### Table 3. Comparison of Competing Branch-and-Bound Algorithms Size Bound CPU CPU-

1998

"... In PAGE 15: ...VII. Comparison of Branch-and-bound Enumeration Table3 compares the performance of the leading branch-and-bound QAP algorithms. These are the Anstreicher-Brixius algorithm [4 and 5], based on a Quadratic Bound, the Hahn, et.... In PAGE 15: ...ahn, et. al. algorithm [12], based on a level-1 RLT bound and the Hightower-Hahn algorithm, based on the level-2 RLT algorithm. The problem instances in Table3 are from the Nugent set, which is considered very difficult.... In PAGE 23: ...B. Five of the results in Table3 were reported in [12]. Recently, the CPU, speed ratios and minutes normalized for corresponding entries in Table 7 of [12] were found to be in error.... ..."

Cited by 19

### Table I. State ReachableFromFinal Bounded

1998

Cited by 5

### Table 7: Branch and bound algorithm on nug05

"... In PAGE 45: ... As an example of the branch and bound algorithm, consider the QAPLIB instance nug05. The iterations of the branch and bound algorithm are sum- marized in Table7 . The GRASP approximation algorithm produced a solution... ..."

### Table 5: Speedup of parallel branch and bound.

1998

"... In PAGE 11: ... We observe that the i860 processors of the MEIKO system are about four times slower than the HP processor. Table5 shows the speedup we obtained for the Branch-and-Bound algorithm when solving our test set QAPs using the di erent bounds. We obtain linear speedup for all lower bounds.... ..."

Cited by 9

### Table 5: Speedup of parallel branch and bound.

1998

"... In PAGE 11: ... We observe that the i860 processors of the MEIKO system are about four times slower than the HP processor. Table5 shows the speedup we obtained for the Branch-and-Bound algorithm when solving our test set QAPs using the di erent bounds. We obtain linear speedup for all lower bounds.... ..."

Cited by 9

### Table 1: Performance of the branch and bound codes.

"... In PAGE 10: ... BB is the simple branch and bound code, while BB1 is the code with the procedure ADDCUT S. Table1 shows the e ectiveness of this procedure, especially for large-scale instances, i.e.... ..."

### Table 2: Results of the branch amp; bound algorithms

"... In PAGE 9: ...epth first search. The PCx code is used for the solution of the linear programs. We have adapted the code such that the interior point method stops if the primary solution is good enough to bound the actual subproblem or if the dual solution shows that we cannot bound the actual subproblem. In Table2 a comparison of our branch amp; bound algorithm with the results from Karisch et al. [10], for our knowledge the best actual code, are presented.... ..."

### Table 1: Experimental Results of the branch and bound algorithms.

"... In PAGE 8: ... We refer the interested reader to [17] for further results. TRANSIT-BFS and TRANSIT-DFS The necessary computation to determine the set of minimal up- date sequences that transform r1 into r2 is shown in Table1 a. The first two columns list the number of databases processed and modification operations executed for building the transition graph.... In PAGE 8: ... We also list the overall number of databases added to the graph together with the number of databases generated as dupli- cates. Table1 a shows a huge difference between the number of modifi- cation operations executed and the number of databases added to the graph or being identified as duplicates for both approaches. This observation indicates that the majority of the generated data- bases are pruned due to their upper and lower bounds.... In PAGE 8: ... It therefore tests several databases at distance levels above the actual update distance. This is reflected by comparing the number of databases added and tested in columns 1 and 3 of Table1 a. For TRANSIF-DFS more databases are tested than added to the graph, due to those data- bases that are added once but tested several times at decreasing ... In PAGE 9: ... We observe that in general the memory requirement for the breadth-first approach is higher than that for the depth-first approach. TRANSIT-BFS (GS) and TRANSIT-DFS (GS) Table1 b shows the necessary effort to determine the set of mini- mal transformers when using the group solution cost as the lower bound for both branch and bound algorithms. In our experiments, this heuristic always computes the correct update distance, but does not find all minimal update sequences.... In PAGE 9: ... In our experiments, this heuristic always computes the correct update distance, but does not find all minimal update sequences. Compared to the numbers in Table1 a, the effort regarding data- bases tested and added is significantly lower for TRANSIT- BFS (GS) and TRANSIT-DFS (GS). As a downside, the computa- tion cost may increase due to the computation of the group solu- tion cost.... ..."

### TABLE 7. Branch and bound algorithm on nug05

1998

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