### Table 2: Separation in subproblems using complementing procedure.

1993

"... In PAGE 19: ... If the separation algorithms succeed in nding violated inequalities for P , the appropriate complementing and lifting procedures are applied. Table2 shows the number of violated inequalities that are obtained by xing variables to one (as described above), calling the separation routines, applying lifting and complementing the corresponding inequalities. For more details on the problem instances we refer to section 5.... ..."

Cited by 4

### Table 3 Cover I. Separation procedures

"... In PAGE 20: ...Table 3 Cover I. Separation procedures In Table3 we can observe that the procedure based on identifying and lifting holes solves most of the problems without resorting to branching, but it is too time consuming. The strategy of looking only for Cliques is very fast on these small problems, but for larger problems we think that we will need more powerful separation procedures.... ..."

### Table 3: Profiling of cutting plane procedure

"... In PAGE 11: ... It is interesting to note that the number of generated rows does not grow exponentially and that the number of problems with size more than 20 is small. Table3 reports on the profiling of the different modules of the exact knapsack separation procedure. Column LP reports on the time spent to solve the separation LP.... ..."

### Table 9. Maximization of lift with pitching moment and separation constraints: Case 7

"... In PAGE 11: ... The optimized airfoil and associated pressure distribution are shown in Fig. 11; further data are given in Table9 . The reduction in the magnitude of the moment coe cient has led to a reduction of the lift coe cient to 1.... ..."

### Table 8. Maximization of lift with separation constraint: Case 6

"... In PAGE 10: ... This constraint ensures that the ow remains fully attached. Results are given in Table8 and Fig. 10.... ..."

### TABLE IV DIFFERENT RESULTS OF SEPARABLE AND NON SEPARABLE LIFTING SCHEME FOR IMAGES OF THE JPEG2000 DATABASE

### Table 5: Efficacy of the probing procedure.

1995

"... In PAGE 30: ... ------------------------------ Insert Table 2 here ------------------------------ All test problems are large-scale, general integer programs which represent problems of actual scale and scope, but their size has prevented us from obtaining the optimal integral solution to any of them. The efficacy of the heuristics can thus be evaluated by comparing the results they produce with each other, with the optimal solution to the initial LP relaxation ( Table5... In PAGE 32: ...25 minutes (not tabled) and produced incremental improvements. The efficacy of the Probing Procedure is shown in Table5 relative to the solution value of the initial LP relaxation. Since no single heuristic dominated the others in terms of consistently prescribing the best solution and since the run time for each heuristic is quite reasonable, a robust approach would involve implementing all heuristics and then selecting the best of the resulting solutions.... In PAGE 50: ... Table5 : Heuristic H8 Prob# STEP 1 LP Relaxation STEP 2 Probing Solution Value Run Time0 (Min) Solution Value Run Time1 (Min) prob1 4568342 0.24 4573637 0.... In PAGE 51: ... Table5 : Heuristic H8 Prob# STEP 1 LP Relaxation STEP 2 Probing STEP 3 Facets for Requirements Polytopes STEP 4 Cutting Planes for Component Availability Constraints STEP 5 Heuristic H3 Solution Value Run Time0 (Min) Solution Value Run Time1 (Min) Solution Value Run Time2 (Min) Solution Value Run Time3 (Min) Solution Value Run Time4 (Min) prob1 4568342 0.24 4573637 0.... ..."

Cited by 2

### Table 2: Cut selection strategies for dicycle separation.

1998

"... In PAGE 17: ... In order to avoid e ects caused by primal heuristics for nding feasible solutions, we initialize the primal bound in the following always with the optimal objective function value. Table2 compares the di erent strategies with respect to the elapsed time for solving the problem and the number of LP reoptimizations. In the case of using only 3-dicycle inequalities, strategy S2 and strategy S3 are the same.... In PAGE 25: ... Despite SIR-separation, in addition to the separation of 3-dicycle inequalities, the time used by the LP solver is more than 90%. Compared with the best sequential solutions ( Table2 ) the number of subproblems of the branch-and-cut tree decreased from 7799 to 633, and in addition the total time could be reduced from 23:16:13h to 13:13:01h. This result is quite satisfactory because... ..."

Cited by 3

### Table 2. Computing times for various solution procedures.

1998

"... In PAGE 3: ... Here, we used MIPO, a branch-and-cut algorithm which uses lift-and-project cuts [1]. The computa- tional results were even worse than with the basic branch-and-bound approach (see Table2 ). This is not surprising since, in this case, the linear programming relaxation has a huge number of basic solutions with value 0.... In PAGE 4: ... Hence, even when we decreased the multi- pliers, we faced space problems. See Table2 . We note that there are other more sophisticated dynamic programming based procedures [14] which could be used here.... In PAGE 4: ... 2.5 Computational Experience Table2 contains our computational experience with the di erent approaches given in Section 2. We choose 4 settings for the problem size: m n =3 20, 4 30, 5 40 and 6 50.... ..."

Cited by 16

### Table 3: Performance of the cutting plane algorithm on the ship problems

"... In PAGE 37: ... So, although these inequalities are not valid for the kNCON polytope, we used them to force the fractional solutions into the creation of longer paths. Table3 gives some computational results of our cutting plane algorithm on the several versions of the ship problem. The entries from left to right are:... In PAGE 40: ... Therefore better separation routines for r-cover inequalities for this special kind of graph are needed. As one can see from Table3 our code is still painfully slow for the problems involving many nodes of type 1. In each iteration, only small progress is made.... ..."