CPLEX 无法求解 Gurobi 可以求解的 .lp 文件
CPLEX cannot solve an .lp file that Gurobi can
我正在 CPLEX 12.8.0 上使用混合整数二次规划 (MIQP)，PythonAPI。我为 .lp 文件生成了一个模型。事实证明该模型是整数不可行的。这很奇怪，因为我之前用 Gurobi 产生了完全相同的问题并且它是可以解决的。
我已将 link 附加到此处的 .lp 文件以及使用 CPLEX 和 Gurobi 求解的结果。我声明了一些半连续变量。我的 objective 函数是二次函数，但我不认为这是导致整数不可行的原因，不是吗？最后，我真的很想在我的工作中使用 CPLEX，因为 CPLEX 可以做一些 Gurobi 做不到的功能。
.lp 文件：
Minimize
obj: - wi0k0 - wi1k0 - wi2k0 - wi3k0 - wi0k1 - wi1k1 - wi2k1 - wi3k1 + [ m0 ^2
+ m1 ^2 + 1.54315034142201 loss0 ^2 + 1.54315034142201 loss1 ^2
+ 1.54315034142201 loss2 ^2 + 1.54315034142201 loss3 ^2 ] / 2
Subject To
c1i0k0: - 2.98563348744947 zi0k0 - ti0k0 <= 0
c2i0k0: - 1.33632173341833 zi0k0 + ti0k0 <= 0
c3i0k0: m0 + 1.33632173341833 zi0k0 - ti0k0 <= 1.33632173341833
c4i0k0: - m0 + 2.98563348744947 zi0k0 + ti0k0 <= 2.98563348744947
c5i0k0: - 2.30258509299405 zi0k0 - wi0k0 <= 0
c6i0k0: 0.22314355131421 zi0k0 + wi0k0 <= 0
c7i0k0: v0 - 0.22314355131421 zi0k0 - wi0k0 <= -0.22314355131421
c8i0k0: - v0 + 2.30258509299405 zi0k0 + wi0k0 <= 2.30258509299405
c1i1k0: - 2.98563348744947 zi1k0 - ti1k0 <= 0
c2i1k0: - 1.33632173341833 zi1k0 + ti1k0 <= 0
c3i1k0: m0 + 1.33632173341833 zi1k0 - ti1k0 <= 1.33632173341833
c4i1k0: - m0 + 2.98563348744947 zi1k0 + ti1k0 <= 2.98563348744947
c5i1k0: - 2.30258509299405 zi1k0 - wi1k0 <= 0
c6i1k0: 0.22314355131421 zi1k0 + wi1k0 <= 0
c7i1k0: v0 - 0.22314355131421 zi1k0 - wi1k0 <= -0.22314355131421
c8i1k0: - v0 + 2.30258509299405 zi1k0 + wi1k0 <= 2.30258509299405
c1i2k0: - 2.98563348744947 zi2k0 - ti2k0 <= 0
c2i2k0: - 1.33632173341833 zi2k0 + ti2k0 <= 0
c3i2k0: m0 + 1.33632173341833 zi2k0 - ti2k0 <= 1.33632173341833
c4i2k0: - m0 + 2.98563348744947 zi2k0 + ti2k0 <= 2.98563348744947
c5i2k0: - 2.30258509299405 zi2k0 - wi2k0 <= 0
c6i2k0: 0.22314355131421 zi2k0 + wi2k0 <= 0
c7i2k0: v0 - 0.22314355131421 zi2k0 - wi2k0 <= -0.22314355131421
c8i2k0: - v0 + 2.30258509299405 zi2k0 + wi2k0 <= 2.30258509299405
c1i3k0: - 2.98563348744947 zi3k0 - ti3k0 <= 0
c2i3k0: - 1.33632173341833 zi3k0 + ti3k0 <= 0
c3i3k0: m0 + 1.33632173341833 zi3k0 - ti3k0 <= 1.33632173341833
c4i3k0: - m0 + 2.98563348744947 zi3k0 + ti3k0 <= 2.98563348744947
c5i3k0: - 2.30258509299405 zi3k0 - wi3k0 <= 0
c6i3k0: 0.22314355131421 zi3k0 + wi3k0 <= 0
