Journal of Computer Applications ›› 2021, Vol. 41 ›› Issue (12): 3692-3701.DOI: 10.11772/j.issn.1001-9081.2021010095
• Frontier and comprehensive applications • Previous Articles Next Articles
Zhisheng SHAO1(), Guofu ZHANG1,2,3,4, Zhaopin SU1,2,3,4, Lei LI1
Received:
2021-01-18
Revised:
2020-03-10
Accepted:
2020-03-17
Online:
2021-12-28
Published:
2021-12-10
Contact:
Zhisheng SHAO
About author:
ZHANG Guofu, born in 1979, Ph. D., professor. His research interests include evolutionary computation, software engineering.Supported by:
邵志胜1(), 张国富1,2,3,4, 苏兆品1,2,3,4, 李磊1
通讯作者:
邵志胜
作者简介:
张国富(1979—),男,安徽合肥人,教授,博士,CCF会员,主要研究方向:进化计算、软件工程基金资助:
CLC Number:
Zhisheng SHAO, Guofu ZHANG, Zhaopin SU, Lei LI. Dynamic testing resource allocation algorithm based on software architecture and generalized differential evolution[J]. Journal of Computer Applications, 2021, 41(12): 3692-3701.
邵志胜, 张国富, 苏兆品, 李磊. 基于软件体系结构和广义差分进化的测试资源动态分配算法[J]. 《计算机应用》唯一官方网站, 2021, 41(12): 3692-3701.
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URL: https://www.joca.cn/EN/10.11772/j.issn.1001-9081.2021010095
系统规模 | 参数 | 取值 |
---|---|---|
简单系统 | 100 | |
{4E+3,1E+5,7E+5} | ||
{0.8,0.9,0.95} | ||
复杂系统 | 150 | |
{8E+3,2E+5,2E+6} | ||
{0.75,0.85,0.95} | ||
大型系统 | 200 | |
{2E+4,5E+5,8E+6} | ||
{0.7,0.85,0.95} |
Tab. 1 Parameters of system model
系统规模 | 参数 | 取值 |
---|---|---|
简单系统 | 100 | |
{4E+3,1E+5,7E+5} | ||
{0.8,0.9,0.95} | ||
复杂系统 | 150 | |
{8E+3,2E+5,2E+6} | ||
{0.75,0.85,0.95} | ||
大型系统 | 200 | |
{2E+4,5E+5,8E+6} | ||
{0.7,0.85,0.95} |
参数 | 取值 | 参数 | 取值 |
---|---|---|---|
[400,1000] | [5.0,15.0] | ||
[0.01,0.1] | [0.25,0.75] | ||
[1.0,3.0] | [0,1.0] |
Tab. 2 Parameter range of components
参数 | 取值 | 参数 | 取值 |
---|---|---|---|
[400,1000] | [5.0,15.0] | ||
[0.01,0.1] | [0.25,0.75] | ||
[1.0,3.0] | [0,1.0] |
实例 | SISO系统 | MIMO系统 | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
第1阶段 | 第2阶段 | 第3阶段 | 第1阶段 | 第2阶段 | 第3阶段 | |||||||
平均值 | 7 500 | 1 208 | 7 500 | 628 | 7 497 | 939 | 7 500 | 1 146 | 7 500 | 623 | 7 500 | 639 |
1 | 7 500 | 1 380 | 7 500 | 0 | 7 500 | 356 | 7 500 | 966 | 7 500 | 190 | 7 500 | 57 |
