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@橘柑橙柠桔柚

微电网两阶段鲁棒优化问题（Matlab代码实现）

目录

​

1 概述

2 运行结果

3 参考文献

4 Matlab代码及文章详细讲解

 

1 概述

参考文献：

站在巨人的肩膀上！！！！！

鲁棒优化（RO）是最近一种处理数据不确定性的优化方法。因为它是为了对冲输入数据中的任何扰动而导出的，所以（单阶段）RO模型的解决方案往往过于保守。为了解决这一问题，已经引入并研究了两阶段RO（以及更一般的多级RO），也称为鲁棒可调或自适应优化[3]，其中第二阶段问题是在第一阶段决策做出并揭示不确定性后对决策进行建模。由于改进的建模能力，两阶段RO已成为一种流行的决策工具。应用包括网络/运输问题、组合优化和电力系统调度问题。 

近年来，我国风电发展迅速，风电已成为我国电能的主要来源之一。至2020年，我国的风电装机容量将占总装机容量的。风电大规模的集中式发展与接入对我国电网调度运行造成严重的影响。与传统能源不同，风电出力存在不确定性。2008年2月，美国德克萨斯州的风电出现大规模的爬坡事件，导致负荷削减事故[1];2008年6月，纽约上州因风暴导致250MW的风电场在8min内全部停机2。如果仍采用传统的日前调度方法，那么电力系统将会面临较大的风险。
考虑风电出力不确定性的机组组合问题本质上就是系统供电容量充裕性问题，目前该方面已有大量的研究成果，如基于场景的机组组合区间机组组合、机会约束机组组合、鲁棒机组组合等。基于机会约束的机组组合由于含有机会约束，因此其模型通常是非凸的，难以直接求解。基于场景的机组组合虽然有较好的经济性，但是该模型考虑大量风电出力场景集，使得整个模型规模较大，难以求解。为了解决这一问题，文献[10]提出考虑风电的区间机组组合。区间机组组合虽然求解速度较快，但是该模型并不能求解含离散随机变量的随机优化，如线路随机停运等4]。鲁棒机组组
合能有效解决上述问题，同时能保证系统运行的鲁棒性，并且该模型能通过 Benders分解、列生成算[法(column-and-constraint generation，C&CG)等方法求解，计算效率较高，因此得到广泛的应用。由于鲁棒调度结果往往过于保守，为了克服这缺点[12]，文献[12]引入弱鲁棒理论，牺牲调度结果的鲁棒性以提升鲁棒机组组合的经济性。文献[13]将场景机组组合与鲁棒机组组合结合以降低鲁棒机组组合的保守性。
 

2 运行结果

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。
>> 

3 参考文献

部分理论来源于网络，如有侵权请联系删除。

[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.

4 Matlab代码及文章详细讲解

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