改进蜂群算法求解大规模着色瓶颈旅行商问题

doi:10.11959/j.issn.1000-436x.2018284

Abstract

Abstract:

In the fields such as intelligent transport and multiple tasks cooperation, the model scale constructed by colored bottleneck traveling salesman problem (CBTSP) tends to large scale, and therefore it is necessary to study the large scale CBTSP and its algorithms. An improved artificial bee colony algorithm (IABC) was applied to solve the large scale CBTSP. IABC employed generating neighboring solution (GNS) to improve artificial bee colony algorithm for CBTSP. GNS generated new solution by deletion and reinsertion operations, during this process, and it can optimized the existed solution for this problem. Experiments show that IABC can demonstrate better solution quality than other compared algorithms for large scale CBTSP.

Key words: improved artificial bee colony algorithm, colored bottleneck traveling salesman problem, colored traveling salesman problem, bottleneck traveling salesman problem, large scale optimization

CLC Number:

TP301

Wenyong DONG,Xueshi DONG,Yufeng WANG. Improved artificial bee colony algorithm for large scale colored bottleneck traveling salesman problem[J]. Journal on Communications, 2018, 39(12): 18-29.

Figures/Tables 14

实例	n	m		GA				GAG				HCGA
实例	n	m	最优解/km	最差解/km	平均解/km	时间/s	最优解/km	最差解/km	平均解/km	时间/s	最优解/km	最差解/km	平均解/km	时间/s
28	2 461	12	4 135.0	4 294.0	4 230.3	2.0	2 486.0	3 400.0	3 110.4	2.6	2 913.0	3 346.0	3 148.3	2.6
29	2 461	24	4 158.0	4 367.0	4 267.7	2.1	3 319.0	3 767.0	3 478.5	2.5	3 400.0	3 828.0	3 543.9	2.6
30	2 461	30	4 118.0	4 315.0	4 237.2	2.4	3 247.0	3 574.0	3 349.1	2.6	3 289.0	3 590.0	3 392.8	2.7
31	2 461	40	4 091.0	4 312.0	4 243.1	2.2	3 376.0	3 963.0	3 705.7	2.7	3 397.0	3 983.0	3 675.1	2.8
32	3 461	12	4 395.0	4 570.0	4 448.0	3.4	2 718.0	3 296.0	3 184.7	4.9	3 216.0	3 246.0	3 231.6	4.9
33	3 461	24	4 355.0	4 590.0	4 471.5	3.1	3 603.0	3 874.0	3 771.0	4.8	3 603.0	3 776.0	3 709.1	4.8
34	3 461	30	4 364.0	4 569.0	4 482.5	3.6	3 505.0	3 932.0	3 726.4	4.9	3 468.0	3 972.0	3 693.3	5.4
35	3 461	40	4 396.0	4 578.0	4 474.8	4.3	3 711.0	3 929.0	3 839.5	5.1	3 798.0	3 988.0	3 895.1	5.0
36	4 461	24	4 393.0	4 516.0	4 457.7	4.7	3 690.0	3 876.0	3 790.0	7.9	3 704.0	3 912.0	3 812.7	8.0
37	4 461	40	4 201.0	4 356.0	4 297.6	5.9	3 915.0	3 924.0	3 921.7	7.9	3 876.0	3 925.0	3 918.6	8.0
38	4 461	50	4 204.0	4 327.0	4 257.7	7.1	3 925.0	3 990.0	3 961.1	8.4	3 927.0	3 992.0	3 949.3	8.4
39	5 397	20	756 425.0	774 005.0	765 435.4	6.9	703 741.0	753 271.0	737 593.1	15.1	702 354.0	753 940.0	736 408.9	14.3
40	5 397	30	758 384.0	780 212.0	771 944.4	8.5	749 813.0	762 970.0	754 940.1	12.4	741 156.0	754 696.0	752 789.1	13.4
41	5 397	40	439 434.0	450 774.0	444 959.6	7.5	379 468.0	407 376.0	384 497.9	11.3	379 400.0	395 854.0	382 088.1	11.6
42	5 397	50	446 551.0	454 389.0	450 046.8	11.5	378 811.0	409 988.0	395 044.5	12.5	379 400.0	410 717.0	391 822.6	13.4
43	5 397	60	441 823.0	450 262.0	447 563.4	10.4	378 811.0	421 749.0	405 826.0	12.0	388 476.0	429 172.0	408 795.5	13.4
44	7 397	40	467 511.0	473 006.0	470 298.6	16.9	386 795.0	393 717.0	389 875.5	20.8	383 743.0	399 676.0	389 341.5	20.8
45	7 397	50	468 228.0	472 997.0	471 522.8	16.4	384 154.0	390 167.0	387 845.5	20.9	385 570.0	400 816.0	389 494.0	21.7
46	7 397	60	468 046.0	473 414.0	470 749.2	20.3	385 570.0	390 167.0	389 483.6	21.0	383 743.0	390 167.0	388 974.6	21.9
47	9 849	30	18 439.0	19 158.0	18 795.0	29.0	17 016.0	18 277.0	17 756.9	39.9	16 454.0	18 355.0	17 430.3	39.3
48	9 849	45	18 679.0	19 198.0	18 919.7	26.2	17 992.0	18 451.0	18 213.2	38.6	17 560.0	18 430.0	18 117.8	39.4
49	9 849	60	18 695.0	18 930.0	18 850.3	36.0	17 313.0	18 416.0	17 925.6	38.1	17 538.0	18 302.0	18 013.7	39.7

