### Table 2. CPU times for solving the optimization layout problem with and without the method. Solved instances are described in [16]

in Using Symmetry of Global Constraints to Speed up the Resolution of Constraint Satisfaction Problems

1998

"... In PAGE 6: ... backtrack() { crtVar = old_variable(); if(crtVar == nil) no_solution(); remove_value_from_var(crtVal,crtVar); for every V permutable with crtVar do { if(not(instantiated(V))) { if(V belong a non instantiated constrained structure) { remove_value_from_var(crtVal,V); } } } forward(); } The correctness of this method is not reported here, for reasons of space limitations. We tested it on a set of instances of the layout problem [16], results are reported in Table2 . The solution reported here to exploit symmetry can be compared with the method proposed in [16], which requires a radically new design of the problem.... In PAGE 6: ... The solution reported here to exploit symmetry can be compared with the method proposed in [16], which requires a radically new design of the problem. 8 EFFICIENCY Table2 shows results on optimization layout problems solved with the BackTalk system [17, 18]. Table 2.... ..."

Cited by 8

### 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 9. Problems solved by the hybrid code and not by the default.

2000

"... In PAGE 21: ... It is also important to make three more notes here: (1) the hybrid method switched into penalty mode on 253 problems, (2) the difference between the default and the hybrid performance in iterations is attributable in most part to five problems, s380, s380a, palmer7a, rk23, and haifam, which together account for a difference of about 14,000 iterations, and (3) the difference between the default and the hybrid performance in runtime is due entirely to one problem reading7, which accounts for a difference of approximately 1000 CPU seconds. We now examine the problems documented in Table9 that were solved by the hybrid code, but not by the default code. There are 28 such problems, and of these, one of the problems, s220, switched to the penalty after predicting that sufficient progress cannot be made using the step directions calculated without the penalty.... ..."

Cited by 48

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

### Table 1. Commands for optimal control of hybrid systems.

"... In PAGE 13: ... The WL P T L handles a piecewise linear DPWLE system as an object. The basic commands for building a PWL system are listed in Table1 . Having partitioned the state space and used the functions for entering data into MATLAB,the system is aggregated into a single record that is passed on to functions for analysis and simulations.... In PAGE 98: ... 3. Understanding the Tools The commands available for solving the control problem are listed in Table1 . There are three main groups of programs: a group of four commands that in various ways approximate the value function of a hybrid optimal control problem, one command for deriving a control signal from the value function, and four commands for simulating hy- brid systems.... In PAGE 105: ... Command Reference This section describes the commands in detail. Being very similar to each other, some of the commands of Table1 are grouped into the same entry on the following pages. The commands ohsf and ohsfe are not found in this section, since they are of little interest to the standard user.... ..."

### Table 1. Results of the Dyn-BCP algorithm for the A and B instances.

2003

Cited by 18

### 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 5. Optimal layout and pipe size solutions obtained with various selection algorithms for Network 2.

"... In PAGE 6: ... The problem is solved for two di erent levels of reliability, namely level 1 and level 2, where the reliability of level n refers to the minimum number of independent paths from source nodes to each and every demand node. Figure 5 and column 2 to 4 of Table5 show the resulting layouts, including pipe diameters for reliability level 1 obtained with three of the selection algorithms used earlier, that is, (b) Roulette wheel with linear scaling; (c) Roulette wheel with ranking; and (d) Roulette wheel with power law scaling. The conventional roulette- wheel method is not included in these tests because of its poor performance in the rst example.... ..."

### Table 1. Comparisons of results over ten seeds

1998

"... In PAGE 6: ... The 600,000 value was appropriate for the larger Armour and Buffa problem while the smaller Bazaraa problem converged in much fewer number of solutions searched. Objective function values from the perimeter metric are in Table1 , where the best, median, worst and standard deviation over ten random seeds are shown. The twenty department Armour and Buffa (A amp;B) problem was studied with maximum aspect ratios of 10, 7, 5, 4, 3 and 2, which represent problems ranging from lightly constrained to extremely constrained.... ..."

Cited by 3

### TABLE l Parameter values fitted by the optimization algorithms for the test problem*

1976