2 | 7 500 | 1 309 | 7 500 | 1 027 | 7 500 | 1 133 | 7 500 | 1 191 | 7 500 | 557 | 7 500 | 73 |
3 | 7 500 | 1 366 | 7 500 | 961 | 7 500 | 574 | 7 500 | 644 | 7 500 | 0 | 7 500 | 389 |
4 | 7 500 | 1 478 | 7 500 | 201 | 7 500 | 379 | 7 500 | 940 | 7 500 | 616 | 7 500 | 449 |
5 | 7 500 | 1 368 | 7 500 | 399 | 7 500 | 794 | 7 500 | 1 316 | 7 500 | 1 063 | 7 500 | 917 |
6 | 7 500 | 1 367 | 7 500 | 401 | 7 500 | 397 | 7 500 | 1 219 | 7 500 | 1 313 | 7 500 | 645 |
7 | 7 500 | 804 | 7 500 | 610 | 7 473 | 1 377 | 7 500 | 1 307 | 7 500 | 1 304 | 7 500 | 1 442 |
8 | 7 500 | 931 | 7 500 | 792 | 7 500 | 1 530 | 7 500 | 1 347 | 7 500 | 567 | 7 500 | 1 590 |
9 | 7 500 | 667 | 7 500 | 955 | 7 500 | 2 464 | 7 500 | 1 407 | 7 500 | 456 | 7 500 | 637 |
10 | 7 500 | 1 412 | 7 500 | 929 | 7 500 | 389 | 7 500 | 1 124 | 7 500 | 163 | 7 500 | 190 |
Tab. 3 Capacity value results of two algorithms in simple system
实例 | SISO系统 | MIMO系统 | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
第1阶段 | 第2阶段 | 第3阶段 | 第1阶段 | 第2阶段 | 第3阶段 | |||||||
平均值 | 7 500 | 1 208 | 7 500 | 628 | 7 497 | 939 | 7 500 | 1 146 | 7 500 | 623 | 7 500 | 639 |
1 | 7 500 | 1 380 | 7 500 | 0 | 7 500 | 356 | 7 500 | 966 | 7 500 | 190 | 7 500 | 57 |
2 | 7 500 | 1 309 | 7 500 | 1 027 | 7 500 | 1 133 | 7 500 | 1 191 | 7 500 | 557 | 7 500 | 73 |
3 | 7 500 | 1 366 | 7 500 | 961 | 7 500 | 574 | 7 500 | 644 | 7 500 | 0 | 7 500 | 389 |
4 | 7 500 | 1 478 | 7 500 | 201 | 7 500 | 379 | 7 500 | 940 | 7 500 | 616 | 7 500 | 449 |
5 | 7 500 | 1 368 | 7 500 | 399 | 7 500 | 794 | 7 500 | 1 316 | 7 500 | 1 063 | 7 500 | 917 |
6 | 7 500 | 1 367 | 7 500 | 401 | 7 500 | 397 | 7 500 | 1 219 | 7 500 | 1 313 | 7 500 | 645 |
7 | 7 500 | 804 | 7 500 | 610 | 7 473 | 1 377 | 7 500 | 1 307 | 7 500 | 1 304 | 7 500 | 1 442 |
8 | 7 500 | 931 | 7 500 | 792 | 7 500 | 1 530 | 7 500 | 1 347 | 7 500 | 567 | 7 500 | 1 590 |
9 | 7 500 | 667 | 7 500 | 955 | 7 500 | 2 464 | 7 500 | 1 407 | 7 500 | 456 | 7 500 | 637 |
10 | 7 500 | 1 412 | 7 500 | 929 | 7 500 | 389 | 7 500 | 1 124 | 7 500 | 163 | 7 500 | 190 |