c7i3k0: v0 - 0.22314355131421 zi3k0 - wi3k0 <= -0.22314355131421
c8i3k0: - v0 + 2.30258509299405 zi3k0 + wi3k0 <= 2.30258509299405
c9k0: - pi0 + omk0j1 + omk0j2 + omk0j3 + omk0j4 = 0
c10k0: - v0 + 5.78057663816274 omk0j1 - 2.88064275681032 gk0j1
+ 2.81415134341597 omk0j2 - 2.06487580075496 gk0j2
+ 1.87716609698306 omk0j3 - 1.64323243986015 gk0j3
+ 1.41062901675158 omk0j4 - 1.35164676471547 gk0j4 = 0
c11k0: gk0j1 + gk0j2 + gk0j3 + gk0j4 = 1
c12k0j1: - omk0j1 + 0.1 gk0j1 <= 0
c13k0j1: omk0j1 - 0.275 gk0j1 <= 0
c12k0j2: - omk0j2 + 0.275 gk0j2 <= 0
c13k0j2: omk0j2 - 0.45 gk0j2 <= 0
c12k0j3: - omk0j3 + 0.45 gk0j3 <= 0
c13k0j3: omk0j3 - 0.625 gk0j3 <= 0
c12k0j4: - omk0j4 + 0.625 gk0j4 <= 0
c13k0j4: omk0j4 - 0.8 gk0j4 <= 0
c14k0: - 4 pi0 + zi0k0 + zi1k0 + zi2k0 + zi3k0 = 0
c15k0: 1.33632173341833 zi0k0 - ti0k0 - 1.17708699624777 zi1k0 - ti1k0
- 2.28656128473847 zi2k0 - ti2k0 - 2.98563348744947 zi3k0 - ti3k0
= 0
c1i0k1: - 2.98563348744947 zi0k1 - ti0k1 <= 0
c2i0k1: - 1.33632173341833 zi0k1 + ti0k1 <= 0
c3i0k1: m1 + 1.33632173341833 zi0k1 - ti0k1 <= 1.33632173341833
c4i0k1: - m1 + 2.98563348744947 zi0k1 + ti0k1 <= 2.98563348744947
c5i0k1: - 2.30258509299405 zi0k1 - wi0k1 <= 0
c6i0k1: 0.22314355131421 zi0k1 + wi0k1 <= 0
c7i0k1: v1 - 0.22314355131421 zi0k1 - wi0k1 <= -0.22314355131421
c8i0k1: - v1 + 2.30258509299405 zi0k1 + wi0k1 <= 2.30258509299405
c1i1k1: - 2.98563348744947 zi1k1 - ti1k1 <= 0
c2i1k1: - 1.33632173341833 zi1k1 + ti1k1 <= 0
c3i1k1: m1 + 1.33632173341833 zi1k1 - ti1k1 <= 1.33632173341833
c4i1k1: - m1 + 2.98563348744947 zi1k1 + ti1k1 <= 2.98563348744947
c5i1k1: - 2.30258509299405 zi1k1 - wi1k1 <= 0
c6i1k1: 0.22314355131421 zi1k1 + wi1k1 <= 0
c7i1k1: v1 - 0.22314355131421 zi1k1 - wi1k1 <= -0.22314355131421
c8i1k1: - v1 + 2.30258509299405 zi1k1 + wi1k1 <= 2.30258509299405
c1i2k1: - 2.98563348744947 zi2k1 - ti2k1 <= 0
c2i2k1: - 1.33632173341833 zi2k1 + ti2k1 <= 0
c3i2k1: m1 + 1.33632173341833 zi2k1 - ti2k1 <= 1.33632173341833
c4i2k1: - m1 + 2.98563348744947 zi2k1 + ti2k1 <= 2.98563348744947
c5i2k1: - 2.30258509299405 zi2k1 - wi2k1 <= 0
c6i2k1: 0.22314355131421 zi2k1 + wi2k1 <= 0
c7i2k1: v1 - 0.22314355131421 zi2k1 - wi2k1 <= -0.22314355131421
