### Table 2: Continuous optimization problems. CPU times and LMI relaxation orders re- quired to reach global optima.

2002

Cited by 42

### Table 6: Solving Sokoban problems with q pattern data bases optimally (continued).

2001

"... In PAGE 13: ... Only an overall searching scheme can prevent the algorithm of getting trapped. In the experiments of Table 5 and Table6 we used a series of 52 automatically generated problems [17]. The screens were then compiled to PDDL, with a one-to-one ball-to-goal mapping such that some problems become unsolvable.... ..."

Cited by 49

### 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. Ideal optimization problem and its implementation

2001

"... In PAGE 5: ... 3. IMPLEMENTATION For the implementation of the optimization problem for finding the Ci , we have the correspondence in terminology and concepts given in Table1 . Each of the continuous domain minimization problems has an associated discrete domain problem with corresponding discrete objective function, discrete feasible solution region , and domain of discrete-valued solution curves.... ..."

Cited by 1

### Tables 2 and 3 present the results obtained for both problems (the 10 bars and 25 bars structures), for both the benchmark continuous problem and a discretized version, where only 36 values were allowed for the areas of the bars. These 36 values included the optimal values found by the gradient-like method in [22].

1996

Cited by 162

### Table 6.1: Experimental results of applying DLM to solve mixed-integer optimization benchmark problemsProblem Constraints Variables Best Orig. Discretized Problems Best DLM Feasibility Avg. ID Total Equality Total Integral Solution Continuous Integral Solution Ratio Time

1998

Cited by 7

### Table 2: Examples of Optimization Applications Field Problem Classi cation

"... In PAGE 3: ... These and other classi cations are summarized in Table 1. Table2 lists application examples from the wide range of elds where optimization is employed and gives their classi cations under this taxonomy. Section 2 details methods appropriate to unconstrained continuous univariate/multivariate problems, and Section 3 mentions methods appropriate to constrained continuous multivari- ate problems.... ..."

### Table 7 Results of the optimization problem with 4-item and 4-location Item

2006

"... In PAGE 12: ... In this case, it can be formulated as a single-period inventory stochastic problem with the mean of the demand depending on the shelf space. For non-perishable products, the problem can be addressed as a continuous review problem, which will constitute the second avenue for the proposed The optimal solution is to select items 1, 2, and 3 and to display them on all shelves with a total profit of 3381, see Table 7) It can be noticed from Table7 that, except for item 1 for which more units are displayed on the first shelf location, almost equal units (after rounding to the nearest integer values) are displayed on all shelves for the Table 7 Results of the optimization problem with 4-item and 4-location Item... ..."

### Table 8: Makespan results for large benchmark problem set

1997

Cited by 35

### Table 6 Test functions (Set B).

2006

"... In PAGE 20: ...2.2 The performance of DTSAPS against other metaheuristics The performance of DTSAPS is compared with other metaheuristics using the test functions listed as Set B in Table6 [19]. We choose two other metaheuris- tics proposed for the continuous optimization problem; Genetic algorithm for numerical optimization of constrained problems (Genocop III) [23], and Scat- ter Search (SS) [19].... ..."

Cited by 7