为什么不考虑 cplex 中解决方案数量的限制？
Why the limits of the number of solutions in cplex is not taken into consideration?
我正在使用从 Julia JuMP 包调用的 CPLEX 解决 MILP 问题。
CPLEX log中显示解数超过3000，但是参数CPXPARAM_MIP_Limits_Solutions设置为55，所以当解数超过55时求解器应该return。
解决方案数量激增导致内存不足错误，因此 Linux 内核终止进程。
这是日志：
CPXPARAM_Emphasis_Memory 1
CPXPARAM_Emphasis_MIP 2
CPXPARAM_MIP_Limits_Solutions 55
CPXPARAM_TimeLimit 60
Warning: Non-integral bounds for integer variables rounded.
2 of 3 MIP starts provided solutions.
MIP start 'm1' defined initial solution with objective 0.0000.
Warning: Non-integral bounds for integer variables rounded.
Tried aggregator 2 times.
MIP Presolve eliminated 12094 rows and 182224 columns.
MIP Presolve added 26 rows and 0 columns.
MIP Presolve modified 17428 coefficients.
Aggregator did 1 substitutions.
Reduced MIP has 5863 rows, 4313 columns, and 28322 nonzeros.
Reduced MIP has 4132 binaries, 175 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.35 sec. (311.81 ticks)
Probing fixed 3059 vars, tightened 200 bounds.
Probing changed sense of 57 constraints.
Probing time = 0.45 sec. (324.14 ticks)
Cover probing fixed 0 vars, tightened 286 bounds.
Tried aggregator 2 times.
MIP Presolve eliminated 4435 rows and 3257 columns.
MIP Presolve modified 923 coefficients.
Aggregator did 2 substitutions.
Reduced MIP has 1426 rows, 1054 columns, and 7403 nonzeros.
Reduced MIP has 929 binaries, 122 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.02 sec. (19.58 ticks)
Probing time = 0.03 sec. (18.90 ticks)
Tried aggregator 1 time.
MIP Presolve eliminated 5 rows and 3 columns.
MIP Presolve modified 1 coefficients.
Reduced MIP has 1421 rows, 1051 columns, and 7378 nonzeros.
Reduced MIP has 927 binaries, 121 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.01 sec. (7.48 ticks)
Probing time = 0.08 sec. (52.47 ticks)
Clique table members: 6451.
MIP emphasis: optimality.
MIP search method: dynamic search.
Parallel mode: deterministic, using up to 32 threads.
Root relaxation solution time = 0.02 sec. (14.70 ticks)
Nodes Cuts/
Node Left Objective IInf Best Integer Best Bound ItCnt Gap
* 0+ 0 0.0000 -106269.5431 ---
0 0 -463.9717 61 0.0000 -463.9717 480 ---
0 0 -454.9015 109 0.0000 Cuts: 86 537 ---
0 0 -434.5372 112 0.0000 Cuts: 87 592 ---
0 0 -426.6747 113 0.0000 Cuts: 97 622 ---
0 0 -418.6204 136 0.0000 Cuts: 62 660 ---
0 0 -413.7867 132 0.0000 Cuts: 55 698 ---
0 0 -409.6387 140 0.0000 Cuts: 16 721 ---
0 0 -407.9923 135 0.0000 Cuts: 39 739 ---
0 0 -407.0012 148 0.0000 Cuts: 34 760 ---
0 0 -406.3034 149 0.0000 Cuts: 11 775 ---
0 0 -405.7757 134 0.0000 Cuts: 17 784 ---
0 0 -405.4831 148 0.0000 Cuts: 59 804 ---
0 2 -405.4831 145 0.0000 -118.6877 804 ---
Elapsed time = 2.12 sec. (1148.70 ticks, tree = 0.02 MB, solutions = 2)
* 282 17 integral 0 0.0000 -118.6877 3889 ---
6415 1365 -0.0974 1 0.0000 -0.1947 20809 ---
11118 1933 -348.8038 138 0.0000 -0.1947 37285 ---
* 11185 11 integral 0 0.0000 -0.1947 37522 ---
* 11206 16 integral 0 -0.0000 -0.1947 37594 ---
12049 384 -0.0974 1 -0.0000 -0.1947 39994 ---
13976 1504 -0.0974 1 -0.0000 -0.1947 44560 ---
15081 1894 -0.0974 1 -0.0000 -0.1947 47408 ---
16098 2205 -0.0000 0 -0.0000 -0.1947 49781 ---
17468 2844 -0.0974 1 -0.0000 -0.1947 52969 ---
18578 3322 -0.0000 0 -0.0000 -0.1947 56013 ---
19990 1939 -0.0000 0 -0.0000 -0.1947 61970 ---
Elapsed time = 14.88 sec. (4728.96 ticks, tree = 2.14 MB, solutions = 3127)
21354 555 cutoff -0.0000 -0.1947 67537 ---