c8i2k1: - v1 + 2.30258509299405 zi2k1 + wi2k1 <= 2.30258509299405
c1i3k1: - 2.98563348744947 zi3k1 - ti3k1 <= 0
c2i3k1: - 1.33632173341833 zi3k1 + ti3k1 <= 0
c3i3k1: m1 + 1.33632173341833 zi3k1 - ti3k1 <= 1.33632173341833
c4i3k1: - m1 + 2.98563348744947 zi3k1 + ti3k1 <= 2.98563348744947
c5i3k1: - 2.30258509299405 zi3k1 - wi3k1 <= 0
c6i3k1: 0.22314355131421 zi3k1 + wi3k1 <= 0
c7i3k1: v1 - 0.22314355131421 zi3k1 - wi3k1 <= -0.22314355131421
c8i3k1: - v1 + 2.30258509299405 zi3k1 + wi3k1 <= 2.30258509299405
c9k1: - pi1 + omk1j1 + omk1j2 + omk1j3 + omk1j4 = 0
c10k1: - v1 + 5.78057663816274 omk1j1 - 2.88064275681032 gk1j1
+ 2.81415134341597 omk1j2 - 2.06487580075496 gk1j2
+ 1.87716609698306 omk1j3 - 1.64323243986015 gk1j3
+ 1.41062901675158 omk1j4 - 1.35164676471547 gk1j4 = 0
c11k1: gk1j1 + gk1j2 + gk1j3 + gk1j4 = 1
c12k1j1: - omk1j1 + 0.1 gk1j1 <= 0
c13k1j1: omk1j1 - 0.275 gk1j1 <= 0
c12k1j2: - omk1j2 + 0.275 gk1j2 <= 0
c13k1j2: omk1j2 - 0.45 gk1j2 <= 0
c12k1j3: - omk1j3 + 0.45 gk1j3 <= 0
c13k1j3: omk1j3 - 0.625 gk1j3 <= 0
c12k1j4: - omk1j4 + 0.625 gk1j4 <= 0
c13k1j4: omk1j4 - 0.8 gk1j4 <= 0
c14k1: - 4 pi1 + zi0k1 + zi1k1 + zi2k1 + zi3k1 = 0
c15k1: 1.33632173341833 zi0k1 - ti0k1 - 1.17708699624777 zi1k1 - ti1k1
- 2.28656128473847 zi2k1 - ti2k1 - 2.98563348744947 zi3k1 - ti3k1
= 0
c16i0: zi0k0 + zi0k1 = 1
c16i1: zi1k0 + zi1k1 = 1
c16i2: zi2k0 + zi2k1 = 1
c16i3: zi3k0 + zi3k1 = 1
c17k0: zi0k0 + zi1k0 + zi2k0 + zi3k0 >= 0.4
c18k0: zi0k0 + zi1k0 + zi2k0 + zi3k0 <= 3.2
c17k1: zi0k1 + zi1k1 + zi2k1 + zi3k1 >= 0.4
c18k1: zi0k1 + zi1k1 + zi2k1 + zi3k1 <= 3.2
c21k0: m0 - m1 <= 0
c22: pi0 + pi1 = 1
c23i0: ti0k0 + ti0k1 + loss0 = 1.33632173341833
c23i1: ti1k0 + ti1k1 + loss1 = -1.17708699624777
c23i2: ti2k0 + ti2k1 + loss2 = -2.28656128473847
c23i3: ti3k0 + ti3k1 + loss3 = -2.98563348744947
Bounds
0.1 <= pi0 <= 0.8
-2.98563348744947 <= m0 <= 1.33632173341833
-2.30258509299405 <= v0 <= -0.22314355131421
0 <= zi0k0 <= 1
-2.98563348744947 <= ti0k0 <= 1.33632173341833
-2.30258509299405 <= wi0k0 <= -0.22314355131421
0 <= zi1k0 <= 1
-2.98563348744947 <= ti1k0 <= 1.33632173341833
-2.30258509299405 <= wi1k0 <= -0.22314355131421
0 <= zi2k0 <= 1
-2.98563348744947 <= ti2k0 <= 1.33632173341833
-2.30258509299405 <= wi2k0 <= -0.22314355131421
