### Table 3: Efficiency of Russian Dolls Search

### Table 5: Results of the capacitated facility locations problems on the AP1000

### Table 3b. Solution Statistics for Model 2 (Minimization)

1999

"... In PAGE 4: ...6 Table 2. Problem Statistics Model 1 Model 2 Pt Rows Cols 0/1 Vars Rows Cols 0/1 Vars 1 4398 4568 4568 4398 4568 170 2 4546 4738 4738 4546 4738 192 3 3030 3128 3128 3030 3128 98 4 2774 2921 2921 2774 2921 147 5 5732 5957 5957 5732 5957 225 6 5728 5978 5978 5728 5978 250 7 2538 2658 2658 2538 2658 120 8 3506 3695 3695 3506 3695 189 9 2616 2777 2777 2616 2777 161 10 1680 1758 1758 1680 1758 78 11 5628 5848 5848 5628 5848 220 12 3484 3644 3644 3484 3644 160 13 3700 3833 3833 3700 3833 133 14 4220 4436 4436 4220 4436 216 15 2234 2330 2330 2234 2330 96 16 3823 3949 3949 3823 3949 126 17 4222 4362 4362 4222 4362 140 18 2612 2747 2747 2612 2747 135 19 2400 2484 2484 2400 2484 84 20 2298 2406 2406 2298 2406 108 Table3 a. Solution Statistics for Model 1 (Maximization) Pt Initial First Heuristic Best Best LP Obj.... In PAGE 5: ...) list the elapsed time when the heuristic procedure is first called and the objective value corresponding to the feasible integer solution returned by the heuristic. For Table3 a, the columns Best LP Obj. and Best IP Obj.... In PAGE 5: ... report, respectively, the LP objective bound corresponding to the best node in the remaining branch-and-bound tree and the incumbent objective value corresponding to the best integer feasible solution upon termination of the solution process (10,000 CPU seconds). In Table3 b, the columns Optimal IP Obj., bb nodes, and Elapsed Time report, respectively, the optimal IP objective value, the total number of branch-and-bound tree nodes solved, and the total elapsed time for the solution process.... ..."

### Table 1 Programmed Search vs. Classical Constraint Solving for OPL and T OY

"... In PAGE 9: ... We have obtained running times for these parameters as the average of four runs. Table1 shows these results and has several columns: The column Size represent the size of the problem in terms of the number of months of the timetable. The column TO stands for the labeling strategy equally specified in both systems that assigns values to variables using their textual (static) order, and its possible values in ascending order.... In PAGE 10: ... The columns Posting and Propagation and Labeling show the time for these processes, whereas the last column shows the total time. The cells in the table follow the same data format as Table1 . Note that there are times shown as 0.... In PAGE 11: ... OY is less than before. The gain of the labeling is, in the average, about 23.5, with small deviations. The last column shows the same data as Table1 and is kept for reference. Next, Table 3 shows the impact of propagation alone over the total computation time for both systems.... ..."

### TABLE II RESULTS OF TABU SEARCH AND REROUTING OPTIMIZATION HEURISTICS FOR SOLVING THE REVENUE MAXIMIZATION PROBLEM IN THE ITALIAN NETWORK.

2003

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### Table 3: Accuracy results for solving the QCQP problems.

1996

"... In PAGE 26: ... This indicates that the computational cost of the line-search for these problems is high. In Table3 the accuracy measures are presented. These columns show the feasibility measures (44) and (45) and the optimal objective values.... ..."

### Table 3: Accuracy results for solving the QCQP problems.

"... In PAGE 26: ... This indicates that the computational cost of the line-search for these problems is high. In Table3 the accuracy measures are presented. These columns show the feasibility measures (44) and (45) and the optimal objective values.... ..."

### Table 3. Due to the small super-row O-space, even BnB alone can solve the instance n = 13 in around 5 minutes. ORDS finds the optimal value for n = 16 in 245 minutes with merely 11002 backtracks. To the best our knowledge, this is the largest instance solved with complete branch and bound search on a pure CSP model. Indeed, our answer is the only witness to the optimal value reported by (Larrosa, Morancho, amp; Niso 2005).

"... In PAGE 6: ... Table3 : Results on super-row model: O-vars. Conclusion Constraint optimization problems are commonly solved by a (simple) branch and bound search on the problem variables.... ..."

### Table 4: Solving the rehearsal problem using ILOG Solver, with implied constraints on the waiting time for each player

2003

"... In PAGE 11: ...Table 4: Solving the rehearsal problem using ILOG Solver, with implied constraints on the waiting time for each player Table4 shows the effect of adding this implied constraint on solving the rehearsal prob- lem (with the symmetry constraint a107 a26a172a90 a107 a82 ). With both search orders, it reduces search dramatically.... ..."

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### Table 4. Problem dimension statistics. Problem Variables Constraints Optimal Value Markowitz 1200 201 -0.526165

2000

"... In PAGE 14: ...able 5. Total timing from each solver in seconds. Solver Markowitz Minimal Nonnegative Structural LANCELOT 503 106 3 mem MINOS sup sup sup inf NPSOL 538 657 191 mem PATH 84 333 2 res PATH (merit) 123 221 4 18,375 SNOPT itr sup sup ini Here a keyword in the table identi es that the solver has di culty solving this problem, where mem identi es that the solver could not allocate enough spaces, sup identi es that the solver reported the superbasics limit is too small, itr identi es that the solver reached its iteration limits, inf identi- es that the solver reported problem is unbounded, res identi es that the solver exceeded the resource limits and ini identi es that the solver found the problem is infeasible due to a bad starting point. Optimal solution val- ues from all successfully solved problems are the same for all solvers, and are reported in Table4 . Note that MINOS and SNOPT failed to solve each of these large problems, while PATHNLP with merit function solved all of them.... ..."

Cited by 3