### Table 14: Performance of Single and Multi-cut L-shaped Methods

2006

"... In PAGE 95: ... This general observation is supported by the results from a computational study that was conducted. The results are shown in Table14 , where the instances are listed in increasing order of size. The computers we use in this chapter have Pentium 4 processor (2.... In PAGE 95: ...2.40GHz) and 2.00 GB of RAM. CPLEX is version 7.0. Table14 shows that for large problems, although the multi-cut L-shaped method takes fewer iterations to solve the problem, it adds many more optimality cuts into the flrst-stage problems and generates much larger mixed-integer problems. Therefore, in terms of the total time to obtain the optimal solutions, it is dominated by the single-cut version for these large problems.... ..."

### Table 3. Performance on tactical problems.

"... In PAGE 16: ... First, the programs were tested against the same suite of one thousand tactical chess problems as used in the multi-cut experiments. The result is shown in Table3 . As before, both the number of nodes searched and problems solved are relative to the performance of an unmodi ed program.... ..."

### Table 1.2: Minimum allowable radii of curvature for different materials and different widths for the cylindrical roll, single cut, and multi-cut models.

in Participants

2002

### Table 1.3: Minimum allowable radii of curvature for different materials and different widths for the cylindrical roll, single cut, and multi-cut models.

in Participants

2002

### Table 1: Node counts and time for instances of multi-commodity network ow problems CPLEX CPLEX + CUTS

2007

"... In PAGE 126: ... CPLEX branch-and-bound was used to solve the two mixed integer programming formulations. Table1 1: Comparison of two formulations: lower and upper bounds were returned at the end of 300s of computation time (P1) (P2) Prob LB UB LB UB E10 10 0.00 0.... In PAGE 127: ... This shows that as an integer programming formulation, with no additional cuts or heuristics added, formulation (P 2) performs better than formulation (P 1). Table1 2: Comparison of two formulations: Node counts and solve times (P1) (P2) Prob Node Count Time Node Count Time E10 10 240 1.5 56 0.... In PAGE 128: ... The time limit was 300s, so if optimal solution is not found in the allotted time for a problem the corresponding entry for solve time is 300s and node count entry is the number of nodes explored in 300s. Table1 3: Comparison of two formulations with cutting planes and heuristics: lower and upper Bounds after 300s of computation time (P1) (P2) Prob LB UB LB UB E10 10 0.00 0.... In PAGE 128: ...00 0.00 Entries in bold represent that optimal solution was found in 300 second Looking at the results from Table1 3, we can see that, with the help of cuts and heuristics, formulation (P 1) was able to provide better results than (P 2). More problems were solved to optimality and for except one, the bounds provided for the problems not solved to optimality in allotted time by formulation (P 1) were stronger than formulation (P 2).... In PAGE 129: ...Table1 4: Comparison of two formulations with cutting Planes and heuristics: node counts and computation times (P1) (P2) Prob Node Count Time Node Count Time E10 10 0 4.01 0 0.... ..."

### Table 2. Summary of 80-game match results.

"... In PAGE 13: ... The programs played each opening once from the white side and once as black. Table2 shows the match results. T T stands for the unmodi ed version of the program and T Tmc(r;c;m) for the version with multi-cut implemented.... ..."

### Table 2: Formulation size for binary and multi-valued state description of problem instances from the IPC2 and IPC3 in number of variables (#va), number of constraints (#co), and number of ordering constraints, or cuts, (#cu) that were added dy- namically through the solution process.

"... In PAGE 32: ... In our recent work (van den Briel, Kambhampati, amp; Vossen, 2007) we analyze different state variable representations in more detail. Table2 compares the encoding size for the G1SC formulation on a set of problems using either a binary or multi-valued state description. The table clearly shows that the encoding size becomes significantly smaller (both before and after CPLEX presolve) when a multi-valued state description is used.... ..."

### Table 8.1. Mirrored instances without place constraints. Instance Breaks TPA PGBA

2007

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### Table 8.2. Non-mirrored instances without place constraints. Instance Breaks TPA PGBA Instance Breaks TPA PGBA

2007

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### Table 2: Linear model estimation

2006

"... In PAGE 9: ...Computational experience (MIPLIB instances) 3 OUR METHOD Table2 compares the size of the measurement tree obtained by the linear model with the actual number of nodes in T. The last column shows the ratio between the two.... ..."

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