0 <= zi3k0 <= 1
-2.98563348744947 <= ti3k0 <= 1.33632173341833
-2.30258509299405 <= wi3k0 <= -0.22314355131421
0.1 <= omk0j1 <= 0.8
0 <= gk0j1 <= 1
0.1 <= omk0j2 <= 0.8
0 <= gk0j2 <= 1
0.1 <= omk0j3 <= 0.8
0 <= gk0j3 <= 1
0.1 <= omk0j4 <= 0.8
0 <= gk0j4 <= 1
0.1 <= pi1 <= 0.8
-2.98563348744947 <= m1 <= 1.33632173341833
-2.30258509299405 <= v1 <= -0.22314355131421
0 <= zi0k1 <= 1
-2.98563348744947 <= ti0k1 <= 1.33632173341833
-2.30258509299405 <= wi0k1 <= -0.22314355131421
0 <= zi1k1 <= 1
-2.98563348744947 <= ti1k1 <= 1.33632173341833
-2.30258509299405 <= wi1k1 <= -0.22314355131421
0 <= zi2k1 <= 1
-2.98563348744947 <= ti2k1 <= 1.33632173341833
-2.30258509299405 <= wi2k1 <= -0.22314355131421
0 <= zi3k1 <= 1
-2.98563348744947 <= ti3k1 <= 1.33632173341833
-2.30258509299405 <= wi3k1 <= -0.22314355131421
0.1 <= omk1j1 <= 0.8
0 <= gk1j1 <= 1
0.1 <= omk1j2 <= 0.8
0 <= gk1j2 <= 1
0.1 <= omk1j3 <= 0.8
0 <= gk1j3 <= 1
0.1 <= omk1j4 <= 0.8
0 <= gk1j4 <= 1
0 <= loss0 <= 4.3219552208678
-2.5134087296661 <= loss1 <= 1.80854649120169
-3.6228830181568 <= loss2 <= 0.699072202710996
-4.3219552208678 <= loss3 <= 0
Binaries
zi0k0 zi1k0 zi2k0 zi3k0 gk0j1 gk0j2 gk0j3 gk0j4 zi0k1 zi1k1 zi2k1
zi3k1 gk1j1 gk1j2 gk1j3 gk1j4
Semi-Continuous
ti0k0 wi0k0 ti1k0 wi1k0 ti2k0 wi2k0 ti3k0 wi3k0 omk0j1 omk0j2
omk0j3 omk0j4 ti0k1 wi0k1 ti1k1 wi1k1 ti2k1 wi2k1 ti3k1 wi3k1
omk1j1 omk1j2 omk1j3 omk1j4
End
这里Gurobi可以求解模型，但不能求解CPLEX
CPLEX 输出：
Gurobi 输出：
我认为您的 LP 文件规格有误。例如，您有
-2.98563348744947 <= ti0k0 <= 1.33632173341833
但同时ti0k0被标记为"semi-continuous"。那是什么意思？ "semi-continuous" 说 "must be 0 or within the specified bounds"。如果指定的边界包括 0，则变量可能只是半连续的。它有助于解决这个问题吗？
我不确定 Gurobi 对这样的变量做了什么。如果您使用 Gurobi 读取 LP，然后将其写出并将新创建的 LP 文件提供给 CPLEX，会发生什么情况？您是否检查过 Gurobi 提供的解决方案实际上是否满足您的所有约束条件？
除了我在其他答案中提到的奇怪之处（无法编辑我的答案，因为我未在此处注册），您的 LP 文件对于 CPLEX 实际上是错误的。如果你看 https://www.ibm.com/support/knowledgecenter/SSSA5P_12.8.0/ilog.odms.cplex.help/CPLEX/UsrMan/topics/discr_optim/semi_cont_var/02_SemiCont_defn.html 那么你可以阅读
The semi-continuous lower bound (sclb) must be greater than or equal
to 0 (zero). An attempt to use a negative value for the
semi-continuous lower bound (sclb) will result in that bound being
treated as 0 (zero).
