### Table 5 Comparison on random optimal base station location with optimal relay allocation Random b

2004

"... In PAGE 8: ... With the preselection process, we can considerably speed up the LP problem- solving process, as indicated in Table 4. Table5 lists the topological network lifetime achieved through random BS location (by exhaustive grid search), time routes, and (b) node energy and lifetime. # Iterations Max RN 55 8.... ..."

### Table 7: Comparison on random or optimal base station loca- tion with optimal relay allocation

"... In PAGE 9: ...1, we can considerably speed up the LP problem-solving process as indicated in Table 6. Table7 lists the topological network lifetime achieved through random BS location, optimal BS location without relaying, and op- timal BS location with optimal relay allocation. We can see the substantial efficacy of the proposed topology control approaches.... ..."

### Table 6: Optimization-Based Allocation Strategy Results (12 Tanks).

"... In PAGE 19: ...onstraints for each tank were reduced to zero (i.e. vlower = 0). This was required to ensure a feasible solution since the lower bounds used in the three-tank allocation problem could not be met given the availability of seven of the crude oils and the total amount of crude oil available. For comparison, Table6... In PAGE 20: ... This is not surprising since the optimization-based strategy takes advantage of all of the available degrees of freedom in the allocation problem to improve the resilience of the blending control; whereas, the blending control problem was not considered in the twelve-tank heuristic allocation strategy. Table6 shows that the optimization-based allocation strategy is much more complex than the heuristic approach. Such a trade-off between allocation strategy complexity and resilience of the blending control problem should be expected.... ..."

### Table 16: Results for the trim loss minimization problems for three strategies: (a) prioritized branching, no bound updates, itermax = 100 (b) prioritized branching, optimization-based bound updates, itermax = 100 (c) prioritized branching, optimization-based bound updates and automatic BB run termination.

2000

"... In PAGE 37: ... The m variables are branched on next, and the r variables follow. The results using this branching strategy, a maximum of one hundred BB iterations and no bound updates are shown in Table16 under strategy (a). Although the average CPU time per run is greatly improved, the standard deviation on every run is large.... In PAGE 37: ....3.2 Variable bound updates The bounds on all integer variables are now tightened through the optimization-based pro- cedure. The results, presented in Table16 under strategy (b), show that the mean number of nodes decreases by 53 to 93% and the mean CPU time decreases by 74 to 94%. 5.... In PAGE 37: ....3.3 Automatic BB run termination The test of lower bound improvement rate is imposed on the BB runs using values of m and r that were successful for the pump network synthesis example, namely m = 3 iterations and r = 30%. The results, shown in Table16 under strategy (c), indicate that the criterion used is too stringent for this problem as a few more nodes must be explored on average before the global optimum solution is found than when one hundred BB iterations are allowed. However, the computational requirements are su ciently close to the best values obtained so far to warrant adopting the automatic stopping criterion with m = 3 iterations and r = 0:3.... ..."

Cited by 6

### Table 14: Results for the pump network synthesis problem using automatic stopping criteria for the BB runs, prioritized variable branching and optimization-based bound updates.

2000

"... In PAGE 34: ...ound updates for the success of a GMIN- BB run. As discussed in Section 4.1, the ideal value of itermax, the maximum number of BB iterations, depends on the structure of the problem. The results shown in Table14 are obtained by imposing the adaptive test of Eq. (20), with di erent values of m and r.... ..."

Cited by 6

### Table 1: Performance of optimization-based heuristic

2006

Cited by 2

### Table 3 Smoothing results for the 2D scalar Poisson problem for the ATM connected SPARC Ultras. We compare the optimization-based approach with a combined approach that uses Laplacian smoothing for high-quality elements.

### Table 4 Smoothing results for the 2D linear elasticity problem for the ATM-connected SPARC Ultras. We compare the optimization-based approach with a combined approach that uses Laplacian smoothing for high-quality elements.

### Table 4: Optimization-Based Allocation Strategy Results (3 Tanks).

"... In PAGE 18: ...2000 (H) 12 0.5500 (M) Table4 gives the calculated results for the optimization-based allocation strategy when three storage tanks are available. Table 5 presents the minimum singular values of the blending constraint matrix for each of the allocation strategies and cases.... ..."