微电网两阶段鲁棒优化（Matlab代码实现）

 欢迎来到本博客❤️❤️

博主优势：博客内容尽量做到思维缜密，逻辑清晰，为了方便读者。

⛳️座右铭：行百里者，半于九十。

目录

1 概述

2两阶段鲁棒模型及求解方法

2.1 两阶段鲁棒优化模型

2.2求解方法 

 3 目标函数和约束条件

3.1 目标函数

3.2 约束条件

3.3 两阶段鲁棒模型:

4 参考文献

5 Matlab代码实现

---

1 概述

站在巨人的肩膀上：

参考文献：

 

2两阶段鲁棒模型及求解方法

2.1 两阶段鲁棒优化模型

2.2求解方法 

 3 目标函数和约束条件

3.1 目标函数

3.2 约束条件

3.3 两阶段鲁棒模型:

高峰电价时段为9:00-11:00和19:00-23:00，电价均为1.35元/kWh，低谷电价时段为24:00-8:00和12:00-18:00，电价分别为0.48元/kWh和0.9元/kWh。

光伏出力:  光伏出力归一值 

风机出力: 风机出力归一值 

CPXPARAM_MIP_Display                             1
Tried aggregator 1 time.
MIP Presolve eliminated 779 rows and 47 columns.
MIP Presolve modified 576 coefficients.
Reduced MIP has 1823 rows, 1110 columns, and 9311 nonzeros.
Reduced MIP has 192 binaries, 0 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.00 sec. (5.00 ticks)
Probing fixed 0 vars, tightened 11 bounds.
Probing time = 0.00 sec. (1.69 ticks)
Tried aggregator 1 time.
Reduced MIP has 1823 rows, 1110 columns, and 9311 nonzeros.
Reduced MIP has 192 binaries, 0 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.02 sec. (3.87 ticks)
Probing time = 0.00 sec. (1.59 ticks)
MIP emphasis: balance optimality and feasibility.
MIP search method: dynamic search.
Parallel mode: deterministic, using up to 16 threads.

Node log . . .
Best integer =   1.558508e+06  Node =       0  Best node =   2.128983e+04
Best integer =   5.306653e+04  Node =       0  Best node =   2.128983e+04
Best integer =   4.746628e+04  Node =       0  Best node =   4.745700e+04
Best integer =   4.746130e+04  Node =       0  Best node =   4.745700e+04
Implied bound cuts applied:  3
Mixed integer rounding cuts applied:  6
Gomory fractional cuts applied:  5
CPXPARAM_MIP_Display                             1
Tried aggregator 3 times.
MIP Presolve eliminated 3609 rows and 1057 columns.
MIP Presolve modified 3183 coefficients.
Aggregator did 61 substitutions.
Reduced MIP has 3054 rows, 2726 columns, and 21043 nonzeros.
Reduced MIP has 1318 binaries, 0 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.02 sec. (30.72 ticks)
Probing fixed 3 vars, tightened 122 bounds.
Probing time = 0.02 sec. (1.13 ticks)
Tried aggregator 3 times.
MIP Presolve eliminated 129 rows and 103 columns.
MIP Presolve modified 618 coefficients.
Aggregator did 79 substitutions.
Reduced MIP has 2846 rows, 2544 columns, and 20519 nonzeros.
Reduced MIP has 1201 binaries, 1 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.02 sec. (24.01 ticks)
Probing time = 0.00 sec. (1.04 ticks)
MIP emphasis: balance optimality and feasibility.
MIP search method: dynamic search.
Parallel mode: deterministic, using up to 16 threads.