因此，“0 或负”的半连续变量可能导致模型不可行，因为它们的下限设置为 0，然后导致变量的边界矛盾。
您必须将这些变量乘以 -1，以便它们变为“0 或在正范围内”。
我正在 CPLEX 12.8.0 上使用混合整数二次规划 (MIQP)，PythonAPI。我为 .lp 文件生成了一个模型。事实证明该模型是整数不可行的。这很奇怪，因为我之前用 Gurobi 产生了完全相同的问题并且它是可以解决的。
我已将 link 附加到此处的 .lp 文件以及使用 CPLEX 和 Gurobi 求解的结果。我声明了一些半连续变量。我的 objective 函数是二次函数，但我不认为这是导致整数不可行的原因，不是吗？最后，我真的很想在我的工作中使用 CPLEX，因为 CPLEX 可以做一些 Gurobi 做不到的功能。
.lp 文件：
Minimize
obj: - wi0k0 - wi1k0 - wi2k0 - wi3k0 - wi0k1 - wi1k1 - wi2k1 - wi3k1 + [ m0 ^2
+ m1 ^2 + 1.54315034142201 loss0 ^2 + 1.54315034142201 loss1 ^2
+ 1.54315034142201 loss2 ^2 + 1.54315034142201 loss3 ^2 ] / 2
Subject To
c1i0k0: - 2.98563348744947 zi0k0 - ti0k0 <= 0
c2i0k0: - 1.33632173341833 zi0k0 + ti0k0 <= 0
c3i0k0: m0 + 1.33632173341833 zi0k0 - ti0k0 <= 1.33632173341833
c4i0k0: - m0 + 2.98563348744947 zi0k0 + ti0k0 <= 2.98563348744947
c5i0k0: - 2.30258509299405 zi0k0 - wi0k0 <= 0
c6i0k0: 0.22314355131421 zi0k0 + wi0k0 <= 0
c7i0k0: v0 - 0.22314355131421 zi0k0 - wi0k0 <= -0.22314355131421
c8i0k0: - v0 + 2.30258509299405 zi0k0 + wi0k0 <= 2.30258509299405
c1i1k0: - 2.98563348744947 zi1k0 - ti1k0 <= 0
c2i1k0: - 1.33632173341833 zi1k0 + ti1k0 <= 0
c3i1k0: m0 + 1.33632173341833 zi1k0 - ti1k0 <= 1.33632173341833
c4i1k0: - m0 + 2.98563348744947 zi1k0 + ti1k0 <= 2.98563348744947
c5i1k0: - 2.30258509299405 zi1k0 - wi1k0 <= 0
c6i1k0: 0.22314355131421 zi1k0 + wi1k0 <= 0
c7i1k0: v0 - 0.22314355131421 zi1k0 - wi1k0 <= -0.22314355131421
c8i1k0: - v0 + 2.30258509299405 zi1k0 + wi1k0 <= 2.30258509299405
c1i2k0: - 2.98563348744947 zi2k0 - ti2k0 <= 0
c2i2k0: - 1.33632173341833 zi2k0 + ti2k0 <= 0
c3i2k0: m0 + 1.33632173341833 zi2k0 - ti2k0 <= 1.33632173341833
c4i2k0: - m0 + 2.98563348744947 zi2k0 + ti2k0 <= 2.98563348744947
c5i2k0: - 2.30258509299405 zi2k0 - wi2k0 <= 0
c6i2k0: 0.22314355131421 zi2k0 + wi2k0 <= 0
c7i2k0: v0 - 0.22314355131421 zi2k0 - wi2k0 <= -0.22314355131421
c8i2k0: - v0 + 2.30258509299405 zi2k0 + wi2k0 <= 2.30258509299405
c1i3k0: - 2.98563348744947 zi3k0 - ti3k0 <= 0
c2i3k0: - 1.33632173341833 zi3k0 + ti3k0 <= 0
c3i3k0: m0 + 1.33632173341833 zi3k0 - ti3k0 <= 1.33632173341833
c4i3k0: - m0 + 2.98563348744947 zi3k0 + ti3k0 <= 2.98563348744947
c5i3k0: - 2.30258509299405 zi3k0 - wi3k0 <= 0
c6i3k0: 0.22314355131421 zi3k0 + wi3k0 <= 0