实例 | SISO系统 | MIMO系统 | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
第1阶段 | 第2阶段 | 第3阶段 | 第1阶段 | 第2阶段 | 第3阶段 | |||||||
平均值 | 7 499 | 463 | 7 495 | 737 | 6 130 | 218 | 7 496 | 538 | 7 499 | 457 | 6 510 | 123 |
1 | 7 500 | 793 | 7 500 | 891 | 6 130 | 127 | 7 498 | 49 | 7 500 | 500 | 7 496 | 25 |
2 | 7 488 | 620 | 7 499 | 1 069 | 7 500 | 297 | 7 491 | 928 | 7 500 | 534 | 7 472 | 59 |
3 | 7 498 | 100 | 7 500 | 32 | 7 500 | 51 | 7 475 | 358 | 7 498 | 5 | 1 865 | 9 |
4 | 7 500 | 8 | 7 497 | 240 | 7 500 | 102 | 7 496 | 591 | 7 492 | 0 | 3 482 | 7 |
5 | 7 500 | 267 | 7 499 | 812 | 7 480 | 201 | 7 500 | 788 | 7 499 | 82 | 7 487 | 116 |
6 | 7 500 | 793 | 7 497 | 543 | 7 500 | 259 | 7 500 | 1 254 | 7 500 | 1 459 | 7 491 | 284 |
7 | 7 500 | 707 | 7 499 | 1 043 | 3 179 | 253 | 7 500 | 316 | 7 500 | 303 | 7 487 | 140 |
8 | 7 500 | 65 | 7 495 | 301 | 7 481 | 243 | 7 498 | 56 | 7 498 | 506 | 7 500 | 351 |
9 | 7 500 | 268 | 7 480 | 1 737 | 6 500 | 368 | 7 497 | 427 | 7 499 | 27 | 7 485 | 226 |
10 | 7 500 | 1 014 | 7 483 | 697 | 7 500 | 277 | 7 500 | 610 | 7 500 | 1 151 | 7 339 | 10 |
Tab. 4 Capacity value results of two algorithms in complex system
实例 | SISO系统 | MIMO系统 | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
第1阶段 | 第2阶段 | 第3阶段 | 第1阶段 | 第2阶段 | 第3阶段 | |||||||
平均值 | 7 499 | 463 | 7 495 | 737 | 6 130 | 218 | 7 496 | 538 | 7 499 | 457 | 6 510 | 123 |
1 | 7 500 | 793 | 7 500 | 891 | 6 130 | 127 | 7 498 | 49 | 7 500 | 500 | 7 496 | 25 |
2 | 7 488 | 620 | 7 499 | 1 069 | 7 500 | 297 | 7 491 | 928 | 7 500 | 534 | 7 472 | 59 |
3 | 7 498 | 100 | 7 500 | 32 | 7 500 | 51 | 7 475 | 358 | 7 498 | 5 | 1 865 | 9 |
4 | 7 500 | 8 | 7 497 | 240 | 7 500 | 102 | 7 496 | 591 | 7 492 | 0 | 3 482 | 7 |
5 | 7 500 | 267 | 7 499 | 812 | 7 480 | 201 | 7 500 | 788 | 7 499 | 82 | 7 487 | 116 |
6 | 7 500 | 793 | 7 497 | 543 | 7 500 | 259 | 7 500 | 1 254 | 7 500 | 1 459 | 7 491 | 284 |
7 | 7 500 | 707 | 7 499 | 1 043 | 3 179 | 253 | 7 500 | 316 | 7 500 | 303 | 7 487 | 140 |
8 | 7 500 | 65 | 7 495 | 301 | 7 481 | 243 | 7 498 | 56 | 7 498 | 506 | 7 500 | 351 |
9 | 7 500 | 268 | 7 480 | 1 737 | 6 500 | 368 | 7 497 | 427 | 7 499 | 27 | 7 485 | 226 |