Node log . . .
Best integer =  -1.749242e+04  Node =       0  Best node =  -2.422582e+04
Best integer =  -1.769821e+04  Node =       0  Best node =  -2.422582e+04
Best integer =  -2.418924e+04  Node =       0  Best node =  -2.422582e+04
Clique cuts applied:  12
Cover cuts applied:  6
Implied bound cuts applied:  52
Mixed integer rounding cuts applied:  151
Gomory fractional cuts applied:  52
CPXPARAM_MIP_Display                             1
Tried aggregator 2 times.
MIP Presolve eliminated 829 rows and 2 columns.
MIP Presolve modified 1008 coefficients.
Aggregator did 144 substitutions.
Reduced MIP has 1053 rows, 723 columns, and 7241 nonzeros.
Reduced MIP has 192 binaries, 0 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.00 sec. (7.29 ticks)
Probing fixed 0 vars, tightened 24 bounds.
Probing time = 0.00 sec. (0.53 ticks)
Tried aggregator 1 time.
MIP Presolve eliminated 144 rows and 72 columns.
Reduced MIP has 909 rows, 651 columns, and 6953 nonzeros.
Reduced MIP has 120 binaries, 0 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.00 sec. (3.64 ticks)
Probing time = 0.00 sec. (0.26 ticks)
MIP emphasis: balance optimality and feasibility.
MIP search method: dynamic search.
Parallel mode: deterministic, using up to 16 threads.

Node log . . .
Best integer =   1.435047e+06  Node =       0  Best node =   4.559537e+04
Best integer =   1.601358e+05  Node =       0  Best node =   4.559537e+04
Best integer =   6.747812e+04  Node =       0  Best node =   6.747487e+04
CPXPARAM_MIP_Display                             1
Tried aggregator 3 times.
MIP Presolve eliminated 3639 rows and 1096 columns.
MIP Presolve modified 3189 coefficients.
Aggregator did 60 substitutions.
Reduced MIP has 3025 rows, 2688 columns, and 20940 nonzeros.
Reduced MIP has 1306 binaries, 0 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.02 sec. (30.45 ticks)
Probing fixed 2 vars, tightened 129 bounds.
Probing time = 0.00 sec. (1.35 ticks)
Tried aggregator 3 times.
MIP Presolve eliminated 145 rows and 116 columns.
MIP Presolve modified 592 coefficients.
Aggregator did 73 substitutions.
Reduced MIP has 2807 rows, 2499 columns, and 20394 nonzeros.
Reduced MIP has 1187 binaries, 1 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.02 sec. (23.83 ticks)
Probing fixed 0 vars, tightened 2 bounds.
Probing time = 0.00 sec. (1.22 ticks)
MIP emphasis: balance optimality and feasibility.
MIP search method: dynamic search.
Parallel mode: deterministic, using up to 16 threads.

Node log . . .
Best integer =  -2.149270e+04  Node =       0  Best node =  -2.676388e+04
Best integer =  -2.181844e+04  Node =       0  Best node =  -2.676289e+04
Clique cuts applied:  16
Cover cuts applied:  23
Implied bound cuts applied:  100
Flow cuts applied:  7
Mixed integer rounding cuts applied:  143
Gomory fractional cuts applied:  60
CPXPARAM_MIP_Display                             1
Tried aggregator 2 times.
MIP Presolve eliminated 829 rows and 2 columns.
MIP Presolve modified 1008 coefficients.
Aggregator did 144 substitutions.
Reduced MIP has 1053 rows, 723 columns, and 7241 nonzeros.
Reduced MIP has 192 binaries, 0 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.00 sec. (7.29 ticks)
Probing fixed 0 vars, tightened 24 bounds.
Probing time = 0.02 sec. (0.50 ticks)
Tried aggregator 1 time.
MIP Presolve eliminated 144 rows and 72 columns.
Reduced MIP has 909 rows, 651 columns, and 6953 nonzeros.
Reduced MIP has 120 binaries, 0 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.00 sec. (3.64 ticks)
Probing time = 0.00 sec. (0.22 ticks)
MIP emphasis: balance optimality and feasibility.
MIP search method: dynamic search.
Parallel mode: deterministic, using up to 16 threads.

