基于评分缓存的节点序空间下BN结构学习

doi:10.12305/j.issn.1001-506X.2024.12.18

摘要/Abstract

摘要：

针对大规模贝叶斯网络结构学习容易陷入局部最优的问题, 提出一种节点序空间下迭代局部搜索算法。在局部搜索环节, 设计评分缓存的选择插入算子和次优解的容忍策略, 评估自适应的纵向插入邻域, 攻克由盲目搜索导致的邻域受限问题。在迭代重启环节, 采用等价类结构和深度优先遍历的转换机制, 避免由随机扰动导致的评分退化问题。通过相融实验分别验证搜索和迭代算法的有效性。实验结果表明，相较于现有的主流方法, 迭代局部搜索算法能够精确地学习大规模网络结构。

关键词: 贝叶斯网络, 结构学习, 节点序, 局部搜索, 迭代重启

Abstract:

Aiming at the problem that large-scale Bayesian network structure learning falls into local optima easily, an iterative local search algorithm in node ordering space is proposed. During the local search step, the selective insertion operator based on score cache and the tolerance strategy for suboptimal solutions are designed. The adaptive longitudinal insertion neighborhood domain is evaluated to overcome the limited neighborhood domain problem caused by blind search. During the iterative restart step, the conversion mechanism of equivalent class structure and depth-first search (DFS) is adopted to prevent score degradation problem caused by random disturbances. After verifying the effectiveness of the search and iterative algorithms through fusion experiments, the experimental results show that compared with existing mainstream methods, the iterative local search algorithm can learn large-scale network structures accurately.

Key words: Bayesian network, structure learning, node ordering, local search, iterative restart

中图分类号:

TP181

高晓光, 闫栩辰, 王紫东, 刘晓寒, 冯奇. 基于评分缓存的节点序空间下BN结构学习[J]. 系统工程与电子技术, 2024, 46(12): 4091-4107.

Xiaoguang GAO, Xuchen YAN, Zidong WANG, Xiaohan LIU, Qi FENG. Bayesian network structure learning based on score cache in node ordering space[J]. Systems Engineering and Electronics, 2024, 46(12): 4091-4107.

图/表 16

图1

图2

图3

图4

图5

表1

表2

图6

表3

现有搜索算法与GBSC算法的BIC评分和运行时间"