实例	n	m		SAGA				ABC				IABC
实例	n	m	最优解/km	最差解/km	平均解/km	时间/s	最优解/km	最差解/km	平均解/km	时间/s	最优解/km	最差解/km	平均解/km	时间/s
28	2 461	12	2 848.0	3 346.0	3 151.9	3.3	3 125.0	3 440.0	3 293.2	0.6	2 853.0	3 250.0	3 121.2	27.1
29	2 461	24	3 389.0	3 713.0	3 471.2	3.2	3 227.0	3 518.0	3 417.9	0.6	3 076.0	3 348.0	3 254.7	25.5
30	2 461	30	3 255.0	3 616.0	3 410.4	3.3	3 192.0	3 609.0	3 417.6	0.6	3 215.0	3 348.0	3 295.5	30.0
31	2 461	40	3 479.0	3 835.0	3 690.4	3.6	3 423.0	3 650.0	3 553.3	0.6	3 313.0	3 387.0	3 359.3	26.7
32	3 461	12	3 039.0	3 355.0	3 225.3	5.9	2 899.0	3 671.0	3 390.7	0.9	3 117.0	3 417.0	3 262.9	59.9
33	3 461	24	3 386.0	3 833.0	3 720.5	5.9	3 316.0	3 961.0	3 654.9	0.9	3 447.0	3 651.0	3 574.7	30.2
34	3 461	30	3 539.0	3 909.0	3 731.4	6.5	3 423.0	3 821.0	3 699.0	0.9	3 364.0	3 690.0	3 609.4	34.2
35	3 461	40	3 416.0	3 988.0	3 848.9	6.2	3 701.0	4 054.0	3 860.3	0.9	3 634.0	3 762.0	3 689.9	34.4
36	4 461	24	3 592.0	3 925.0	3 804.5	9.3	3 557.0	3 794.0	3 679.8	2.9	3 571.0	3 783.0	3 676.9	84.1
37	4 461	40	3 862.0	3 925.0	3 900.3	9.7	3 749.0	3 873.0	3 812.9	1.4	3 657.0	3 808.0	3 751.9	40.2
38	4 461	50	3 925.0	3 990.0	3 956.9	10.6	3 793.0	3 966.0	3 854.9	1.4	3 740.0	3 845.0	3 801.7	43.4
39	5 397	20	721 353.0	745 529.0	736 433.3	16.0	658 782.0	724 479.0	694 587.3	1.9	647 907.0	716 462.0	691 543.9	46.8
40	5 397	30	745 641.0	754 696.0	752 651.6	14.4	692 948.0	757 082.0	719 167.2	2.7	691 427.0	732 859.0	708 554.2	90.1
41	5 397	40	378 205.0	400 275.0	382 742.8	13.3	362 481.0	398 786.0	378 308.2	3.8	343 807.0	359 429.0	348 243.1	157.8
42	5 397	50	379 485.0	421 292.0	397 081.7	14.7	360 451.0	401 925.0	385 596.5	1.8	365 276.0	379 057.0	373 301.7	74.8
43	5 397	60	379 017.0	425 689.0	399 861.4	13.4	374 381.0	406 586.0	387 701.2	2.2	365 736.0	378 814.0	373 814.4	78.3
44	7 397	40	380 524.0	390 167.0	386 329.7	22.6	372 323.0	405 007.0	388 947.3	6.3	361 228.0	386 953.0	373 885.2	227.6
45	7 397	50	382 415.0	392 069.0	388 398.7	22.9	370 492.0	422 161.0	393 903.4	6.4	365 971.0	385 573.0	377 878.9	208.4
46	7 397	60	383 743.0	406 234.0	390 629.1	25.0	375 577.0	421 114.0	387 579.7	6.3	372 701.0	388 126.0	379 130.1	209.3
47	9 849	30	16 744.0	18 199.0	17 589.6	40.5	14 840.0	16 382.0	1 5830.2	7.7	15 251.0	16 229.0	15 763.8	225.1
48	9 849	45	17 539.0	18 528.0	18 113.1	46.6	15 528.0	16 824.0	1 6275.3	7.6	15 808.0	16 644.0	16 260.5	198.9
49	9 849	60	17 589.0	18 240.0	17 908.6	42.8	15 645.0	16 997.0	1 6421.7	7.2	15 614.0	16 934.0	16 316.3	174.3

