### Table 6.5. Compaction results for GATTO test sets

### Table 6.6. Compaction results for SYMBAT test sets

### Table 6.7. Compaction results for HITEC test sets

### Table 1 Local optimization Interval global optimization

### Table 7 Comparison with the global optimal solutions

2005

"... In PAGE 14: ... By this way, we tested these three approaches on 300 points. Table7 shows the relative difference values for the MPJ method versus SBA using BARON, and SBA using MINOS versus SBA using BARON. Results show that both MPJ and MINOS find solutions very close to global optimum.... In PAGE 14: ...ersus SBA using BARON. Results show that both MPJ and MINOS find solutions very close to global optimum. There are cases where MINOS achieves the global optimal solution. We also see from Table7 that when we increase the number of jobs from 7 to 10, the CPU time required by BARON increases by a factor of 140. Up to this point we have discussed the pointwise solution quality and computational requirements for both methods.... ..."

### Table 1. Classification of global optimization methods based on the degree of history dependence.

"... In PAGE 2: ... Finally, the small energy difference between the correct and incorrect minima and the exponential growth of the density of the non-native states with energy impose strict requirements on the accuracy of energy evaluation (less than about 1 kcal/mol)5. Numerous approaches have been used to attack the global optimization problem in protein structure prediction, with some success1-8 ( Table1 ). These methods are initially classified according to whether they are deterministic or not; stochastic methods are further subdivided according to the degree of similarity between conformations generated in consecutive iterations of the search algorithm.... In PAGE 3: ... Most of the MC-like stochastic global optimization strategies employ a three-step iteration: (i) modify the current conformation by means of a random move; (ii) evaluate its energy; (iii) accept or reject the new conformation according to an acceptance criterion. The random moves can be ranked by magnitude of change with respect to the current conformation ( Table1 ). The first group contains algorithms in which the generated conformations do not depend on the previous ones.... ..."

### Table 4: Globally optimal results for JIT system design [12]

"... In PAGE 14: ... The best solution obtained by the DPSM for this case (Table 3) yields an assignment of (4, 2, 2, 2) machines to the four stages with a total equipment related cost of $211,883. On the other hand, the global solution for the same problem ( Table4 ) yields an assignment of (3, 3, 3, 3) machines to four stages and results into an optimal cost of $173,983. This represents an improvement of the heuristic solution by $37,900 or 18%.... ..."

### Table 3. Test Functions for Global Optimization Function Constraints

1995

"... In PAGE 8: ... 123 { 141. Berlin: Springer{Verlag 1995 For the test functions of Table3 we get the results shown in Figure 5 (Schwe- fel apos;s function F7 is normalized to make a log-plot possible) which con rm the relation (6). For these function we observe di erent regions of convergence.... In PAGE 15: ...able 5. lt;feval gt; vs. n for Function F6 (left) with f 9 10?1, I = 1:4, Rm = 0:1 , Rmin = 10?1 , pm = 1=n , bm = 2, 20 runs, and for Function F7 (right) with f fopt + 5 10?4 jfoptj , I = 1:4, Rm = 0:75 ,Rmin = 10?4 , pm = 1=n , bm = 2, 20 runs, lt;feval gt; vs. n for Function F8 (left) with f 10?3, I = 1:4, Rm = 0:1 , Rmin = 10?6 , pm = 1=n , bm = 2, 20 runs, and for Function F9 (right) with f 10?3 , I = 1:4, Rm = 0:1 ,Rmin = 10?4, pm = 1=n , bm = 2, 20 runs, BGA data from [10] Rastrigin apos;s Function F6 Schwefel apos;s Function F7 n EASY BGA n EASY BGA N lt;feval gt; N lt;feval gt; N lt;feval gt; N lt;feval gt; 20 20 6098 20 3608 20 20 10987 500 16100 100 20 45118 20 25040 100 20 101458 1000 92000 200 20 98047 20 52948 200 20 241478 2000 248000 400 20 243068 20 112634 400 20 430084 4000 699803 1000 20 574561 20 337570 1000 20 1067221 || ||| Griewangk apos;s Function F8 Ackley apos;s Function F9 n EASY BGA n EASY BGA N lt;feval gt; N lt;feval gt; N lt;feval gt; N lt;feval gt; 20 500 26700 500 66000 30 20 13997 20 19420 100 500 77250 500 361722 100 20 57628 20 53860 200 500 128875 500 748300 200 20 122347 20 107800 400 500 229750 500 1630000 400 20 262606 20 220820 1000 500 563350 | ||| 1000 20 686614 20 548306 The test functions given in Table3 are very popular in the literature on global optimization. The main results of this paper are summarized in Table 5 with n the number of variables, N the population size, and feval the average number of function evaluations for 20 runs.... ..."

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### Table 1: Sequence of operations for implementation of global optimization in spherical mosaicing.

"... In PAGE 15: ...otation optimization. It then calls the function computeCorrelationRotations for all valid image pairs. The set of valid image pairs changes depending on where the function is called in the overall operation. As may be seen from Table1 , the function will use non-rejected images during loops 1 and 2, and rejected images during loop 3. The computeCorrelationRotations routine requires camera parameters, image rotations, and image data to compute the error gradients and Hessians with respect to the quaternions.... ..."

### Table 1: Sequence of operations for implementation of global optimization in spherical mosaicing.

1999

"... In PAGE 15: ...otation optimization. It then calls the function computeCorrelationRotations for all valid image pairs. The set of valid image pairs changes depending on where the function is called in the overall operation. As may be seen from Table1 , the function will use non-rejected images during loops 1 and 2, and rejected images during loop 3. The computeCorrelationRotations routine requires camera parameters, image rotations, and image data to compute the error gradients and Hessians with respect to the quaternions.... ..."