Magny-Cours v.s. Istanbul その１

以下の二つの計算サーバを用いて比較実験を行う。計算サーバ２(Magny-Cours) と計算サーバ１(Istanbul) の理論的な計算性能比は 2.2GHz x 48コア : 2.8GHz x 24 コア = 105.6 : 67.2 = 1.57 : 1 となる。MIP を CPLEX と Gurobi を用いて解いてみたのだが、計算サーバ２の方が遅い例が出てきた。以下の例では Magny-Cours の優位性ははっきりしない。

○問題 S-20-20-2-3.mps（ロットサイズ決定問題）: 最適解 337697
○計算サーバ１
１：CPLEX 12.2.0.2 : 218.55秒

Implied bound cuts applied: 4
Flow cuts applied: 219
Mixed integer rounding cuts applied: 39
Flow path cuts applied: 289
Gomory fractional cuts applied: 19

Root node processing (before b&c):
Real time = 1.27
Parallel b&c, 24 threads:
Real time = 217.28
Sync time (average) = 7.74
Wait time (average) = 0.19
-------
Total (root+branch&cut) = 218.55 sec.

MIP - Integer optimal, tolerance (0.0001/1e-06): Objective = 3.3769700000e+05
Current MIP best bound = 3.3766323187e+05 (gap = 33.7681, 0.01%)
Solution time = 218.59 sec. Iterations = 20676442 Nodes = 1325256 (15413)

２：Gurobi 4.0.1 : 78.02秒
289562 16724 cutoff 42 337696.998 337524.559 0.05% 18.2 75s

Cutting planes:
Gomory: 34
Cover: 37
Flow cover: 269
Flow path: 192

Explored 308448 nodes (5431613 simplex iterations) in 78.02 seconds
Thread count was 24 (of 24 available processors)

○計算サーバ２
１：CPLEX 12.2.0.2 : 162.29秒
Implied bound cuts applied: 7
Flow cuts applied: 230
Mixed integer rounding cuts applied: 41
Flow path cuts applied: 300
Gomory fractional cuts applied: 20

Root node processing (before b&c):
Real time = 1.57
Parallel b&c, 48 threads:
Real time = 160.73
Sync time (average) = 3.89
Wait time (average) = 0.09
-------
Total (root+branch&cut) = 162.29 sec.

Solution pool: 71 solutions saved.

MIP - Integer optimal, tolerance (0.0001/1e-06): Objective = 3.3769700000e+05
Current MIP best bound = 3.3766323062e+05 (gap = 33.7694, 0.01%)
Solution time = 162.33 sec. Iterations = 25689460 Nodes = 1736077 (19169)

２：Gurobi 4.0.1 : 118.31秒
574562 23307 cutoff 53 337697.000 337539.109 0.05% 21.9 115s

Cutting planes:
Gomory: 46
Cover: 50
Flow cover: 325
Flow path: 348

Explored 599849 nodes (12807576 simplex iterations) in 118.31 seconds
Thread count was 48 (of 48 available processors)

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○問題 gmpl-10-0.2.mps (仮想マシンマイグレーション問題)：最適解 155
○計算サーバ１
１：CPLEX 12.2.0.2 : 226.91秒
Clique cuts applied: 33
Cover cuts applied: 233
Implied bound cuts applied: 14
Zero-half cuts applied: 10
Gomory fractional cuts applied: 10

Root node processing (before b&c):
Real time = 0.07
Parallel b&c, 24 threads:
Real time = 226.84
Sync time (average) = 10.37
Wait time (average) = 0.92
-------
Total (root+branch&cut) = 226.91 sec.

Solution pool: 5 solutions saved.

MIP - Integer optimal solution: Objective = 1.5500000000e+02
Solution time = 227.01 sec. Iterations = 39342639 Nodes = 8550323

２：Gurobi 4.0.1 : 332.10秒
17036680 2823 154.00000 41 4 155.00000 154.00000 0.65% 4.6 330s

Cutting planes:
Clique: 2
MIR: 10

Explored 17166935 nodes (78343888 simplex iterations) in 332.1 seconds
Thread count was 24 (of 24 available processors)

○計算サーバ２
１：CPLEX 12.2.0.2 : 345.42秒
Clique cuts applied: 33
Cover cuts applied: 239
Implied bound cuts applied: 15
Zero-half cuts applied: 10
Gomory fractional cuts applied: 10

Root node processing (before b&c):
Real time = 0.11
Parallel b&c, 48 threads:
Real time = 345.30
Sync time (average) = 12.58
Wait time (average) = 2.00
-------
Total (root+branch&cut) = 345.42 sec.

Solution pool: 5 solutions saved.

MIP - Integer optimal solution: Objective = 1.5499999179e+02
Solution time = 345.63 sec. Iterations = 72239030 Nodes = 10974216

２：Gurobi 4.0.1 : 221.57秒
H13587647 122 154.0000920 154.00000 0.00% 4.9 221s

Cutting planes:
Cover: 1
Clique: 2
MIR: 10

Explored 13588519 nodes (66009101 simplex iterations) in 221.57 seconds
Thread count was 48 (of 48 available processors)


○計算サーバ１ (4 CPU x 6 コア = 24 コア)
CPU : AMD Opteron 8439 (2.80GHz / 6MB L3) x 4
Memory : 128GB (32 x 4GB / 800MHz)
OS : Fedora 14 for x86_64

○計算サーバ２ (4 CPU x 12 コア = 48 コア)
CPU : AMD Opteron 6174 (2.20GHz / 12MB L3) x 4
Memory : 256GB (16 x 16GB / 1066MHz)
OS : Fedora 14 for x86_64