				GA			GAG			HCGA
实例	n	m	最优解/km	最差解/km	平均解/km	最优解/km	最差解/km	平均解/km	最优解/km	最差解/km	平均解/km
28	2 461	12	4 002.0	4 119.0	4 071.3	2 923.0	3 338.0	3 113.9	2 586.0	3 274.0	3 098.6
29	2 461	24	4 014.0	4 156.0	4 085.1	3 265.0	3 646.0	3 459.6	2 923.0	3 782.0	3 427.3
30	2 461	30	4 026.0	4 160.0	4 085.0	3 031.0	3 491.0	3 279.8	3 020.0	3 491.0	3 321.0
31	2 461	40	4 063.0	4 142.0	4 100.5	3 470.0	3 829.0	3 611.9	3 373.0	3 833.0	3 653.6
32	3 461	12	4 248.0	4 436.0	4 327.7	3 223.0	3 247.0	3 238.3	3 004.0	3 247.0	3 194.8
33	3 461	24	4 275.0	4 426.0	4 335.5	3 613.0	3 879.0	3 745.8	3 247.0	3 823.0	3 695.2
34	3 461	30	4 308.0	4 398.0	4 347.9	3 186.0	3 818.0	3 616.2	3 196.0	3 860.0	3 709.4
35	3 461	40	4 276.0	4 368.0	4 333.1	3 750.0	3 970.0	3 825.7	3 507.0	3 940.0	3 761.5
36	4 461	24	4 297.0	4 420.0	4 369.7	3 787.0	3 901.0	3 822.5	3 535.0	3 925.0	3 813.1
37	4 461	40	4 095.0	4 297.0	4 182.1	3 881.0	3 935.0	3 915.9	3 884.0	3 935.0	3 910.4
38	4 461	50	4 054.0	4 205.0	4 147.0	3 935.0	4 000.0	3 957.8	3 935.0	4 000.0	3 959.0
39	5 397	20	736 678.0	758 028.0	750 605.3	712 840.0	746 752.0	731 960.2	706 674.0	744 073.0	733 884.5
40	5 397	30	754 173.0	773 217.0	763 099.6	743 522.0	762 428.0	753 954.5	724 412.0	755 626.0	748 212.3
41	5 397	40	437 395.0	442 597.0	439 481.0	379 492.0	395 707.0	384 952.9	378 814.0	395 445.0	381 881.8
42	5 397	50	433 617.0	446 073.0	441 648.5	379 488.0	406 741.0	390 684.2	379 020.0	422 460.0	396 792.7
43	5 397	60	437 340.0	447 956.0	443 090.8	383 986.0	421 451.0	407 524.6	392 942.0	417 598.0	405 457.9
44	7 397	40	463 795.0	469 159.0	467 062.4	373 927.0	390 545.0	387 626.6	378 019.0	405 309.0	390 461.8
45	7 397	50	461 311.0	470 253.0	467 359.5	383 746.0	392 193.0	387 998.4	383 591.0	390 170.0	387 770.9
46	7 397	60	465 640.0	471 291.0	468 483.6	384 438.0	396 602.0	390 347.6	384 157.0	396 122.0	390 101.6
47	9 849	30	18 634.0	18 959.0	18 803.0	16 400.0	18 085.0	17 355.2	16 581.0	18 079.0	17 437.6
48	9 849	45	18 413.0	19 077.0	18 759.9	17 650.0	18 504.0	18 112.6	17 788.0	18 389.0	18 229.2
49	9 849	60	18 734.0	18 891.0	18 819.2	17 482.0	18 366.0	17 986.6	17 617.0	18 366.0	17 950.2