Node log . . .
Best integer =   1.434795e+06  Node =       0  Best node =   4.387395e+04
Best integer =   1.597238e+05  Node =       0  Best node =   4.387395e+04
Best integer =   6.835990e+04  Node =       0  Best node =   6.835665e+04
CPXPARAM_MIP_Display                             1
Tried aggregator 3 times.
MIP Presolve eliminated 3833 rows and 1275 columns.
MIP Presolve modified 3181 coefficients.
Aggregator did 67 substitutions.
Reduced MIP has 2824 rows, 2502 columns, and 20363 nonzeros.
Reduced MIP has 1221 binaries, 0 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.02 sec. (30.34 ticks)
Probing fixed 0 vars, tightened 97 bounds.
Probing time = 0.00 sec. (1.31 ticks)
Tried aggregator 3 times.
MIP Presolve eliminated 137 rows and 108 columns.
MIP Presolve modified 552 coefficients.
Aggregator did 61 substitutions.
Reduced MIP has 2626 rows, 2333 columns, and 19897 nonzeros.
Reduced MIP has 1122 binaries, 3 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.02 sec. (19.99 ticks)
Probing time = 0.00 sec. (1.14 ticks)
MIP emphasis: balance optimality and feasibility.
MIP search method: dynamic search.
Parallel mode: deterministic, using up to 16 threads.

Node log . . .
Best integer =  -2.439674e+04  Node =       0  Best node =  -2.890634e+04
Best integer =  -2.886494e+04  Node =     524  Best node =  -2.890295e+04
Clique cuts applied:  16
Cover cuts applied:  16
Implied bound cuts applied:  31
Flow cuts applied:  7
Mixed integer rounding cuts applied:  100
Gomory fractional cuts applied:  56
CPXPARAM_MIP_Display                             1
Tried aggregator 2 times.
MIP Presolve eliminated 829 rows and 2 columns.
MIP Presolve modified 1008 coefficients.
Aggregator did 144 substitutions.
Reduced MIP has 1053 rows, 723 columns, and 7241 nonzeros.
Reduced MIP has 192 binaries, 0 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.00 sec. (7.29 ticks)
Probing fixed 0 vars, tightened 24 bounds.
Probing time = 0.02 sec. (0.49 ticks)
Tried aggregator 1 time.
MIP Presolve eliminated 144 rows and 72 columns.
Reduced MIP has 909 rows, 651 columns, and 6953 nonzeros.
Reduced MIP has 120 binaries, 0 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.00 sec. (3.64 ticks)
Probing time = 0.00 sec. (0.22 ticks)
MIP emphasis: balance optimality and feasibility.
MIP search method: dynamic search.
Parallel mode: deterministic, using up to 16 threads.

Node log . . .
Best integer =   1.435291e+06  Node =       0  Best node =   4.228469e+04
Best integer =   1.616469e+05  Node =       0  Best node =   4.228469e+04
Best integer =   6.925787e+04  Node =       0  Best node =   6.925463e+04
CPXPARAM_MIP_Display                             1
Tried aggregator 3 times.
MIP Presolve eliminated 3924 rows and 1372 columns.
MIP Presolve modified 3186 coefficients.
Aggregator did 72 substitutions.
Reduced MIP has 2728 rows, 2400 columns, and 20066 nonzeros.
Reduced MIP has 1180 binaries, 0 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.00 sec. (30.04 ticks)
Probing fixed 0 vars, tightened 82 bounds.
Probing time = 0.00 sec. (1.30 ticks)
Tried aggregator 1 time.
MIP Presolve eliminated 150 rows and 120 columns.
MIP Presolve modified 451 coefficients.
Reduced MIP has 2578 rows, 2280 columns, and 19692 nonzeros.
Reduced MIP has 1130 binaries, 6 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.02 sec. (8.66 ticks)
Probing time = 0.00 sec. (1.16 ticks)
MIP emphasis: balance optimality and feasibility.
MIP search method: dynamic search.
Parallel mode: deterministic, using up to 16 threads.