数据集	OBS算法		INOBS算法		WINOBS算法		PSCOBS算法		GBSC算法
数据集	BIC评分	运行时间/s	BIC评分	运行时间/s	BIC评分	运行时间/s	BIC评分	运行时间/s	BIC评分	运行时间/s
Asia-1000	-2 303.4±33.5	0	-2 292.6±32.0	0	-2 292.2±31.9	0	-2 293.3±31.8	0	-2 291.2±32.0	0
Child-1000	-13 331.9±275.3^*	0	-12 786.1±109.5	0.1	-12 784.9±102.4	0.3	-12 783.7±102.1	0.1	-12 779.4±117.2	0.1
Insurance-1000	-15 147.0±235.1^*	0	-14 570.3±138.7	0.1	-14 573.0±154.3	0.6	-14 576.8±145.9	0.3	-14 568.8±149.6	0.3
Alarm-1000	-12 351.7±266.9^*	0	-11 676.0±176.2	0.3	-11 657.5±176.0	1.8	-11 657.5±178.0	0.8	-11 655.1±180.5	0.8
Hailfinder-1000	-54 150.8±627.6^*	0	-53 215.4±117.0	0.4	-53 213.3±113.5	2.6	-53 205.3±121.5	0.6	-53 204.4±118.5	0.5
Hepar2-1000	-33 532.2±171.2^*	0	-33 268.9±152.3	0.7	-33 265.5±151.7	3.9	-33 263.8±153.9	0.5	-33 260.1±152.4	0.5
Win95pts-1000	-11 065.4±185.2^*	0	-10 448.5±174.2	2.8	-10 438.6±180.8	19.0	-10 434.6±178.5	8.0	-10 431.8±184.6	6.9
Pathfinder-1000	-36 650.5±560.2^*	0	-34 754.3±454.5	4.5	-34 612.6±392.5	36.4	-34 628.0±387.5	14.2	-34 591.2±402.1	8.4
Andes-1000	-100 411.5±560.1^*	0	-96 535.1±225.0	21.3	-96 485.9±231.0	163.3	-96 452.9±237.9	32.9	-96 447.0±231.7	26.3
Asia-5000	-11 271.4±65.9	0	-11 250.6±65.8	0	-11 249.9±64.7	0	-11 249.9±66.4	0	-11 248.9±66.7	0
Child-5000	-64 071.3±965.0^*	0	-61 846.4±301.0	0.1	-61 818.9±251.7	0.5	-61 814.4±330.9	0.2	-61 791.3±319.2	0.2
Insurance-5000	-70 942.7±939.8^*	0	-67 897.0±300.0	0.3	-67 852.7±244.5	1.3	-67 867.5±274.4	0.6	-67 846.6±267.0	0.6
Alarm-5000	-56 958.4±643.0^*	0	-54 050.5±288.2	0.5	-54 005.7±266.2	3.0	-54 005.3±268.4	1.4	-53 974.5±269.7	1.4
Hailfinder-5000	-257 927.7±2289.2^*	0	-252 226.4±299.2	0.8	-252 181.5±305.2	4.7	-252 137.3±301.1	2.1	-252 130.0±292.8	1.4
Hepar2-5000	-165 248.0±679.4^*	0	-163 738.2±328.0	1.2	-163 727.4±326.5	6.6	-163 718.0±324.1	1.8	-163 704.6±329.5	1.7
Win95pts-5000	-52 287.6±663.5^*	0	-49 082.2±307.2	5.1	-49 076.4±321.0	31.5	-49 022.9±343.6	18.2	-49 021.6±334.1	16.1
Pathfinder-5000	-162 495.0±2 821.9^*	0.1	-148 717.4±527.6	5.3	-148 628.6±525.9	32.7	-148 613.4±495.0	20.9	-148 581.9±512.2	15.4
Andes-5000	-497 126.1±3 033.3^*	0.1	-475 832.1±584.9^*	25.9	-475 422.6±497.5	200.3	-475 375.6±506.2	63.4	-475 294.4±420.0	45.8
Asia-10000	-22 453.3±125.3	0	-22 433.3±119.8	0	-22 431.2±120.6	0	-22 431.6±120.2	0	-22 431.2±120.7	0
Child-10000	-126 543.6±1 593.5^*	0	-123 051.8±355.8	0.1	-123 007.6±282.2	0.6	-123 013.0±307.5	0.2	-123 005.8±284.4	0.2
Insurance-10000	-139 636.7±1 780.5^*	0	-133 954.8±325.2	0.3	-133 797.2±365.1	2.0	-133 893.4±331.0	0.7	-133 856.1±364.0	0.7
Alarm-10000	-112 285.2±1 151.2^*	0	-106 556.1±434.8	0.6	-106 526.8±456.7	3.8	-106 518.4±416.4	1.9	-106 516.8±425.9	1.8
Hailfinder-10000	-510 507.2±4 335.2^*	0	-499 586.9±333.6	1.9	-499 542.6±336.6	11.7	-499 549.5±408.5	6.4	-499 515.5±404.2	5.2
Hepar2-10000	-329 423.4±1 060.6^*	0	-326 953.4±508.1	1.7	-326 918.5±509.3	9.3	-326 921.7±491.2	3.3	-326 898.4±495.9	2.7
Win95pts-10000	-103 307.7±1 842.4^*	0	-97 140.7±608.0	6.0	-97 143.4±608.4	36.4	-97 135.0±612.7	23.5	-96 995.9±568.2	19.0
Pathfinder-10000	-311 090.8±8 049.7^*	0.1	-281 102.2±693.9^*	7.4	-280 756.4±616.2	38.9	-280 617.9±611.0	20.6	-280 526.7±574.8	19.6
Andes-10000	-1 001 135.0±5 230.8^*	0	-953 897.3±2 865.0	21.8	-953 215.8±2 778.2	160.2	-953 290.6±3 036.0	45.8	-952 881.7±2 765.0	32.3
W/D/L	24/3/0		2/25/0		0/27/0		0/27/0		-

表3

图7

图8

图9

表4

PC-Stable, GFCI, MMHC和GB-DF算法的BIC评分对比"