References 21

[1]	LI J , ZHOU M C , SUN Q , et al. Colored traveling salesman problem[J]. IEEE Transactions on Cybernetics, 2015,45(11): 2390-2401.
[2]	LI J , QIRU S , ZHOU M C , et al. A new multiple traveling salesman problem and its genetic algorithm-based solution[C]// The 2013 IEEE International Conference on Systems Man and Cybernetics, 2013: 1-6.
[3]	MENG X H , LI J , DAI X Z , et al. Variable neighborhood search for a colored traveling salesman problem[J]. IEEE Transactions on Intelligent Transport Systems, 2018,19(4): 1018-1025.
[4]	DONG X S , DONG W Y , CAI Y L . Ant colony optimization for colored traveling salesman problem by multi-task learning[J]. IET Intelligent Transport Systems, 2018,12(8): 774-782.
[5]	KAO M Y , SANGHI M . An approximation algorithm for a bottleneck traveling salesman problem[J]. Journal of Discrete Algorithms, 2009,7(3): 315-326.
[6]	LARUSIC J , PUNNEN A P . The asymmetric bottleneck traveling salesman problem: algorithms, complexity and empirical analysis[J]. Computer & Operation Research, 2014,43:20-35.
[7]	AHMED Z H . A hybrid genetic algorithm for the bottleneck traveling salesman problem[J]. ACM Transactions on Embedded Computing Systems, 2013,12(1):9:1-9:10.
[8]	VAIRAKTARAKIS G . VAIRAKTARAKIS L . On Gilmore-Gomorys open question for the bottleneck TSP[J]. Operations Research Letters, 2003,31:483-491.
[9]	KABADI S N . Polynomial solvable cases of the TSP[M]. Traveling Salesman Problem and its Variants, 2007,12:489-583.
[10]	董学士，董文永，蔡永乐 . 混合算法求解着色瓶颈旅行商问题[J]. 计算机研究与发展， 2018,55(11): 2372-2385.
	DONG X S , DONG W Y , CAI Y L . Hybrid algorithm for colored bot-tleneck traveling salesman problem[J]. Journal of Computer Research and Development, 2018,55(11): 2372-2385.
[11]	CHENG R , JIN Y C . A competitive swarm optimizer for large scale optimization[J]. IEEE Transaction on Cybernetics, 2015,45(2): 191-204.
[12]	YE B L , WU W M , LI L X , et al. A hierarchical model predictive control approach for signal splits optimization in large-scale urban road networks[J]. IEEE Transaction on Intelligent Transport Systems, 2016,17(8): 2182-2192.
[13]	OMIDVAR M N , YANG M , MEI Y , et al. DG2: a faster and more accurate differential grouping for large-scale black-box optimization[J]. IEEE Transaction on Evolutionary Computation, 2017,21(6): 929-942.
[14]	ZHANG X Y , TIAN Y , CHENG R , et al. A decision variable clustering-based evolutionary algorithm for large-scale many-objective optimization[J]. IEEE Transaction on Evolutionary Computation, 2018,22(1): 97-112.
[15]	HU X M , HE F L , CHEN W N , et al. Cooperation coevolution with fast interdependency identification for large scale optimization[J]. Information Science, 2017,381: 142-160.
[16]	GAO W F , HUANG L L , LIU S Y , et al. Artificial bee colony algorithm based on information learning[J]. IEEE Transactions on Cybernetics, 2015,45(12): 2827-2838.
[17]	KARABOGA D . An idea based on honey bee swarm for numerical optimization[R]. Computers Engineering Department, Engineering Faculty, Erciyes University, 2015.
[18]	LI J Q , PAN Q K , DUAN P Y . An improved artificial bee colony algorithm for solving hybrid flexible flowshop with dynamic operation skipping[J]. IEEE Transactions on Cybernetics, 2016,46(6): 1311-1323.
[19]	MANUEL L , CARLOS G M , FRANCISCO , , et al. Optimizing network attacks by artificial bee colony[J]. Information Sciences, 2017,377: 30-50.
[20]	VENKATESH P , SINGH A . Two metaheuristic approaches for the multiple traveling salesperson problem[J]. Applied Soft Computing, 2015,26: 74-89.
[21]	ZHANG H G , ZHOU J . Dynamic multicale region search algorithm using vitality selection for traveling salesman problem[J]. Expert Systems with Applications, 2016,60: 81-95.