c7i3k0: v0 - 0.22314355131421 zi3k0 - wi3k0 <= -0.22314355131421
c8i3k0: - v0 + 2.30258509299405 zi3k0 + wi3k0 <= 2.30258509299405
c9k0: - pi0 + omk0j1 + omk0j2 + omk0j3 + omk0j4 = 0
c10k0: - v0 + 5.78057663816274 omk0j1 - 2.88064275681032 gk0j1
+ 2.81415134341597 omk0j2 - 2.06487580075496 gk0j2
+ 1.87716609698306 omk0j3 - 1.64323243986015 gk0j3
+ 1.41062901675158 omk0j4 - 1.35164676471547 gk0j4 = 0
c11k0: gk0j1 + gk0j2 + gk0j3 + gk0j4 = 1
c12k0j1: - omk0j1 + 0.1 gk0j1 <= 0
c13k0j1: omk0j1 - 0.275 gk0j1 <= 0
c12k0j2: - omk0j2 + 0.275 gk0j2 <= 0
c13k0j2: omk0j2 - 0.45 gk0j2 <= 0
c12k0j3: - omk0j3 + 0.45 gk0j3 <= 0
c13k0j3: omk0j3 - 0.625 gk0j3 <= 0
c12k0j4: - omk0j4 + 0.625 gk0j4 <= 0
c13k0j4: omk0j4 - 0.8 gk0j4 <= 0
c14k0: - 4 pi0 + zi0k0 + zi1k0 + zi2k0 + zi3k0 = 0
c15k0: 1.33632173341833 zi0k0 - ti0k0 - 1.17708699624777 zi1k0 - ti1k0
- 2.28656128473847 zi2k0 - ti2k0 - 2.98563348744947 zi3k0 - ti3k0
= 0
c1i0k1: - 2.98563348744947 zi0k1 - ti0k1 <= 0
c2i0k1: - 1.33632173341833 zi0k1 + ti0k1 <= 0
c3i0k1: m1 + 1.33632173341833 zi0k1 - ti0k1 <= 1.33632173341833
c4i0k1: - m1 + 2.98563348744947 zi0k1 + ti0k1 <= 2.98563348744947
c5i0k1: - 2.30258509299405 zi0k1 - wi0k1 <= 0
c6i0k1: 0.22314355131421 zi0k1 + wi0k1 <= 0
c7i0k1: v1 - 0.22314355131421 zi0k1 - wi0k1 <= -0.22314355131421
c8i0k1: - v1 + 2.30258509299405 zi0k1 + wi0k1 <= 2.30258509299405
c1i1k1: - 2.98563348744947 zi1k1 - ti1k1 <= 0
c2i1k1: - 1.33632173341833 zi1k1 + ti1k1 <= 0
c3i1k1: m1 + 1.33632173341833 zi1k1 - ti1k1 <= 1.33632173341833
c4i1k1: - m1 + 2.98563348744947 zi1k1 + ti1k1 <= 2.98563348744947
c5i1k1: - 2.30258509299405 zi1k1 - wi1k1 <= 0
c6i1k1: 0.22314355131421 zi1k1 + wi1k1 <= 0
c7i1k1: v1 - 0.22314355131421 zi1k1 - wi1k1 <= -0.22314355131421
c8i1k1: - v1 + 2.30258509299405 zi1k1 + wi1k1 <= 2.30258509299405
c1i2k1: - 2.98563348744947 zi2k1 - ti2k1 <= 0
c2i2k1: - 1.33632173341833 zi2k1 + ti2k1 <= 0
c3i2k1: m1 + 1.33632173341833 zi2k1 - ti2k1 <= 1.33632173341833
c4i2k1: - m1 + 2.98563348744947 zi2k1 + ti2k1 <= 2.98563348744947
c5i2k1: - 2.30258509299405 zi2k1 - wi2k1 <= 0
c6i2k1: 0.22314355131421 zi2k1 + wi2k1 <= 0
c7i2k1: v1 - 0.22314355131421 zi2k1 - wi2k1 <= -0.22314355131421
c8i2k1: - v1 + 2.30258509299405 zi2k1 + wi2k1 <= 2.30258509299405