数据集	PC-Stable	GFCI	MMHC	GB-DF
Asia-1000	-2 470.1±51.3^*	-2 291.3±32.2	-2 479.9±44.6^*	-2 291.1±31.9
Child-1000	-14 600.4±548.2^*	-13 334.7±247.2^*	-13 207.4±173.0^*	-12 775.5±110.6
Insurance-1000	-16 213.3±159.7^*	-15 400.2±326.6^*	-15 834.4±252.4^*	-14 516.8±127.4
Alarm-1000	-15 480.2±575.3^*	-12 428.9±429.0^*	-14 004.1±315.6^*	-11 643.5±180.7
Hailfinder-1000	-60 327.0±524.5^*	-60 205.4±10 417.2^*	-59 209.4±165.3^*	-53 187.7±121.1
Hepar2-1000	-33 792.3±165.9^*	-33 519.0±185.6^*	-33 561.8±156.0^*	-33 255.2±151.5
Win95pts-1000	-13 111.6±394.7^*	-11 089.5±644.3^*	-12 921.6±340.3^*	-10 411.9±180.2
Pathfinder-1000	-61 003.6±531.2^*	-38 841.4±4 130.6^*	-55 094.5±573.8^*	-34 667.9±385.4
Andes-1000	-104 991.4±1 406.6^*	-98 901.2±1 922.6^*	-100 217.6±270.8^*	-96 334.0±229.3
Asia-5000	-12 162.1±99.7^*	-11 250.7±66.6	-12 158.7±95.2^*	-11 248.1±66.0
Child-5000	-63 777.5±1 385.7^*	-62 925.0±330.2^*	-66 413.7±799.6^*	-61 782.6±317.8
Insurance-5000	-73 691.1±821.0^*	-72 611.0±2 847.7^*	-72 843.9±595.4^*	-67 718.7±268.5
Alarm-5000	-67 241.4±3 129.0^*	-55 718.8±1 268.0^*	-61 612.7±1 186.1^*	-53 962.5±276.2
Hailfinder-5000	-294 300.1±2 758.8^*	-268 969.0±13 147.0^*	-288 414.6±310.4^*	-252 051.8±307.5
Hepar2-5000	-166 060.5±465.1^*	-165 553.6±367.6^*	-165 032.9±330.5^*	-163 678.8±318.5
Win95pts-5000	-60 129.2±1 486.9^*	-52 850.9±3 701.7^*	-59 239.4±951.5^*	-48 971.1±331.9
Pathfinder-5000	-297 497.2±2 279.4^*	-178 502.3±36 556.0^*	-283 083.2±1 131.7^*	-148 546.8±513.6
Andes-5000	-513 214.1±9 998.8^*	-493 742.3±13 756.1^*	-484 179.7±803.4^*	-474 902.6±485.4
Asia-10000	-24 266.8±153.6^*	-22 454.4±152.1	-24 255.0±173.3^*	-22 430.3±120.4
Child-10000	-127 083.0±1 878.0^*	-125 265.1±283.0^*	-133 227.7±570.3^*	-122 990.6±292.9
Insurance-10000	-142 906.7±1 955.1^*	-147 837.6±7 329.3^*	-144 500.2±1 561.0^*	-133 631.7±295.7
Alarm-10000	-126 881.2±8 392.2^*	-113 240.5±2 140.0^*	-126 244.1±2 211.6^*	-106 491.0±423.2
Hailfinder-10000	-582 295.6±5 262.5^*	-563 303.7±41 475.4^*	-574 629.2±266.3^*	-499 356.0±392.1
Hepar2-10000	-332 279.4±883.6^*	-330 654.0±619.4^*	-328 860.6±532.4^*	-326 818.2±473.4
Win95pts-10000	-117 244.9±4 873.1^*	-104 896.0±7 863.3^*	-114 273.2±982.2^*	-96 761.8±553.0
Pathfinder-10000	-592 945.0±1 133.4^*	-351 817.2±62 338.8^*	-561 484.3±2 287.1^*	280 451.0±532.1
Andes-10000	-1 031 871.0±6 610.5^*	-976 332.9±24 497.0^*	-959 375.2±2191.9^*	-951 983.0±2 684.0
W/D/L	27/0/0	24/3/0	27/0/0	-

表4

表5

SaiyanH, FGES, MAHC和GB-DF算法的BIC评分对比"