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				SAGA			IABC
实例	n	m	最优解/km	最差解/km	平均解/km	最优解/km	最差解/km	平均解/km
28	2 461	12	2 485.0	3 161.0	2 882.4	2 972.0	3 109.0	3 034.4
29	2 461	24	2 491.0	3 377.0	3 109.4	3 182.0	3 338.0	3 261.8
30	2 461	30	2 623.0	3 460.0	3 168.6	3 257.0	3 366.0	3 300.4
31	2 461	40	2 759.0	4 007.0	3 400.8	3 266.0	3 378.0	3 345.9
32	3 461	12	2 297.0	3 226.0	2 878.0	3 115.0	3 438.0	3 297.2
33	3 461	24	3 087.0	3 816.0	3 384.6	3 348.0	3 668.0	3 533.8
34	3 461	30	2 817.0	3 785.0	3 340.2	3 542.0	3 678.0	3 602.8
35	3 461	40	3 428.0	3 982.0	3 734.3	3 542.0	3 746.0	3 675.9
36	4 461	24	3 274.0	3 925.0	3 760.0	3 546.0	3 777.0	3 693.4
37	4 461	40	3 846.0	3 935.0	3 894.2	3 707.0	3 793.0	3 763.3
38	4 461	50	3 793.0	4 000.0	3 933.4	3 694.0	3 832.0	3 785.6
39	5 397	20	688 742.0	742 086.0	716 422.0	680 127.0	718 184.0	702 975.7
40	5 397	30	720 156.0	755 626.0	749 964.3	698 025.0	731 559.0	717 923.6
41	5 397	40	378 019.0	381 318.0	379 823.6	348 806.0	371 211.0	357 535.5
42	5 397	50	379 403.0	396 641.0	385 390.0	363 034.0	377 332.0	372 615.8
43	5 397	60	378 814.0	414 017.0	395 917.5	363 617.0	376 153.0	371 825.8
44	7 397	40	381 270.0	390 062.0	387 131.0	368 258.0	383 746.0	376 920.0
45	7 397	50	383 746.0	401 910.0	388 487.9	376 786.0	403 051.0	386 373.6
46	7 397	60	378 259.0	404 300.0	390 003.6	372 758.0	399 247.0	386 434.1
47	9 849	30	16 326.0	17 954.0	17 098.3	15 333.0	164 31.0	15 970.3
48	9 849	45	17 701.0	18 511.0	18 272.8	15 355.0	16 463.0	16 074.4
49	9 849	60	17 595.0	18 249.0	17 866.2	16 360.0	17 112.0	16 733.0