10 | 7 500 | 1 014 | 7 483 | 697 | 7 500 | 277 | 7 500 | 610 | 7 500 | 1 151 | 7 339 | 10 |
实例 | SISO系统 | MIMO系统 | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
第1阶段 | 第2阶段 | 第3阶段 | 第1阶段 | 第2阶段 | 第3阶段 | |||||||
平均值 | 7 497 | 0 | 7 186 | 0 | 7 497 | 8 | 7 495 | 0 | 7 261 | 0 | 7 500 | 4 |
1 | 7 500 | 0 | 7 500 | 0 | 7 500 | 0 | 7 498 | 0 | 7 492 | 0 | 7 500 | 0 |
2 | 7 499 | 0 | 7 441 | 0 | 7 500 | 0 | 7 497 | 0 | 6 617 | 0 | 7 500 | 0 |
3 | 7 494 | 0 | 7 470 | 0 | 7 500 | 0 | 7 497 | 0 | 7 479 | 0 | 7 500 | 0 |
4 | 7 495 | 0 | 7 186 | 0 | 7 500 | 0 | 7 500 | 0 | 7 411 | 0 | 7 500 | 0 |
5 | 7 491 | 0 | 6 752 | 0 | 7 500 | 1 | 7 500 | 0 | 7 500 | 0 | 7 500 | 2 |
6 | 7 500 | 0 | 7 429 | 0 | 7 500 | 0 | 7 498 | 0 | 7 468 | 0 | 7 500 | 0 |
7 | 7 498 | 0 | 6 076 | 0 | 7 473 | 6 | 7 492 | 0 | 7 462 | 0 | 7 500 | 0 |
8 | 7 496 | 0 | 7 388 | 0 | 7 500 | 1 | 7 466 | 0 | 7 036 | 0 | 7 500 | 5 |
9 | 7 500 | 0 | 7 397 | 0 | 7 500 | 2 | 7 500 | 0 | 6 651 | 0 | 7 500 | 13 |
10 | 7 499 | 0 | 7 221 | 0 | 7 500 | 68 | 7 500 | 0 | 7 490 | 0 | 7 500 | 23 |
Tab. 5 Capacity value results of two algorithms in large system
实例 | SISO系统 | MIMO系统 | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
第1阶段 | 第2阶段 | 第3阶段 | 第1阶段 | 第2阶段 | 第3阶段 | |||||||
平均值 | 7 497 | 0 | 7 186 | 0 | 7 497 | 8 | 7 495 | 0 | 7 261 | 0 | 7 500 | 4 |
1 | 7 500 | 0 | 7 500 | 0 | 7 500 | 0 | 7 498 | 0 | 7 492 | 0 | 7 500 | 0 |
2 | 7 499 | 0 | 7 441 | 0 | 7 500 | 0 | 7 497 | 0 | 6 617 | 0 | 7 500 | 0 |
3 | 7 494 | 0 | 7 470 | 0 | 7 500 | 0 | 7 497 | 0 | 7 479 | 0 | 7 500 | 0 |
4 | 7 495 | 0 | 7 186 | 0 | 7 500 | 0 | 7 500 | 0 | 7 411 | 0 | 7 500 | 0 |
5 | 7 491 | 0 | 6 752 | 0 | 7 500 | 1 | 7 500 | 0 | 7 500 | 0 | 7 500 | 2 |
6 | 7 500 | 0 | 7 429 | 0 | 7 500 | 0 | 7 498 | 0 | 7 468 | 0 | 7 500 | 0 |
7 | 7 498 | 0 | 6 076 | 0 | 7 473 | 6 | 7 492 | 0 | 7 462 | 0 | 7 500 | 0 |
8 | 7 496 | 0 | 7 388 | 0 | 7 500 | 1 | 7 466 | 0 | 7 036 | 0 | 7 500 | 5 |
9 | 7 500 | 0 | 7 397 | 0 | 7 500 | 2 | 7 500 | 0 | 6 651 | 0 | 7 500 | 13 |
10 | 7 499 | 0 | 7 221 | 0 | 7 500 | 68 | 7 500 | 0 | 7 490 | 0 | 7 500 | 23 |