c1i3k1: - 2.98563348744947 zi3k1 - ti3k1 <= 0
c2i3k1: - 1.33632173341833 zi3k1 + ti3k1 <= 0
c3i3k1: m1 + 1.33632173341833 zi3k1 - ti3k1 <= 1.33632173341833
c4i3k1: - m1 + 2.98563348744947 zi3k1 + ti3k1 <= 2.98563348744947
c5i3k1: - 2.30258509299405 zi3k1 - wi3k1 <= 0
c6i3k1: 0.22314355131421 zi3k1 + wi3k1 <= 0
c7i3k1: v1 - 0.22314355131421 zi3k1 - wi3k1 <= -0.22314355131421
c8i3k1: - v1 + 2.30258509299405 zi3k1 + wi3k1 <= 2.30258509299405
c9k1: - pi1 + omk1j1 + omk1j2 + omk1j3 + omk1j4 = 0
c10k1: - v1 + 5.78057663816274 omk1j1 - 2.88064275681032 gk1j1
+ 2.81415134341597 omk1j2 - 2.06487580075496 gk1j2
+ 1.87716609698306 omk1j3 - 1.64323243986015 gk1j3
+ 1.41062901675158 omk1j4 - 1.35164676471547 gk1j4 = 0
c11k1: gk1j1 + gk1j2 + gk1j3 + gk1j4 = 1
c12k1j1: - omk1j1 + 0.1 gk1j1 <= 0
c13k1j1: omk1j1 - 0.275 gk1j1 <= 0
c12k1j2: - omk1j2 + 0.275 gk1j2 <= 0
c13k1j2: omk1j2 - 0.45 gk1j2 <= 0
c12k1j3: - omk1j3 + 0.45 gk1j3 <= 0
c13k1j3: omk1j3 - 0.625 gk1j3 <= 0
c12k1j4: - omk1j4 + 0.625 gk1j4 <= 0
c13k1j4: omk1j4 - 0.8 gk1j4 <= 0
c14k1: - 4 pi1 + zi0k1 + zi1k1 + zi2k1 + zi3k1 = 0
c15k1: 1.33632173341833 zi0k1 - ti0k1 - 1.17708699624777 zi1k1 - ti1k1
- 2.28656128473847 zi2k1 - ti2k1 - 2.98563348744947 zi3k1 - ti3k1
= 0
c16i0: zi0k0 + zi0k1 = 1
c16i1: zi1k0 + zi1k1 = 1
c16i2: zi2k0 + zi2k1 = 1
c16i3: zi3k0 + zi3k1 = 1
c17k0: zi0k0 + zi1k0 + zi2k0 + zi3k0 >= 0.4
c18k0: zi0k0 + zi1k0 + zi2k0 + zi3k0 <= 3.2
c17k1: zi0k1 + zi1k1 + zi2k1 + zi3k1 >= 0.4
c18k1: zi0k1 + zi1k1 + zi2k1 + zi3k1 <= 3.2
c21k0: m0 - m1 <= 0
c22: pi0 + pi1 = 1
c23i0: ti0k0 + ti0k1 + loss0 = 1.33632173341833
c23i1: ti1k0 + ti1k1 + loss1 = -1.17708699624777
c23i2: ti2k0 + ti2k1 + loss2 = -2.28656128473847
c23i3: ti3k0 + ti3k1 + loss3 = -2.98563348744947
Bounds
0.1 <= pi0 <= 0.8
-2.98563348744947 <= m0 <= 1.33632173341833
-2.30258509299405 <= v0 <= -0.22314355131421
0 <= zi0k0 <= 1
-2.98563348744947 <= ti0k0 <= 1.33632173341833
-2.30258509299405 <= wi0k0 <= -0.22314355131421
0 <= zi1k0 <= 1
-2.98563348744947 <= ti1k0 <= 1.33632173341833
-2.30258509299405 <= wi1k0 <= -0.22314355131421
0 <= zi2k0 <= 1
-2.98563348744947 <= ti2k0 <= 1.33632173341833
-2.30258509299405 <= wi2k0 <= -0.22314355131421
0 <= zi3k0 <= 1
-2.98563348744947 <= ti3k0 <= 1.33632173341833