Node log . . .
Best integer =  -3.044507e+04  Node =       0  Best node =  -3.202296e+04
Best integer =  -3.044582e+04  Node =       0  Best node =  -3.093878e+04
Best integer =  -3.044609e+04  Node =       0  Best node =  -3.089980e+04
Best integer =  -3.050281e+04  Node =       0  Best node =  -3.089980e+04
Clique cuts applied:  12
Cover cuts applied:  44
Implied bound cuts applied:  19
Flow cuts applied:  7
Mixed integer rounding cuts applied:  53
Gomory fractional cuts applied:  28
CPXPARAM_MIP_Display                             1
Tried aggregator 2 times.
MIP Presolve eliminated 829 rows and 2 columns.
MIP Presolve modified 1008 coefficients.
Aggregator did 144 substitutions.
Reduced MIP has 1053 rows, 723 columns, and 7241 nonzeros.
Reduced MIP has 192 binaries, 0 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.00 sec. (7.29 ticks)
Probing fixed 0 vars, tightened 24 bounds.
Probing time = 0.00 sec. (0.48 ticks)
Tried aggregator 1 time.
MIP Presolve eliminated 144 rows and 72 columns.
Reduced MIP has 909 rows, 651 columns, and 6953 nonzeros.
Reduced MIP has 120 binaries, 0 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.02 sec. (3.64 ticks)
Probing time = 0.00 sec. (0.21 ticks)
MIP emphasis: balance optimality and feasibility.
MIP search method: dynamic search.
Parallel mode: deterministic, using up to 16 threads.

Node log . . .
Best integer =   1.435399e+06  Node =       0  Best node =   4.081637e+04
Best integer =   1.629365e+05  Node =       0  Best node =   4.081637e+04
Best integer =   6.995436e+04  Node =       0  Best node =   6.995241e+04
CPXPARAM_MIP_Display                             1
Tried aggregator 3 times.
MIP Presolve eliminated 3888 rows and 1329 columns.
MIP Presolve modified 3183 coefficients.
Aggregator did 72 substitutions.
Reduced MIP has 2764 rows, 2443 columns, and 20191 nonzeros.
Reduced MIP has 1195 binaries, 0 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.00 sec. (30.24 ticks)
Probing fixed 1 vars, tightened 95 bounds.
Probing time = 0.02 sec. (1.36 ticks)
Tried aggregator 3 times.
MIP Presolve eliminated 143 rows and 113 columns.
MIP Presolve modified 522 coefficients.
Aggregator did 51 substitutions.
Reduced MIP has 2570 rows, 2279 columns, and 19730 nonzeros.
Reduced MIP has 1102 binaries, 6 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.03 sec. (19.77 ticks)
Probing time = 0.00 sec. (1.23 ticks)
MIP emphasis: balance optimality and feasibility.
MIP search method: dynamic search.
Parallel mode: deterministic, using up to 16 threads.

Node log . . .
Best integer =  -3.229320e+04  Node =       0  Best node =  -3.386904e+04
Best integer =  -3.229448e+04  Node =       0  Best node =  -3.274230e+04
Best integer =  -3.231160e+04  Node =      36  Best node =  -3.273753e+04
Best integer =  -3.267385e+04  Node =     527  Best node =  -3.273693e+04
Clique cuts applied:  10
Cover cuts applied:  31
Implied bound cuts applied:  27
Flow cuts applied:  2
Mixed integer rounding cuts applied:  50
Gomory fractional cuts applied:  31
CPXPARAM_MIP_Display                             1
Tried aggregator 2 times.
MIP Presolve eliminated 829 rows and 2 columns.
MIP Presolve modified 1008 coefficients.
Aggregator did 144 substitutions.
Reduced MIP has 1053 rows, 723 columns, and 7241 nonzeros.
Reduced MIP has 192 binaries, 0 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.00 sec. (7.29 ticks)
Probing fixed 0 vars, tightened 24 bounds.
Probing time = 0.00 sec. (0.46 ticks)
Tried aggregator 1 time.
MIP Presolve eliminated 144 rows and 72 columns.
Reduced MIP has 909 rows, 651 columns, and 6953 nonzeros.
Reduced MIP has 120 binaries, 0 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.00 sec. (3.64 ticks)
Probing time = 0.02 sec. (0.19 ticks)
MIP emphasis: balance optimality and feasibility.
MIP search method: dynamic search.
Parallel mode: deterministic, using up to 16 threads.

