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

### Table 2 - Levels of abstraction along different dimensions

"... In PAGE 8: ...C. Dimensions Table2 describes the five levels of abstraction with respect to some particular dimensions. Ideally, the software components/classes at each level can be built using only the components/classes from the adjacent lower level.... In PAGE 8: ... In other words, drawing strict dividing lines between the levels of abstraction is not an easy task, and can lead to inflexible knowledge and problem representations. However, it is also our experience that the distribution of concepts, techniques, operations, methods, and tools as shown in Table2 , closely corresponds to that of today apos;s IMSs. Table 1 - Levels of abstraction in the proposed approach Level Objective Semantics 1 Integration A complex IMS, containing multiple intelligent agents; each agent takes care of its own problem solving process; coordination and synchronization of individual agents in contributing to the overall problem solving process; domain-dependent level.... ..."

### Table 2: Technology Mapping results

"... In PAGE 8: ... The results show that the Boolean approach reduces the number of matching algorithm calls, nd smaller area circuits in better CPU time, and reduces the initial network graph because generic 2-input base function are used. Table2 presents a comparison between SIS and Land for the library 44-2.genlib, which is distributed with the SIS package.... ..."

### Table 1. CPU time of monitoring the water level controller example as a function of the time horizon (signal length). The number of positive intervals in the Boolean abstractions is given as another indication for the complexity of the problem.

2004

"... In PAGE 11: ... We use variable integration/sampling step with average step size of 2 seconds so the number of sampling point in the input is roughly half the number of seconds. The results are depicted in Table1 and one can see that monitoring can be done very quickly and it adds a negligible overhead to the simulation of complex systems. For example, the simulation of the water level controller for a time horizon of million seconds takes 45... ..."

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### 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: Node counts and time for instances of multi-commodity network ow problems CPLEX CPLEX + CUTS

2007

"... In PAGE 126: ... CPLEX branch-and-bound was used to solve the two mixed integer programming formulations. Table1 1: Comparison of two formulations: lower and upper bounds were returned at the end of 300s of computation time (P1) (P2) Prob LB UB LB UB E10 10 0.00 0.... In PAGE 127: ... This shows that as an integer programming formulation, with no additional cuts or heuristics added, formulation (P 2) performs better than formulation (P 1). Table1 2: Comparison of two formulations: Node counts and solve times (P1) (P2) Prob Node Count Time Node Count Time E10 10 240 1.5 56 0.... In PAGE 128: ... The time limit was 300s, so if optimal solution is not found in the allotted time for a problem the corresponding entry for solve time is 300s and node count entry is the number of nodes explored in 300s. Table1 3: Comparison of two formulations with cutting planes and heuristics: lower and upper Bounds after 300s of computation time (P1) (P2) Prob LB UB LB UB E10 10 0.00 0.... In PAGE 128: ...00 0.00 Entries in bold represent that optimal solution was found in 300 second Looking at the results from Table1 3, we can see that, with the help of cuts and heuristics, formulation (P 1) was able to provide better results than (P 2). More problems were solved to optimality and for except one, the bounds provided for the problems not solved to optimality in allotted time by formulation (P 1) were stronger than formulation (P 2).... In PAGE 129: ...Table1 4: Comparison of two formulations with cutting Planes and heuristics: node counts and computation times (P1) (P2) Prob Node Count Time Node Count Time E10 10 0 4.01 0 0.... ..."

### Table 1: Comparison of the number of cycles needed to solve satisfiable 3-coloring problems of various sizes and densities by AWC and APO.

2006

"... In PAGE 27: ...06 Table 4: Link statistics for satisfiable, high-density problems. ing at the associated table ( Table1 ), however, reveals that overall, the pairwise T-test indicates that with 99% confidence, APO outperforms AWC on these graphs. As the density, or average degree, of the graph increases, the difference becomes more apparent.... In PAGE 36: ...04 4379.97 Table1 0: Comparison of the number of seconds needed to solve random 3-coloring problems of various sizes and densities using AWC, APO, and centralized Backtracking.... In PAGE 43: ...00 Overall 0.00 Table1 1: Number of cycles needed to solve random target configurations in a field of 224 sensors using AWC and APO.... In PAGE 44: ...00 Overall 0.00 Table1 2: Number of messages needed to solve random target configurations targets in a field of 224 sensors using AWC and APO.... ..."

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### Table 8: Results of using warm starting to solve bicriteria optimization problems.

"... In PAGE 8: ...ing the initial solution procedure for the chosen instance (rule 3 from Section 5). In Table8 , the first chart com- pares the results for t equal to 0 and 100, whereas the second chart compares the results for values of t equal to 0 and 20. The results with t = 20 show a clear and marked improvement over those with t = 0.... ..."

### Table 8: Results of using warm starting to solve bicriteria optimization problems.

"... In PAGE 8: ...ing the initial solution procedure for the chosen instance (rule 3 from Section 5). In Table8 , the first chart com- pares the results for t equal to 0 and 100, whereas the second chart compares the results for values of t equal to 0 and 20. The results with t = 20 show a clear and marked improvement over those with t = 0.... ..."

### Table 4. CPU times (in seconds) using multiple abstractions

2005

"... In PAGE 9: ...dditional token per level in decreasing order (7, then 6, then 5 etc.). Similarly, the complementary abstraction for the 14-Pancake puzzle abstracts tokens 7- 13 (the default abstracts tokens 0-6) and then abstracts one additional token per level in decreasing order. The results are shown in Table4 . The all and none rows in Table 4 have the same meaning and can be directly compared to the corresponding rows in Table 2.... In PAGE 9: ... The results are shown in Table 4. The all and none rows in Table4 have the same meaning and can be directly compared to the corresponding rows in Table 2. The multiple abstractions in this experiment increase the CPU time for solving individual problems in isolation (the all rows) but significantly decrease the time for solving small batches of problems (the none rows).... In PAGE 9: ... One of them abstracts 8 tiles, the others abstract 9 tiles (the default abstracts only 7 tiles). Comparing the all rows in Table4 to the corresponding rows in Table 2 we see that individual problems are solved much more quickly using multiple abstractions. The average time for solving individual problems, 131 seconds for the 15-puzzle and 88 seconds for Macro-15, is two orders of mag- nitude less than the time required to build a high-performance pattern database for these puzzles.... In PAGE 10: ....C. Holte, J. Grajkowski, and B. Tanner all levels. This enables batches of problems to be solved without ever clearing any caches, producing the results shown in the none rows in Table4 . In both spaces the entire batch of 100 test problems is solved in well under an hour.... ..."

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