26500 824 -0.0974 1 -0.0000 -0.1431 79682 ---
Killed
版本：
CPLEX 12.9.0
茱莉亚 1.2.0
JuMP 0.20.1
编辑：
CPXPARAM_MIP_Limits_Solutions parameter controls the maximum number of incumbent solution to be found before stopping the optimization. However this number is not enough to control the number of solutions that the solver keeps in memory, because there may be the case when there are multiple solutions that are equivalent in terms of their value of the objective function, and in this case they just count for one solution for CPXPARAM_MIP_Limits_Solutions purpose. Therefore, to avoid memory consumption caused by solutions stored by the solver the right parameter is CPXPARAM_MIP_Pool_Capacity（控制解算器探索的解决方案的数量）我设置为 0（因为我对取回 CPLEX 探索的所有解决方案不感兴趣，而只想取回最好的解决方案）。
在这个配置之后，程序终止了它的 运行 而没有被内核杀死。
解决方案的数量很可能不是内存不足错误的原因。它是分支定界树的大小和需要存储和处理的节点数。您应该尝试限制用于减少内存占用的线程数。
此外，没有找到那么多合适的解决方案。对于每个新任职者，您会在相应行的开头看到一个标记（* 或 H），例如，
* 282 17 integral 0 0.0000 -118.6877 3889 ---
6415 1365 -0.0974 1 0.0000 -0.1947 20809 ---
11118 1933 -348.8038 138 0.0000 -0.1947 37285 ---
* 11185 11 integral 0 0.0000 -0.1947 37522 ---
* 11206 16 integral 0 -0.0000 -0.1947 37594 ---
12049 384 -0.0974 1 -0.0000 -0.1947 39994 ---
我不知道日志中报告的解决方案数量是指什么。可能这些是不会改善 objective.
的其他解决方案
请注意CPLEX docu中参数CPXPARAM_MIP_Limits_Solutions的说明：
Sets the number of MIP solutions to be found before stopping.
This integer solution limit does not apply to the populate procedure, which generates solutions to store in the solution pool. For a limit on the number of solutions generated by populate, see the populate limit parameter: maximum number of solutions generated for solution pool by populate.
我正在使用从 Julia JuMP 包调用的 CPLEX 解决 MILP 问题。 CPLEX log中显示解数超过3000，但是参数CPXPARAM_MIP_Limits_Solutions设置为55，所以当解数超过55时求解器应该return。 解决方案数量激增导致内存不足错误，因此 Linux 内核终止进程。
这是日志：
CPXPARAM_Emphasis_Memory 1
CPXPARAM_Emphasis_MIP 2
CPXPARAM_MIP_Limits_Solutions 55
CPXPARAM_TimeLimit 60
Warning: Non-integral bounds for integer variables rounded.
2 of 3 MIP starts provided solutions.
MIP start 'm1' defined initial solution with objective 0.0000.
Warning: Non-integral bounds for integer variables rounded.
Tried aggregator 2 times.
MIP Presolve eliminated 12094 rows and 182224 columns.
MIP Presolve added 26 rows and 0 columns.
MIP Presolve modified 17428 coefficients.
Aggregator did 1 substitutions.
Reduced MIP has 5863 rows, 4313 columns, and 28322 nonzeros.
Reduced MIP has 4132 binaries, 175 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.35 sec. (311.81 ticks)
Probing fixed 3059 vars, tightened 200 bounds.
Probing changed sense of 57 constraints.
Probing time = 0.45 sec. (324.14 ticks)
Cover probing fixed 0 vars, tightened 286 bounds.
Tried aggregator 2 times.
MIP Presolve eliminated 4435 rows and 3257 columns.
MIP Presolve modified 923 coefficients.
Aggregator did 2 substitutions.
Reduced MIP has 1426 rows, 1054 columns, and 7403 nonzeros.
Reduced MIP has 929 binaries, 122 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.02 sec. (19.58 ticks)
Probing time = 0.03 sec. (18.90 ticks)
Tried aggregator 1 time.
MIP Presolve eliminated 5 rows and 3 columns.
MIP Presolve modified 1 coefficients.
Reduced MIP has 1421 rows, 1051 columns, and 7378 nonzeros.
Reduced MIP has 927 binaries, 121 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.01 sec. (7.48 ticks)
Probing time = 0.08 sec. (52.47 ticks)
Clique table members: 6451.
MIP emphasis: optimality.
MIP search method: dynamic search.