Node log . . .
Best integer =   1.435498e+06  Node =       0  Best node =   3.945881e+04
Best integer =   1.641265e+05  Node =       0  Best node =   3.945881e+04
Best integer =   7.050950e+04  Node =       0  Best node =   7.050625e+04
CPXPARAM_MIP_Display                             1
Tried aggregator 3 times.
MIP Presolve eliminated 3969 rows and 1400 columns.
MIP Presolve modified 3173 coefficients.
Aggregator did 73 substitutions.
Reduced MIP has 2682 rows, 2371 columns, and 19965 nonzeros.
Reduced MIP has 1161 binaries, 0 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.00 sec. (30.19 ticks)
Probing fixed 1 vars, tightened 86 bounds.
Probing time = 0.02 sec. (1.35 ticks)
Tried aggregator 3 times.
MIP Presolve eliminated 143 rows and 113 columns.
MIP Presolve modified 482 coefficients.
Aggregator did 41 substitutions.
Reduced MIP has 2498 rows, 2217 columns, and 19535 nonzeros.
Reduced MIP has 1078 binaries, 10 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.02 sec. (19.45 ticks)
Probing time = 0.02 sec. (1.27 ticks)
MIP emphasis: balance optimality and feasibility.
MIP search method: dynamic search.
Parallel mode: deterministic, using up to 16 threads.

Node log . . .
Best integer =  -3.433272e+04  Node =       0  Best node =  -3.434461e+04
Clique cuts applied:  23
Cover cuts applied:  19
Implied bound cuts applied:  64
Flow cuts applied:  19
Mixed integer rounding cuts applied:  91
Gomory fractional cuts applied:  51
CPXPARAM_MIP_Display                             1
Tried aggregator 2 times.
MIP Presolve eliminated 829 rows and 2 columns.
MIP Presolve modified 1008 coefficients.
Aggregator did 144 substitutions.
Reduced MIP has 1053 rows, 723 columns, and 7241 nonzeros.
Reduced MIP has 192 binaries, 0 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.02 sec. (7.29 ticks)
Probing fixed 0 vars, tightened 24 bounds.
Probing time = 0.00 sec. (0.46 ticks)
Tried aggregator 1 time.
MIP Presolve eliminated 144 rows and 72 columns.
Reduced MIP has 909 rows, 651 columns, and 6953 nonzeros.
Reduced MIP has 120 binaries, 0 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.00 sec. (3.64 ticks)
Probing time = 0.00 sec. (0.19 ticks)
MIP emphasis: balance optimality and feasibility.
MIP search method: dynamic search.
Parallel mode: deterministic, using up to 16 threads.

Node log . . .
Best integer =   1.435587e+06  Node =       0  Best node =   3.820272e+04
Best integer =   1.652181e+05  Node =       0  Best node =   3.820272e+04
Best integer =   7.091213e+04  Node =       0  Best node =   7.090888e+04
CPXPARAM_MIP_Display                             1
Tried aggregator 3 times.
MIP Presolve eliminated 4084 rows and 1509 columns.
MIP Presolve modified 3167 coefficients.
Aggregator did 80 substitutions.
Reduced MIP has 2560 rows, 2255 columns, and 19615 nonzeros.
Reduced MIP has 1109 binaries, 0 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.02 sec. (30.05 ticks)
Probing fixed 1 vars, tightened 69 bounds.
Probing time = 0.00 sec. (1.38 ticks)
Tried aggregator 3 times.
MIP Presolve eliminated 149 rows and 117 columns.
MIP Presolve modified 435 coefficients.
Aggregator did 31 substitutions.
Reduced MIP has 2380 rows, 2107 columns, and 19204 nonzeros.
Reduced MIP has 1037 binaries, 14 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.02 sec. (21.84 ticks)
Probing time = 0.02 sec. (1.32 ticks)
MIP emphasis: balance optimality and feasibility.
MIP search method: dynamic search.
Parallel mode: deterministic, using up to 16 threads.