实例 | SISO系统 | MIMO系统 | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
第1阶段 | 第2阶段 | 第3阶段 | 第1阶段 | 第2阶段 | 第3阶段 | |||||||
平均值 | 82.24 | 15.57 | 98.55 | 2.01 | 92.99 | 25.04 | 84.01 | 15.22 | 98.95 | 3.10 | 93.59 | 18.18 |
1 | 78.99 | 8.44 | 100.00 | 0.00 | 99.72 | 0.21 | 89.54 | 12.19 | 100.00 | 0.00 | 100.00 | 0.05 |
2 | 88.69 | 12.95 | 98.93 | 0.43 | 82.70 | 61.13 | 80.10 | 17.53 | 97.49 | 6.65 | 100.00 | 0.00 |
3 | 83.97 | 22.77 | 98.96 | 4.61 | 93.90 | 41.11 | 89.60 | 4.64 | 100.00 | 0.00 | 100.00 | 1.92 |
4 | 79.57 | 16.23 | 100.00 | 0.05 | 99.74 | 0.72 | 87.98 | 13.19 | 99.51 | 1.77 | 93.10 | 18.31 |
5 | 77.49 | 22.52 | 99.75 | 0.89 | 98.49 | 5.83 | 78.65 | 17.20 | 96.24 | 5.99 | 92.37 | 14.95 |
6 | 81.42 | 22.81 | 99.50 | 0.04 | 98.99 | 5.09 | 81.62 | 19.87 | 97.64 | 8.79 | 94.42 | 15.47 |
7 | 86.82 | 12.51 | 96.56 | 3.73 | 90.78 | 49.15 | 84.01 | 18.29 | 99.69 | 4.56 | 88.63 | 31.51 |
8 | 83.78 | 5.09 | 98.23 | 0.88 | 78.82 | 33.29 | 83.82 | 17.87 | 99.82 | 0.17 | 70.75 | 86.19 |
9 | 80.36 | 16.41 | 94.55 | 8.21 | 88.07 | 50.87 | 74.91 | 22.16 | 99.12 | 3.11 | 97.17 | 10.08 |
10 | 81.30 | 15.96 | 99.03 | 1.23 | 98.71 | 3.03 | 89.86 | 9.27 | 100.00 | 0.00 | 99.47 | 3.33 |
Tab. 6 Coverage value results of two algorithms in simple system
实例 | SISO系统 | MIMO系统 | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
第1阶段 | 第2阶段 | 第3阶段 | 第1阶段 | 第2阶段 | 第3阶段 | |||||||
平均值 | 82.24 | 15.57 | 98.55 | 2.01 | 92.99 | 25.04 | 84.01 | 15.22 | 98.95 | 3.10 | 93.59 | 18.18 |
1 | 78.99 | 8.44 | 100.00 | 0.00 | 99.72 | 0.21 | 89.54 | 12.19 | 100.00 | 0.00 | 100.00 | 0.05 |
2 | 88.69 | 12.95 | 98.93 | 0.43 | 82.70 | 61.13 | 80.10 | 17.53 | 97.49 | 6.65 | 100.00 | 0.00 |
3 | 83.97 | 22.77 | 98.96 | 4.61 | 93.90 | 41.11 | 89.60 | 4.64 | 100.00 | 0.00 | 100.00 | 1.92 |
4 | 79.57 | 16.23 | 100.00 | 0.05 | 99.74 | 0.72 | 87.98 | 13.19 | 99.51 | 1.77 | 93.10 | 18.31 |
5 | 77.49 | 22.52 | 99.75 | 0.89 | 98.49 | 5.83 | 78.65 | 17.20 | 96.24 | 5.99 | 92.37 | 14.95 |
6 | 81.42 | 22.81 | 99.50 | 0.04 | 98.99 | 5.09 | 81.62 | 19.87 | 97.64 | 8.79 | 94.42 | 15.47 |