-2.30258509299405 <= wi3k0 <= -0.22314355131421
0.1 <= omk0j1 <= 0.8
0 <= gk0j1 <= 1
0.1 <= omk0j2 <= 0.8
0 <= gk0j2 <= 1
0.1 <= omk0j3 <= 0.8
0 <= gk0j3 <= 1
0.1 <= omk0j4 <= 0.8
0 <= gk0j4 <= 1
0.1 <= pi1 <= 0.8
-2.98563348744947 <= m1 <= 1.33632173341833
-2.30258509299405 <= v1 <= -0.22314355131421
0 <= zi0k1 <= 1
-2.98563348744947 <= ti0k1 <= 1.33632173341833
-2.30258509299405 <= wi0k1 <= -0.22314355131421
0 <= zi1k1 <= 1
-2.98563348744947 <= ti1k1 <= 1.33632173341833
-2.30258509299405 <= wi1k1 <= -0.22314355131421
0 <= zi2k1 <= 1
-2.98563348744947 <= ti2k1 <= 1.33632173341833
-2.30258509299405 <= wi2k1 <= -0.22314355131421
0 <= zi3k1 <= 1
-2.98563348744947 <= ti3k1 <= 1.33632173341833
-2.30258509299405 <= wi3k1 <= -0.22314355131421
0.1 <= omk1j1 <= 0.8
0 <= gk1j1 <= 1
0.1 <= omk1j2 <= 0.8
0 <= gk1j2 <= 1
0.1 <= omk1j3 <= 0.8
0 <= gk1j3 <= 1
0.1 <= omk1j4 <= 0.8
0 <= gk1j4 <= 1
0 <= loss0 <= 4.3219552208678
-2.5134087296661 <= loss1 <= 1.80854649120169
-3.6228830181568 <= loss2 <= 0.699072202710996
-4.3219552208678 <= loss3 <= 0
Binaries
zi0k0 zi1k0 zi2k0 zi3k0 gk0j1 gk0j2 gk0j3 gk0j4 zi0k1 zi1k1 zi2k1
zi3k1 gk1j1 gk1j2 gk1j3 gk1j4
Semi-Continuous
ti0k0 wi0k0 ti1k0 wi1k0 ti2k0 wi2k0 ti3k0 wi3k0 omk0j1 omk0j2
omk0j3 omk0j4 ti0k1 wi0k1 ti1k1 wi1k1 ti2k1 wi2k1 ti3k1 wi3k1
omk1j1 omk1j2 omk1j3 omk1j4
End
这里Gurobi可以求解模型，但不能求解CPLEX
CPLEX 输出：
Gurobi 输出：
我认为您的 LP 文件规格有误。例如，您有
-2.98563348744947 <= ti0k0 <= 1.33632173341833
但同时ti0k0被标记为"semi-continuous"。那是什么意思？ "semi-continuous" 说 "must be 0 or within the specified bounds"。如果指定的边界包括 0，则变量可能只是半连续的。它有助于解决这个问题吗？
我不确定 Gurobi 对这样的变量做了什么。如果您使用 Gurobi 读取 LP，然后将其写出并将新创建的 LP 文件提供给 CPLEX，会发生什么情况？您是否检查过 Gurobi 提供的解决方案实际上是否满足您的所有约束条件？
除了我在其他答案中提到的奇怪之处（无法编辑我的答案，因为我未在此处注册），您的 LP 文件对于 CPLEX 实际上是错误的。如果你看 https://www.ibm.com/support/knowledgecenter/SSSA5P_12.8.0/ilog.odms.cplex.help/CPLEX/UsrMan/topics/discr_optim/semi_cont_var/02_SemiCont_defn.html 那么你可以阅读
The semi-continuous lower bound (sclb) must be greater than or equal to 0 (zero). An attempt to use a negative value for the semi-continuous lower bound (sclb) will result in that bound being treated as 0 (zero).
因此，“0 或负”的半连续变量可能导致模型不可行，因为它们的下限设置为 0，然后导致变量的边界矛盾。
您必须将这些变量乘以 -1，以便它们变为“0 或在正范围内”。