2-opt for symmetric TSP, with reduced 3-opt for ATSP. Three di erent versions of MMAS and local search are considered. The runs were stopped after k n 100 steps of O(n2). The average solution quality is calculated over 10 runs. The best version for a speci c problem instance is indicated by bold face numbers.

1997

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### Table 1: Comparison of TCNN with and without clustering TCNN without clustering No. of clusters Error rate [%] CPU time

1998

"... In PAGE 4: ...ormer 101-city problem, eil101.tsp. At first, we have to determine the number of clusters because of K-mean method. Table1 shows the numerical result of both methods. In this table, CPU time of our method refers to the relative value when that of TCNN is assumed 100.... ..."

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### Table 3: Benchmark Features: Compiler ( ), Naive( ), Advanced( )

"... In PAGE 22: ... Benchmark Description Problem Size tsp Find sub-optimal tour for traveling salesperson problem 32K cites power Optimization Problem based on a variable k-nary tree 10,000 leaves nqueen Search for all legal queen con gurations on a chess board 12x12 quicksort Parallel version of quicksort 512K integers mmult Matrix Multiplication 512x512 oats tomcatv SPEC benchmark 258x258 Table 2: Benchmark Programs and EARTH-C Features For the rst four benchmarks, we started with the original sequential programs and intro- duced EARTH constructs for parallelism and locality. In Table3 , we summarize the EARTH-C features used in this group of benchmarks. We give two versions for each benchmark, a naive version and an advanced version.... ..."

### Table 3. Results of Meta ACS-TSP algorithm runs on TSP/ATSP instances. Average values for each problem are averages over 8 runs (eil51), 4 runs (eil76), and 3 runs (kroA100, p43, ry48p, ft70). Best values are best fitness (tour) results over all the runs of a problem. Overall average values are calculated from the table data. The simulations were run for 1K-3K iterations depending on the problem and setup.

2002

"... In PAGE 5: ...2 with our mutation operator. Table3 summarizes our results. For most problems, the average values of the experimental variables were similar to the best values.... In PAGE 6: ...values used by Dorigo and Gambardella in ACS-TSP [4]. Meta ACS-TSP results are from Table3 . Values we feel should yield best solutions are listed as suggested values.... ..."

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### Table 8.1. Mirrored instances without place constraints. Instance Breaks TPA PGBA

2007

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### Table 8.2. Non-mirrored instances without place constraints. Instance Breaks TPA PGBA Instance Breaks TPA PGBA

2007

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### Table 2. Summary TSP results. In the `Optimum apos; column, gures given in bold font represent the known optimum value; other gures are estimates. For the RAN-20 prob- lem, the optimum is an estimate based on the fact that SA reached this value on 30 consecutive runs, and given the small size of the problem. For the RAN-50 problem, the estimated gure is based on the expected limiting value of an optimal tour [6], and similarly for EUC-50 and EUC-100, the estimates are based on the formula for expected tour length = KpNA with N the number of cities, A = 1:0 the area in which the cities are placed, and K 0:7124 [6]. Algorithm Problem num evals Optimum Best Mean

2001

"... In PAGE 12: ... The choice of city pairs to be used in the multi-objective algorithms is in- vestigated. First, we present results ( Table2 ) in which - for the multi-objective algorithms, PAES and PESA - a single, random pair of cities was selected and this pair used in all runs. Later, we report the maximum deviation from these re- sults for other choices of city pairs.... In PAGE 13: ...From Table2 we can see that, without exception, the results of the PAES algorithm are superior to the SHC algorithm at a statistically signi cant level3, over the range of problem instances in the Table. This shows that the number of local optima in the TSP problem, using the 2-change neighbourhood, is reduced by the method of multi-objectivization we have proposed.... In PAGE 13: ... Then, with cities in opposite corners of the plane the results were: best = 5:818185, mean = 6:09, = 0:16. So both are worse than the `random apos; choice used in the results in Table2 : best = 5:801026, mean = 6:03, = 0:13. However, although there is some seeming dependence on city choice, all three of these results are better than the results of the SHC algorithm on this problem.... ..."

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### Table 2. Required Our Numbers

1996

"... In PAGE 10: ... [3] were run with our algorithm, using K = 15. The problem name listed in Table2 refers to the problem code used by Solomon, followed by the route number. Neither Potvin nor Gendreau could guarantee the optimality of a solution even if their solution was optimal.... In PAGE 10: ... Neither Potvin nor Gendreau could guarantee the optimality of a solution even if their solution was optimal. The entry for \Required K quot; in Table2 indicates what value of K would be needed for a guarantee of optimality. Our algorithm solved 14 of these problems with a guarantee of optimality.... In PAGE 10: ... Note that the solution we received from Gendreau was sometimes di erent than the solution portrayed in the results found in [3]. (see Table 2) As mentioned above, the problems in Table2 added an additional level of di culty in that the objective was to minimize total distance rather than total time. For the reasons illustrated by Figure 3, we could not just keep the best... In PAGE 12: ... This adds another dimension to the auxiliary graph, which we call the thickness of the graph, represented by the constant q, a bound on the number of partial solutions kept. Based on the problems in Table2 , the value of q required to nd the best solution (q0 in Table 2) was small, but the value of q required to guarantee a best solution for the given value of K = 15 (q in Table 2). was much larger Five 500-city asymmetric TSP apos;s were generated using the genlarge problem generator, which Repetto [8] kindly gave to us.... In PAGE 12: ... This adds another dimension to the auxiliary graph, which we call the thickness of the graph, represented by the constant q, a bound on the number of partial solutions kept. Based on the problems in Table 2, the value of q required to nd the best solution (q0 in Table2 ) was small, but the value of q required to guarantee a best solution for the given value of K = 15 (q in Table 2). was much larger Five 500-city asymmetric TSP apos;s were generated using the genlarge problem generator, which Repetto [8] kindly gave to us.... In PAGE 12: ... This adds another dimension to the auxiliary graph, which we call the thickness of the graph, represented by the constant q, a bound on the number of partial solutions kept. Based on the problems in Table 2, the value of q required to nd the best solution (q0 in Table 2) was small, but the value of q required to guarantee a best solution for the given value of K = 15 (q in Table2 ). was much larger Five 500-city asymmetric TSP apos;s were generated using the genlarge problem generator, which Repetto [8] kindly gave to us.... ..."

Cited by 5