Improved artificial bee colony algorithm for large scale colored bottleneck traveling salesman problem

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Figures/Tables 14

References 21

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实例尺度	城市数量n	旅行者数m	共享城市s	独享城市e
1	21	2	11	5
2	21	3	9	4
3	31	2	19	6
4	31	3	16	5
5	31	4	15	4
6	41	2	21	10
7	41	3	23	6
8	41	4	21	5
9	51	3	21	10
10	51	5	21	6
11	76	3	31	15
12	76	4	36	10
13	76	5	26	10
14	76	6	40	6
15	101	4	21	20
16	101	5	53	10
17	101	6	41	10
18	101	7	21	10
19	202	12	82	10
20	202	25	77	5
21	202	35	62	4
22	431	12	191	20
23	431	25	181	10
24	431	40	231	5
25	655	33	160	15
26	1379	20	50	379
27	2361	40	561	45
28	2 461	12	661	150
29	2 461	24	661	75
30	2 461	30	661	60
31	2 461	40	661	45
32	3 461	12	461	250
33	3 461	24	461	125
34	3 461	30	461	100
35	3 461	40	461	75
36	4 461	24	1 461	125
37	4 461	40	461	100
38	4 461	50	461	50
39	5 397	20	397	250
40	5 397	30	897	150
41	5 397	40	1 397	100
42	5 397	50	397	100
43	5397	60	597	80
44	7 397	40	1 397	150
45	7 397	50	397	120
46	7 397	60	597	100
47	9 849	30	849	300
48	9 849	45	849	200
49	9 849	60	849	150

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[6]	Fang LYU,Jun BAI,Junheng HUANG,Bailing WANG. Discovering the backbone network with a novel designed ant colony algorithm [J]. Journal on Communications, 2020, 41(11): 74-85.
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[8]	Ruizhang HUANG,Ruina BAI,Yanping CHEN,Yongbin QIN,Xinyu CHENG,Youliang TIAN. CMDC:an iterative algorithm for complementary multi-view document clustering [J]. Journal on Communications, 2020, 41(8): 155-164.
[9]	Xun SU,Yanfang LI,Ning ZONG,Wei WEI,Juan LI,Ying DING. Network real-time scheduling algorithm based on multi-feature dynamic priority [J]. Journal on Communications, 2020, 41(5): 159-167.
[10]	Yingzhuo XIANG,Zhengguo XU,Ling YOU. Instruction flow mining algorithm based on the temporal sequence of node communication actions [J]. Journal on Communications, 2019, 40(9): 51-60.
[11]	GUO Chen,XIAO Zhifang,LEMG Ming,PENG Shuo,WANG Bo. (t,k)-diagnosability of exchanged crossed cube under the PMC model [J]. Journal on Communications, 2019, 40(6): 190-202.
[12]	Chunguang HUANG,Hai CHENG,Qun DING. Logistic chaotic sequence generator based on physical unclonable function [J]. Journal on Communications, 2019, 40(3): 182-189.
[13]	Daoguang DONG,Guosheng RUI,Wenbiao TIAN,Jian KANG,Ge LIU. Nonparametric Bayesian dictionary learning algorithm based on structural similarity [J]. Journal on Communications, 2019, 40(1): 43-50.
[14]	Yihan YU,Yu FU,Xiaoping WU. Metric and classification model for privacy data based on Shannon information entropy and BP neural network [J]. Journal on Communications, 2018, 39(12): 10-17.
[15]	Yihan YU,Yu FU,Xiaoping WU. Stochastic gradient descent algorithm preserving differential privacy in MapReduce framework [J]. Journal on Communications, 2018, 39(1): 70-77.