数据集	SaiyanH	FGES	MAHC	GB-DF
Asia-1000	-2 298.5±31.4	-2 291.2±31.8	-2 292.1±31.5	-2 291.1±31.9
Child-1000	-12 779.9±110.7	-12 947.8±111.2^*	-12 947.8±142.9^*	-12 775.5±110.6
Insurance-1000	-14 615.1±152.3^*	-14 693.3±139.1^*	-15 048.1±184.2^*	-14 516.8±127.4
Alarm-1000	-11 794.2±197.4^*	-11 789.9±187.0^*	-12 125.4±195.3^*	-11 643.5±180.7
Hailfinder-1000	-54 776.9±740.0^*	-53 904.0±118.6^*	-53 318.9±121.6^*	-53 187.7±121.1
Hepar2-1000	-33 366.3±153.3^*	-33 470.3±151.2^*	-33 281.4±152.7	-33 255.2±151.5
Win95pts-1000	-10 526.1±208.0	-10 658.7±197.7^*	-11 122.8±197.9^*	-10 411.9±180.2
Pathfinder-1000	-39 435.8±703.6^*	-35 885.0±399.9^*	-36 660.8±469.1^*	-34 667.9±385.4
Andes-1000	NA	-97 992.4±303.3^*	-96 164.6±266.6	-96 334.0±229.3
Asia-5000	-11 268.5±80.7	-11 248.1±66.0	-11 256.0±64.0	-11 248.1±66.0
Child-5000	-61 847.2±328.2	-62 857.1±321.3^*	-62 100.7±497.5^*	-61 782.6±317.8
Insurance-5000	-68 556.8±306.3^*	-69 179.1±317.7^*	-69 543.3±287.8^*	-67 718.7±268.5
Alarm-5000	-54 304.8±326.7^*	-55 041.0±380.2^*	-55 490.3±481.2^*	-53 962.5±276.2
Hailfinder-5000	-255 508.7±523.1^*	-257 603.3±403.2^*	-253 137.2±326.0^*	-252 051.8±307.5
Hepar2-5000	-163 962.1±302.7^*	-165 322.9±321.9^*	-163 795.9±315.1	-163 678.8±318.5
Win95pts-5000	-48 889.7±645.8	-50 365.0±398.2^*	-51 549.3±530.5^*	-48 971.1±331.9
Pathfinder-5000	-168 888.9±2 839.8^*	-159 475.9±848.9^*	-162 705.3±1 161.5^*	-148 546.8±513.6
Andes-5000	NA	-482 606.6±775.7^*	-469 372.9±369.3	-474 902.6±485.4
Asia-10000	-22 457.8±116.1	-22 430.3±120.4	-22 449.9±119.5	-22 430.3±120.4
Child-10000	-123 142.8±299.6	-125 228.6±284.1^*	-123 108.3±301.2	-122 990.6±292.9
Insurance-10000	-136 046.0±442.0^*	-136 976.4±362.1^*	-134 186.2±289.6^*	-133 631.7±295.7
Alarm-10000	-106 793.6±757.9	-108 475.1±428.4^*	-107 560.1±409.4^*	-106 491.0±423.2
Hailfinder-10000	-507 216.1±660.0^*	-510 948.4±732.4^*	-501 274.1±399.3^*	-499 356.0±392.1
Hepar2-10000	-327 266.9±517.5^*	-330 406.6±571.4^*	-326 994.3±505.6	-326 818.2±473.4
Win95pts-10000	-96 280.9±920.9	-99 748.8±782.3^*	-101 524.5±971.4^*	-96 761.8±553.0
Pathfinder-10000	-321 440.4±5 027.1^*	-309 747.4±893.6^*	-303 423.9±2 762.4^*	280 451.0±532.1
Andes-10000	NA	-961 355.0±1 600.0^*	-933 685.8±940.2	-951 983.0±2 684.0
W/D/L	14/10/0	24/3/0	17/8/2	-

表5

表6

7种算法的TPR对比"