7 | 86.82 | 12.51 | 96.56 | 3.73 | 90.78 | 49.15 | 84.01 | 18.29 | 99.69 | 4.56 | 88.63 | 31.51 |
8 | 83.78 | 5.09 | 98.23 | 0.88 | 78.82 | 33.29 | 83.82 | 17.87 | 99.82 | 0.17 | 70.75 | 86.19 |
9 | 80.36 | 16.41 | 94.55 | 8.21 | 88.07 | 50.87 | 74.91 | 22.16 | 99.12 | 3.11 | 97.17 | 10.08 |
10 | 81.30 | 15.96 | 99.03 | 1.23 | 98.71 | 3.03 | 89.86 | 9.27 | 100.00 | 0.00 | 99.47 | 3.33 |
实例 | SISO系统 | MIMO系统 | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
第1阶段 | 第2阶段 | 第3阶段 | 第1阶段 | 第2阶段 | 第3阶段 | |||||||
平均值 | 94.80 | 5.34 | 90.72 | 12.03 | 99.51 | 4.49 | 91.08 | 9.63 | 95.94 | 4.56 | 98.77 | 0.71 |
1 | 80.45 | 19.68 | 74.30 | 23.08 | 100.00 | 0.49 | 100.00 | 0.31 | 99.60 | 2.91 | 100.00 | 0.00 |
2 | 92.90 | 12.71 | 83.26 | 3.47 | 100.00 | 0.04 | 83.84 | 9.80 | 91.01 | 12.08 | 100.00 | 2.89 |
3 | 96.00 | 5.43 | 100.00 | 0.01 | 100.00 | 0.00 | 93.58 | 5.16 | 100.00 | 0.00 | 88.89 | 3.75 |
4 | 100.00 | 0.00 | 97.92 | 3.36 | 100.00 | 0.01 | 90.36 | 31.38 | 100.00 | 0.00 | 100.00 | 0.00 |
5 | 78.65 | 12.13 | 83.99 | 17.68 | 100.00 | 0.56 | 87.18 | 11.17 | 97.56 | 1.13 | 100.00 | 0.00 |
6 | 100.00 | 1.15 | 94.84 | 15.74 | 99.61 | 14.39 | 83.65 | 19.44 | 90.68 | 12.15 | 100.00 | 0.00 |
7 | 100.00 | 0.63 | 89.55 | 18.80 | 97.23 | 16.67 | 96.20 | 4.16 | 98.68 | 3.03 | 99.29 | 0.01 |
8 | 100.00 | 0.11 | 97.34 | 11.23 | 100.00 | 0.98 | 94.64 | 0.04 | 92.29 | 0.97 | 100.00 | 0.40 |
9 | 100.00 | 0.27 | 90.73 | 2.63 | 99.73 | 3.40 | 94.61 | 4.44 | 100.00 | 0.00 | 99.56 | 0.03 |
10 | 100.00 | 1.29 | 95.27 | 24.32 | 98.56 | 8.36 | 86.72 | 10.41 | 89.57 | 13.37 | 100.00 | 0.00 |
Tab. 7 Coverage value results of two algorithms in complex system
实例 | SISO系统 | MIMO系统 | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
第1阶段 | 第2阶段 | 第3阶段 | 第1阶段 | 第2阶段 | 第3阶段 | |||||||
平均值 | 94.80 | 5.34 | 90.72 | 12.03 | 99.51 | 4.49 | 91.08 | 9.63 | 95.94 | 4.56 | 98.77 | 0.71 |
1 | 80.45 | 19.68 | 74.30 | 23.08 | 100.00 | 0.49 | 100.00 | 0.31 | 99.60 | 2.91 | 100.00 | 0.00 |
2 | 92.90 | 12.71 | 83.26 | 3.47 | 100.00 | 0.04 | 83.84 | 9.80 | 91.01 | 12.08 | 100.00 | 2.89 |