Parallel mode: deterministic, using up to 32 threads.
Root relaxation solution time = 0.02 sec. (14.70 ticks)
Nodes Cuts/
Node Left Objective IInf Best Integer Best Bound ItCnt Gap
* 0+ 0 0.0000 -106269.5431 ---
0 0 -463.9717 61 0.0000 -463.9717 480 ---
0 0 -454.9015 109 0.0000 Cuts: 86 537 ---
0 0 -434.5372 112 0.0000 Cuts: 87 592 ---
0 0 -426.6747 113 0.0000 Cuts: 97 622 ---
0 0 -418.6204 136 0.0000 Cuts: 62 660 ---
0 0 -413.7867 132 0.0000 Cuts: 55 698 ---
0 0 -409.6387 140 0.0000 Cuts: 16 721 ---
0 0 -407.9923 135 0.0000 Cuts: 39 739 ---
0 0 -407.0012 148 0.0000 Cuts: 34 760 ---
0 0 -406.3034 149 0.0000 Cuts: 11 775 ---
0 0 -405.7757 134 0.0000 Cuts: 17 784 ---
0 0 -405.4831 148 0.0000 Cuts: 59 804 ---
0 2 -405.4831 145 0.0000 -118.6877 804 ---
Elapsed time = 2.12 sec. (1148.70 ticks, tree = 0.02 MB, solutions = 2)
* 282 17 integral 0 0.0000 -118.6877 3889 ---
6415 1365 -0.0974 1 0.0000 -0.1947 20809 ---
11118 1933 -348.8038 138 0.0000 -0.1947 37285 ---
* 11185 11 integral 0 0.0000 -0.1947 37522 ---
* 11206 16 integral 0 -0.0000 -0.1947 37594 ---
12049 384 -0.0974 1 -0.0000 -0.1947 39994 ---
13976 1504 -0.0974 1 -0.0000 -0.1947 44560 ---
15081 1894 -0.0974 1 -0.0000 -0.1947 47408 ---
16098 2205 -0.0000 0 -0.0000 -0.1947 49781 ---
17468 2844 -0.0974 1 -0.0000 -0.1947 52969 ---
18578 3322 -0.0000 0 -0.0000 -0.1947 56013 ---
19990 1939 -0.0000 0 -0.0000 -0.1947 61970 ---
Elapsed time = 14.88 sec. (4728.96 ticks, tree = 2.14 MB, solutions = 3127)
21354 555 cutoff -0.0000 -0.1947 67537 ---
26500 824 -0.0974 1 -0.0000 -0.1431 79682 ---
Killed
版本：
CPLEX 12.9.0 茱莉亚 1.2.0 JuMP 0.20.1
编辑：
CPXPARAM_MIP_Limits_Solutions parameter controls the maximum number of incumbent solution to be found before stopping the optimization. However this number is not enough to control the number of solutions that the solver keeps in memory, because there may be the case when there are multiple solutions that are equivalent in terms of their value of the objective function, and in this case they just count for one solution for CPXPARAM_MIP_Limits_Solutions purpose. Therefore, to avoid memory consumption caused by solutions stored by the solver the right parameter is CPXPARAM_MIP_Pool_Capacity（控制解算器探索的解决方案的数量）我设置为 0（因为我对取回 CPLEX 探索的所有解决方案不感兴趣，而只想取回最好的解决方案）。 在这个配置之后，程序终止了它的 运行 而没有被内核杀死。
解决方案的数量很可能不是内存不足错误的原因。它是分支定界树的大小和需要存储和处理的节点数。您应该尝试限制用于减少内存占用的线程数。
此外，没有找到那么多合适的解决方案。对于每个新任职者，您会在相应行的开头看到一个标记（* 或 H），例如，
* 282 17 integral 0 0.0000 -118.6877 3889 ---
6415 1365 -0.0974 1 0.0000 -0.1947 20809 ---
11118 1933 -348.8038 138 0.0000 -0.1947 37285 ---
* 11185 11 integral 0 0.0000 -0.1947 37522 ---
* 11206 16 integral 0 -0.0000 -0.1947 37594 ---
12049 384 -0.0974 1 -0.0000 -0.1947 39994 ---
我不知道日志中报告的解决方案数量是指什么。可能这些是不会改善 objective.
的其他解决方案请注意CPLEX docu中参数CPXPARAM_MIP_Limits_Solutions的说明：
Sets the number of MIP solutions to be found before stopping.
This integer solution limit does not apply to the populate procedure, which generates solutions to store in the solution pool. For a limit on the number of solutions generated by populate, see the populate limit parameter: maximum number of solutions generated for solution pool by populate.