数据集	PC-Stable	GFCI	MMHC	SaiyanH	FGES	MAHC	GB-DF
Asia-1000	0.244±0.118	0.775±0.112	0.569±0.076	0.681±0.131	0.713±0.071	0.681±0.064	0.769±0.102
Child-1000	0.340±0.088	0.564±0.066	0.452±0.026	0.754±0.049	0.672±0.036	0.668±0.035	0.782±0.053
Insurance-1000	0.223±0.036	0.375±0.039	0.263±0.029	0.410±0.059	0.387±0.032	0.390±0.025	0.511±0.048
Alarm-1000	0.291±0.052	0.603±0.039	0.448±0.034	0.674±0.073	0.651±0.027	0.585±0.037	0.748±0.054
Hailfinder-1000	0.290±0.034	0.486±0.047	0.402±0.016	0.357±0.041	0.367±0.033	0.465±0.028	0.565±0.037
Hepar2-1000	0.107±0.024	0.242±0.023	0.249±0.016	0.279±0.037	0.209±0.024	0.331±0.023	0.351±0.036
Win95pts-1000	0.193±0.038	0.456±0.055	0.355±0.023	0.466±0.038	0.436±0.036	0.378±0.021	0.452±0.040
Pathfinder-1000	0.008±0.004	0.160±0.016	0.079±0.006	0.142±0.020	0.148±0.011	0.135±0.009	0.176±0.011
Andes-1000	0.321±0.044	0.548±0.080	0.580±0.010	NA	0.571±0.014	0.654±0.014	0.616±0.017
Asia-5000	0.381±0.028	0.800±0.085	0.631±0.049	0.731±0.093	0.750±0.000	0.662±0.059	0.812±0.064
Child-5000	0.642±0.088	0.648±0.046	0.550±0.018	0.852±0.039	0.680±0.000	0.822±0.046	0.922±0.033
Insurance-5000	0.383±0.026	0.408±0.072	0.354±0.019	0.491±0.043	0.408±0.033	0.530±0.049	0.679±0.090
Alarm-5000	0.524±0.052	0.755±0.021	0.599±0.038	0.828±0.059	0.741±0.031	0.627±0.029	0.833±0.061
Hailfinder-5000	0.314±0.063	0.491±0.031	0.480±0.007	0.466±0.024	0.505±0.045	0.620±0.020	0.695±0.040
Hepar2-5000	0.192±0.021	0.299±0.042	0.360±0.016	0.439±0.033	0.289±0.015	0.514±0.018	0.515±0.024
Win95pts-5000	0.388±0.056	0.489±0.092	0.484±0.025	0.564±0.024	0.503±0.024	0.496±0.025	0.456±0.039
Pathfinder-5000	0.008±0.005	0.138±0.019	0.076±0.004	0.169±0.011	0.137±0.012	0.178±0.007	0.230±0.010
Andes-5000	0.412±0.074	0.550±0.144	0.749±0.009	NA	0.629±0.014	0.824±0.012	0.621±0.018
Asia-10000	0.350±0.087	0.756±0.137	0.662±0.071	0.762±0.056	0.738±0.056	0.644±0.046	0.769±0.046
Child-10000	0.700±0.063	0.658±0.030	0.528±0.016	0.872±0.038	0.680±0.000	0.816±0.046	0.922±0.035
Insurance-10000	0.476±0.039	0.355±0.091	0.361±0.029	0.520±0.040	0.399±0.025	0.575±0.012	0.747±0.019
Alarm-10000	0.608±0.114	0.761±0.014	0.630±0.041	0.855±0.049	0.782±0.005	0.677±0.008	0.798±0.070
Hailfinder-10000	0.369±0.053	0.397±0.108	0.498±0.010	0.511±0.018	0.528±0.046	0.702±0.020	0.691±0.056
Hepar2-10000	0.204±0.024	0.317±0.022	0.406±0.016	0.507±0.028	0.298±0.015	0.578±0.014	0.596±0.018
Win95pts-10000	0.461±0.076	0.514±0.117	0.558±0.028	0.600±0.032	0.530±0.034	0.550±0.032	0.476±0.042
Pathfinder-10000	0.010±0.008	0.127±0.012	0.083±0.006	0.191±0.013	0.122±0.009	0.249±0.007	0.291±0.012
Andes-10000	0.393±0.026	0.595±0.129	0.797±0.009	NA	0.641±0.014	0.866±0.010	0.593±0.021

表6

表7

7种算法的F1分数对比"

