### 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: Global optimal solution for different problem settings Exp

"... In PAGE 5: ... This information can be used as a base line to evaluate the performance of the proposed heuristics, as we will see in the following experiments. Three different sets of experiments are conducted as shown in Table1 . In all experiments, the time-varying observations on the different zones were generated randomly following a uniform distribution U(0,200).... In PAGE 5: ... Sensors reliability is assumed to be fixed with time and no lifespan loss associated with their moves. As expected and as shown in Table1 , the algorithm running time increases with the increase in number of zones, number of sensing sensors and length of the monitoring period. For example, in the first set of experiments, increasing the number of zones from 10 to 30 results in a jump in the solution running time from 1542.... ..."

### TABLE I MONTE CARLO RESULTS: GLOBAL STRUCTURE, MARKOV STRUCTURE, AND OPTIMAL SOLUTIONS FOR HORIZON DEPTH d = 3.

### Table 4: Trends in Number of System Analyses to Locate Optimal Solution factors may in uence the number of system analyses required to identify the global optimal solution, for the example problems studied to date the e ect of dou- bling the size of the design space results in an increase of only 70% in the number of system analyses for iden- ti cation of the global optimum. VI. Conclusions

in Response Surface Approximations for Discipline Coordination in Multidisciplinary Design Optimization

1996

Cited by 14

### Table 2. Solutions of the STPPU in Fig. 1. First four rows: assignments to the variables. Fifth row: global preference of the solution. Last row: optimal preference level of the STPP that is the projection of the corresponding situation

2004

"... In PAGE 13: ...t is -DC is 0.9. In fact, if we choose to assign to SA either 4 or 5 units of time (i.e. any element in the intersection of intervals [t SC;SA; q SC;SA] for from 0:5 to 0:9), the pref- erence of the complete solution is at least greater or equal to that of the corresponding projection, for those projections that have optimal preference 0:9. We obtain the set of solutions represented in Table2... ..."

Cited by 9

### Table 2. Solutions of the STPPU in Fig. 1. The first four columns are the assignments to the variables, the fifth column is the global preference of the solution and the last column is the optimal preference level of the STPP that is the projection of the corresponding situation

"... In PAGE 13: ...t is AB-DC is 0.9. In fact, if we choose to assign to CBBT either BG or BH units of time (i.e. any element in the intersection of intervals CJD8AB CBBVBNCBBTBN D5AB CBBVBNCBBTCL for AB from BCBMBH to BCBMBL), the pref- erence of the complete solution is at least greater or equal to that of the corresponding projection, for those projections that have optimal preference AK BCBMBL. We obtain the set of solutions represented in Table2 , according to the value assigned by Nature to BXBV. 8 Comparing and Using Controllability In all, we have introduced five new notions of controllability.... ..."

### Table 2. Solutions of the STPPU in Fig. 1. The first four columns are the assignments to the variables, the fifth column is the global preference of the solution and the last column is the optimal preference level of the STPP that is the projection of the corresponding situation

2004

"... In PAGE 13: ...nits of time (i.e. any element in the intersection of intervals a72 a35 a238 a23a25a24a27a26 a23a29a28 a47a64a195 a238 a23a30a24a27a26 a23a29a28 a74 for a186 from a94a112a173 a146 to a94a112a173 a177 ), the pref- erence of the complete solution is at least greater or equal to that of the corresponding projection, for those projections that have optimal preference a11a60a94a112a173 a177 . We obtain the set of solutions represented in Table2 , according to the value assigned by Nature to a153a112a151 . 8 Comparing and Using Controllability In all, we have introduced five new notions of controllability.... ..."

Cited by 9

### Table 1. Comparison table for different applications. Results are given as: Energy (runtime in seconds). For each problem the energies are scaled to the range of 0 to 999. Note that an energy of 0 in the last two rows does not mean that this is the global optimal solution. The last two columns show the percentage of unlabeled nodes for QPBO and QPBOP, where GM means global minimum. For segmentation BC means boundary constraint and RC region constraint. Also, for segmentation, graph cut was run 2n (n = number BC) times with flow and search tree recycling to obtain the global minimum. Note, ICM and simulated annealing do not perform well for applications with hard pairwise constraints (infinite links), such as segmentation and new view synthesis.

2007

"... In PAGE 7: ... Furthermore, running TRW-S until convergence of the lower bound is much slower than QPBO in practice.) Table1 lists the comparison of all methods for one or two examples of each of the six applications. Diagram Recognition Shape recognition in hand-drawn diagrams is an application where the QPBOP method con- siderably outperforms standard QPBO.... In PAGE 9: ... We have also used the deconvolution MRF with only two labels to reconstruct binary images. Table1 gives two re- sults with different convolution kernels. The main conclu- sion is that for highly connected MRFs, e.... ..."

Cited by 1

### Table 10: Response Surface Maximum Solution: Solution 4

"... In PAGE 51: ...05 km/s, which is less than the jet tip velocities for solutions 1, 2, or 3, and hence it is not the global optimal solution. ( Table10 ). This illustrates that while the solutions may converge pointwise as the mesh is refined, the convergence may not be uniform throughout the problem domain.... ..."

### Table 1: Average of the best solutions over 30 iterations obtained using di erent crossover operators. Global optimal tness = 10.0.

1998

Cited by 4