Node log . . .
Best integer =  -3.531202e+04  Node =       0  Best node =  -3.670811e+04
Clique cuts applied:  15
Cover cuts applied:  47
Implied bound cuts applied:  57
Flow cuts applied:  14
Mixed integer rounding cuts applied:  102
Gomory fractional cuts applied:  72
CPXPARAM_MIP_Display                             1
Tried aggregator 2 times.
MIP Presolve eliminated 829 rows and 2 columns.
MIP Presolve modified 1008 coefficients.
Aggregator did 144 substitutions.
Reduced MIP has 1053 rows, 723 columns, and 7241 nonzeros.
Reduced MIP has 192 binaries, 0 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.02 sec. (7.29 ticks)
Probing fixed 0 vars, tightened 24 bounds.
Probing time = 0.00 sec. (0.45 ticks)
Tried aggregator 1 time.
MIP Presolve eliminated 144 rows and 72 columns.
Reduced MIP has 909 rows, 651 columns, and 6953 nonzeros.
Reduced MIP has 120 binaries, 0 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.00 sec. (3.65 ticks)
Probing time = 0.00 sec. (0.18 ticks)
MIP emphasis: balance optimality and feasibility.
MIP search method: dynamic search.
Parallel mode: deterministic, using up to 16 threads.

Node log . . .
Best integer =   1.435666e+06  Node =       0  Best node =   3.703968e+04
Best integer =   7.123725e+04  Node =       0  Best node =   3.703968e+04
Best integer =   7.117944e+04  Node =       0  Best node =   7.117749e+04
CPXPARAM_MIP_Display                             1
Tried aggregator 3 times.
MIP Presolve eliminated 4124 rows and 1544 columns.
MIP Presolve modified 3156 coefficients.
Aggregator did 78 substitutions.
Reduced MIP has 2522 rows, 2222 columns, and 19509 nonzeros.
Reduced MIP has 1094 binaries, 0 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.02 sec. (30.03 ticks)
Probing fixed 2 vars, tightened 69 bounds.
Probing time = 0.02 sec. (1.55 ticks)
Tried aggregator 3 times.
MIP Presolve eliminated 158 rows and 124 columns.
MIP Presolve modified 429 coefficients.
Aggregator did 31 substitutions.
Reduced MIP has 2333 rows, 2067 columns, and 19089 nonzeros.
Reduced MIP has 1023 binaries, 17 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.02 sec. (21.70 ticks)
Probing time = 0.00 sec. (1.32 ticks)
MIP emphasis: balance optimality and feasibility.
MIP search method: dynamic search.
Parallel mode: deterministic, using up to 16 threads.

Node log . . .
Best integer =  -3.655283e+04  Node =       0  Best node =  -3.786446e+04
Best integer =  -3.692724e+04  Node =       0  Best node =  -3.693466e+04
Clique cuts applied:  16
Cover cuts applied:  10
Implied bound cuts applied:  50
Flow cuts applied:  13
Mixed integer rounding cuts applied:  96
Zero-half cuts applied:  1
Lift and project cuts applied:  1
Gomory fractional cuts applied:  36
CPXPARAM_MIP_Display                             1
Tried aggregator 2 times.
MIP Presolve eliminated 829 rows and 2 columns.
MIP Presolve modified 1008 coefficients.
Aggregator did 144 substitutions.
Reduced MIP has 1053 rows, 723 columns, and 7241 nonzeros.
Reduced MIP has 192 binaries, 0 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.02 sec. (7.29 ticks)
Probing fixed 0 vars, tightened 24 bounds.
Probing time = 0.00 sec. (0.45 ticks)
Tried aggregator 1 time.
MIP Presolve eliminated 144 rows and 72 columns.
Reduced MIP has 909 rows, 651 columns, and 6953 nonzeros.
Reduced MIP has 120 binaries, 0 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.00 sec. (3.65 ticks)
Probing time = 0.00 sec. (0.18 ticks)
MIP emphasis: balance optimality and feasibility.
MIP search method: dynamic search.
Parallel mode: deterministic, using up to 16 threads.