数据集	PC-Stable	GFCI	MMHC	SaiyanH	FGES	MAHC	GB-DF
Asia-1000	0.359±0.066	0.814±0.119	0.717±0.063	0.687±0.125	0.749±0.081	0.715±0.067	0.805±0.108
Child-1000	0.468±0.083	0.607±0.065	0.541±0.030	0.800±0.046	0.722±0.032	0.733±0.030	0.829±0.049
Insurance-1000	0.328±0.049	0.480±0.045	0.378±0.038	0.499±0.072	0.483±0.036	0.498±0.034	0.617±0.060
Alarm-1000	0.388±0.059	0.637±0.040	0.562±0.038	0.707±0.074	0.680±0.030	0.633±0.040	0.773±0.056
Hailfinder-1000	0.399±0.045	0.525±0.054	0.557±0.021	0.386±0.044	0.396±0.036	0.528±0.031	0.606±0.040
Hepar2-1000	0.165±0.036	0.338±0.030	0.381±0.023	0.356±0.046	0.291±0.032	0.460±0.029	0.465±0.045
Win95pts-1000	0.269±0.051	0.526±0.059	0.496±0.027	0.519±0.043	0.489±0.039	0.450±0.023	0.461±0.040
Pathfinder-1000	0.016±0.007	0.206±0.021	0.142±0.010	0.182±0.025	0.191±0.014	0.174±0.012	0.211±0.012
Andes-1000	0.390±0.054	0.593±0.089	0.711±0.013	NA	0.610±0.016	0.730±0.013	0.616±0.018
Asia-5000	0.462±0.028	0.845±0.093	0.770±0.045	0.736±0.091	0.792±0.018	0.700±0.064	0.858±0.068
Child-5000	0.713±0.099	0.654±0.048	0.638±0.015	0.874±0.034	0.686±0.008	0.840±0.046	0.921±0.034
Insurance-5000	0.511±0.031	0.491±0.087	0.470±0.021	0.584±0.048	0.482±0.041	0.618±0.053	0.748±0.095
Alarm-5000	0.610±0.051	0.782±0.024	0.687±0.043	0.840±0.064	0.759±0.034	0.643±0.035	0.847±0.069
Hailfinder-5000	0.414±0.083	0.519±0.032	0.646±0.009	0.496±0.026	0.515±0.046	0.678±0.020	0.710±0.047
Hepar2-5000	0.273±0.028	0.390±0.054	0.502±0.021	0.545±0.038	0.374±0.020	0.642±0.019	0.616±0.027
Win95pts-5000	0.489±0.069	0.549±0.103	0.622±0.025	0.622±0.024	0.545±0.024	0.555±0.028	0.427±0.040
Pathfinder-5000	0.015±0.010	0.164±0.023	0.138±0.006	0.214±0.014	0.162±0.014	0.208±0.009	0.256±0.011
Andes-5000	0.457±0.079	0.601±0.158	0.842±0.007	NA	0.672±0.017	0.880±0.010	0.613±0.020
Asia-10000	0.435±0.041	0.782±0.142	0.792±0.055	0.767±0.052	0.764±0.073	0.658±0.041	0.794±0.037
Child-10000	0.778±0.069	0.662±0.028	0.622±0.015	0.890±0.029	0.684±0.009	0.819±0.045	0.922±0.035
Insurance-10000	0.592±0.048	0.415±0.107	0.477±0.030	0.608±0.047	0.460±0.031	0.631±0.012	0.808±0.020
Alarm-10000	0.674±0.126	0.783±0.016	0.720±0.042	0.859±0.054	0.788±0.007	0.677±0.008	0.802±0.079
Hailfinder-10000	0.482±0.072	0.408±0.112	0.663±0.012	0.532±0.020	0.520±0.044	0.751±0.020	0.684±0.068
Hepar2-10000	0.281±0.032	0.404±0.027	0.550±0.018	0.620±0.030	0.376±0.018	0.695±0.016	0.688±0.019
Win95pts-10000	0.557±0.089	0.574±0.132	0.688±0.029	0.657±0.034	0.565±0.037	0.591±0.035	0.428±0.039
Pathfinder-10000	0.024±0.011	0.144±0.013	0.150±0.010	0.238±0.016	0.137±0.009	0.284±0.008	0.323±0.013
Andes-10000	0.427±0.029	0.646±0.140	0.880±0.007	NA	0.682±0.015	0.914±0.008	0.589±0.020

表7

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参数	定义	取值
l	变量的最大入度	4
w_max	WINOBS算法的最大插入窗口长度	5
λ_const	GBSC算法的固定局部搜索深度	5
p_s	迭代算法的扰动因子	0.03
r_s	迭代算法软启动的连续未改进次数上限	5
r_h	迭代算法硬启动的总搜索次数上限	50

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