			GA		GAG		HCGA			SAGA		ABC		IABC
实例	n	m	PD_best	PD_av	PD_best	PD_av	PD_best	PD_av	PD_best		PD_av	PD_best	PD_av	PD_best	PD_av
28	2461	12	66.3	36.0	0.0	0.0	17.1	1.2	14.5		1.3	25.7	5.8	14.7	0.3
29	2461	24	35.1	31.1	7.8	6.8	10.5	8.8	10.1		6.6	4.9	5.0	0.0	0.0
30	2461	30	29.0	28.5	1.7	1.6	3.0	2.9	1.9		3.4	0.0	3.7	0.7	0.0
31	2461	40	23.4	26.3	1.9	10.3	2.5	9.4	5.0		9.8	3.3	5.7	0.0	0.0
32	3461	12	61.6	39.6	0.0	0.0	18.3	1.4	11.8		1.2	6.6	6.4	14.6	2.4
33	3461	24	31.3	25.0	8.6	5.4	8.6	3.7	2.1		4.0	0.0	2.2	3.9	0.0
34	3461	30	29.7	24.1	4.1	3.2	3.0	2.3	5.2		3.3	1.7	2.4	0.0	0.0
35	3461	40	28.6	21.2	8.6	4.0	11.1	5.5	0.0		4.3	8.3	4.6	6.3	0.0
36	4461	24	23.5	21.2	3.7	3.0	4.1	3.6	0.9		3.4	0.0	0.07	0.3	0.0
37	4461	40	14.8	14.5	7.0	4.5	5.9	4.4	5.6		3.9	2.5	1.6	0.0	0.0
38	4461	50	12.4	11.9	4.9	4.1	5.0	3.8	4.9		4.0	1.4	1.3	0.0	0.0
39	5397	20	16.7	10.6	8.6	6.6	8.4	6.4	11.3		6.4	1.6	0.4	0.0	0.0
40	5397	30	9.6	8.9	8.4	6.5	7.1	6.2	7.8		6.2	0.2	1.4	0.0	0.0
41	5397	40	27.8	27.7	10.3	10.4	10.3	9.7	10.0		9.9	5.4	8.6	0.0	0.0
42	5397	50	23.8	20.5	5.0	5.8	5.2	4.9	5.2		6.3	0.0	3.2	1.3	0.0
43	5397	60	20.8	19.7	3.5	8.5	6.2	9.3	3.6		6.9	2.3	3.7	0.0	0.0
44	7397	40	29.4	25.7	7.0	4.2	6.2	4.1	5.3		3.3	3.0	4.0	0.0	0.0
45	7397	50	27.9	24.7	4.9	2.6	5.3	3.0	4.4		2.7	1.2	4.2	0.0	0.0
46	7397	60	25.5	24.1	3.4	2.7	2.9	2.5	2.9		3.0	0.7	2.2	0.0	0.0
47	9849	30	24.2	19.2	14.6	12.6	10.8	10.5	12.8		11.5	0.0	0.4	2.7	0.0
48	9849	45	20.2	16.3	15.8	12.0	13.0	11.4	12.9		11.3	0.0	0.09	1.8	0.0
49	9849	60	19.7	15.5	10.8	9.8	12.3	10.4	12.6		9.7	0.1	0.6	0.0	0.0
总平均			7.9	22.4	3.6	5.7	3.6	5.7	3.8		5.6	3.2	3.1	2.9	0.1