Node log . . .
Best integer =   1.435737e+06  Node =       0  Best node =   3.596200e+04
Best integer =   7.145608e+04  Node =       0  Best node =   3.596200e+04
Best integer =   7.139956e+04  Node =       0  Best node =   7.139632e+04
CPXPARAM_MIP_Display                             1
Tried aggregator 3 times.
MIP Presolve eliminated 4159 rows and 1563 columns.
MIP Presolve modified 3122 coefficients.
Aggregator did 61 substitutions.
Reduced MIP has 2504 rows, 2220 columns, and 19481 nonzeros.
Reduced MIP has 1091 binaries, 0 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.02 sec. (30.08 ticks)
Probing fixed 1 vars, tightened 66 bounds.
Probing time = 0.00 sec. (1.43 ticks)
Tried aggregator 3 times.
MIP Presolve eliminated 143 rows and 113 columns.
MIP Presolve modified 416 coefficients.
Aggregator did 28 substitutions.
Reduced MIP has 2333 rows, 2079 columns, and 19119 nonzeros.
Reduced MIP has 1028 binaries, 21 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.03 sec. (18.87 ticks)
Probing time = 0.00 sec. (1.35 ticks)
MIP emphasis: balance optimality and feasibility.
MIP search method: dynamic search.
Parallel mode: deterministic, using up to 16 threads.

Node log . . .
Best integer =  -3.761882e+04  Node =       0  Best node =  -3.873746e+04
Clique cuts applied:  14
Cover cuts applied:  24
Implied bound cuts applied:  39
Flow cuts applied:  7
Mixed integer rounding cuts applied:  69
Gomory fractional cuts applied:  49
CPXPARAM_MIP_Display                             1
Tried aggregator 2 times.
MIP Presolve eliminated 829 rows and 2 columns.
MIP Presolve modified 1008 coefficients.
Aggregator did 144 substitutions.
Reduced MIP has 1053 rows, 723 columns, and 7241 nonzeros.
Reduced MIP has 192 binaries, 0 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.00 sec. (7.29 ticks)
Probing fixed 0 vars, tightened 24 bounds.
Probing time = 0.00 sec. (0.45 ticks)
Tried aggregator 1 time.
MIP Presolve eliminated 144 rows and 72 columns.
Reduced MIP has 909 rows, 651 columns, and 6953 nonzeros.
Reduced MIP has 120 binaries, 0 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.00 sec. (3.66 ticks)
Probing time = 0.00 sec. (0.18 ticks)
MIP emphasis: balance optimality and feasibility.
MIP search method: dynamic search.
Parallel mode: deterministic, using up to 16 threads.

Node log . . .
Best integer =   1.435804e+06  Node =       0  Best node =   3.496271e+04
Best integer =   7.166073e+04  Node =       0  Best node =   3.496271e+04
Best integer =   7.160422e+04  Node =       0  Best node =   7.160097e+04
CPXPARAM_MIP_Display                             1
Tried aggregator 3 times.
MIP Presolve eliminated 4184 rows and 1592 columns.
MIP Presolve modified 3120 coefficients.
Aggregator did 59 substitutions.
Reduced MIP has 2481 rows, 2193 columns, and 19405 nonzeros.
Reduced MIP has 1082 binaries, 0 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.02 sec. (29.99 ticks)
Probing fixed 0 vars, tightened 54 bounds.
Probing time = 0.02 sec. (1.41 ticks)
Tried aggregator 3 times.
MIP Presolve eliminated 140 rows and 113 columns.
MIP Presolve modified 378 coefficients.
Aggregator did 14 substitutions.
Reduced MIP has 2327 rows, 2066 columns, and 19068 nonzeros.
Reduced MIP has 1023 binaries, 23 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.02 sec. (18.77 ticks)
Probing time = 0.00 sec. (1.25 ticks)
MIP emphasis: balance optimality and feasibility.
MIP search method: dynamic search.
Parallel mode: deterministic, using up to 16 threads.

Node log . . .
Best integer =  -3.841269e+04  Node =       0  Best node =  -3.942486e+04
Best integer =  -3.869170e+04  Node =       0  Best node =  -3.868681e+04
Clique cuts applied:  13
Cover cuts applied:  3
Implied bound cuts applied:  23
Flow cuts applied:  6
Mixed integer rounding cuts applied:  94
Gomory fractional cuts applied:  31
CPXPARAM_MIP_Display                             1
Tried aggregator 2 times.
MIP Presolve eliminated 829 rows and 2 columns.
MIP Presolve modified 1008 coefficients.
Aggregator did 144 substitutions.
Reduced MIP has 1053 rows, 723 columns, and 7241 nonzeros.
Reduced MIP has 192 binaries, 0 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.00 sec. (7.29 ticks)
Probing fixed 0 vars, tightened 24 bounds.
Probing time = 0.00 sec. (0.45 ticks)
Tried aggregator 1 time.
MIP Presolve eliminated 144 rows and 72 columns.
Reduced MIP has 909 rows, 651 columns, and 6953 nonzeros.
Reduced MIP has 120 binaries, 0 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.02 sec. (3.67 ticks)
Probing time = 0.00 sec. (0.18 ticks)
MIP emphasis: balance optimality and feasibility.
MIP search method: dynamic search.
Parallel mode: deterministic, using up to 16 threads.

Node log . . .
Best integer =   1.436049e+06  Node =       0  Best node =   3.422789e+04
Best integer =   7.175970e+04  Node =       0  Best node =   3.422789e+04
Best integer =   7.170318e+04  Node =       0  Best node =   7.169994e+04
CPXPARAM_MIP_Display                             1
Tried aggregator 3 times.
MIP Presolve eliminated 4181 rows and 1592 columns.
MIP Presolve modified 3115 coefficients.
Aggregator did 55 substitutions.
Reduced MIP has 2488 rows, 2197 columns, and 19425 nonzeros.
Reduced MIP has 1086 binaries, 0 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.03 sec. (29.92 ticks)
Probing fixed 1 vars, tightened 57 bounds.
Probing time = 0.00 sec. (1.40 ticks)
Tried aggregator 3 times.
MIP Presolve eliminated 138 rows and 112 columns.
MIP Presolve modified 381 coefficients.
Aggregator did 14 substitutions.
Reduced MIP has 2336 rows, 2071 columns, and 19091 nonzeros.
Reduced MIP has 1027 binaries, 26 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.02 sec. (18.81 ticks)
Probing time = 0.00 sec. (1.43 ticks)
MIP emphasis: balance optimality and feasibility.
MIP search method: dynamic search.
Parallel mode: deterministic, using up to 16 threads.

Node log . . .
Best integer =  -3.896327e+04  Node =       0  Best node =  -3.993966e+04
Best integer =  -3.897429e+04  Node =       0  Best node =  -3.923728e+04
Best integer =  -3.914657e+04  Node =      17  Best node =  -3.923781e+04
Clique cuts applied:  10
Cover cuts applied:  19
Implied bound cuts applied:  30
Flow cuts applied:  11
Mixed integer rounding cuts applied:  60
Gomory fractional cuts applied:  43
时间已过 39.528332 秒。
>> 

4 参考文献

[1]晏鸣宇,艾小猛,张艺镨,舒康安,甘伟,文劲宇.考虑机组禁止运行区间的含风电鲁棒机组组合[J].中国电机工程学报,2018,38(11):3195-3203.DOI:10.13334/j.0258-8013.pcsee.171138.

5 Matlab代码实现

​