3 | 96.00 | 5.43 | 100.00 | 0.01 | 100.00 | 0.00 | 93.58 | 5.16 | 100.00 | 0.00 | 88.89 | 3.75 |
4 | 100.00 | 0.00 | 97.92 | 3.36 | 100.00 | 0.01 | 90.36 | 31.38 | 100.00 | 0.00 | 100.00 | 0.00 |
5 | 78.65 | 12.13 | 83.99 | 17.68 | 100.00 | 0.56 | 87.18 | 11.17 | 97.56 | 1.13 | 100.00 | 0.00 |
6 | 100.00 | 1.15 | 94.84 | 15.74 | 99.61 | 14.39 | 83.65 | 19.44 | 90.68 | 12.15 | 100.00 | 0.00 |
7 | 100.00 | 0.63 | 89.55 | 18.80 | 97.23 | 16.67 | 96.20 | 4.16 | 98.68 | 3.03 | 99.29 | 0.01 |
8 | 100.00 | 0.11 | 97.34 | 11.23 | 100.00 | 0.98 | 94.64 | 0.04 | 92.29 | 0.97 | 100.00 | 0.40 |
9 | 100.00 | 0.27 | 90.73 | 2.63 | 99.73 | 3.40 | 94.61 | 4.44 | 100.00 | 0.00 | 99.56 | 0.03 |
10 | 100.00 | 1.29 | 95.27 | 24.32 | 98.56 | 8.36 | 86.72 | 10.41 | 89.57 | 13.37 | 100.00 | 0.00 |
实例 | SISO系统 | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
第1阶段 | 第2阶段 | 第3阶段 | ||||||||||
A | B | A | B | A | B | |||||||
均值 | 标准差 | 均值 | 标准差 | 均值 | 标准差 | 均值 | 标准差 | 均值 | 标准差 | 均值 | 标准差 | |
1 | 2.63E+5 | 170.7 | 2.53E+5 | 3 011 | 1.10E+7 | 1.48E+5 | 0 | 0 | 1.80E+9 | 6.37E+6 | 1.12E+9 | 2.15E+8 |
2 | 2.49E+5 | 445.5 | 2.35E+5 | 6 283 | 1.16E+8 | 9.56E+4 | 1.08E+8 | 1.18E+6 | 1.09E+9 | 1.36E+7 | 9.99E+8 | 2.73E+7 |
3 | 8.10E+5 | 1 365.0 | 7.64E+5 | 8 732 | 4.96E+8 | 1.24E+6 | 4.41E+8 | 1.66E+7 | 1.75E+10 | 1.32E+8 | 1.40E+10 | 1.59E+9 |
4 | 2.87E+5 | 431.7 | 2.73E+5 | 2 938 | 1.75E+7 | 1.32E+5 | 3.73E+6 | 4.12E+6 | 1.03E+9 | 5.92E+6 | 6.61E+8 | 1.49E+8 |
5 | 4.74E+5 | 693.9 | 4.46E+5 | 5 022 | 1.11E+8 | 2.64E+5 | 8.33E+7 | 2.11E+7 | 1.16E+10 | 4.24E+7 | 8.61E+9 | 1.28E+9 |
6 | 6.51E+5 | 716.0 | 6.26E+5 | 9 515 | 1.47E+8 | 2.25E+5 | 1.06E+8 | 2.59E+7 | 1.14E+10 | 2.69E+7 | 1.01E+10 | 6.65E+8 |
7 | 3.38E+5 | 840.1 | 2.70E+5 | 9.38E+4 | 2.37E+8 | 6.34E+5 | 1.98E+8 | 1.60E+7 | 2.97E+10 | 1.20E+8 | 2.84E+10 | 5.76E+8 |
8 | 1.28E+5 | 232.7 | 1.07E+5 | 3.02E+4 | 1.04E+8 | 1.97E+5 | 9.29E+7 | 1.31E+6 | 3.96E+9 | 7.16E+6 | 3.68E+9 | 4.23E+7 |
9 | 3.53E+5 | 1 162.0 | 2.42E+5 | 1.36E+5 | 6.01E+8 | 1.00E+6 | 5.82E+8 | 7.31E+6 | 1.87E+10 | 6.28E+7 | 1.87E+10 | 6.78E+8 |
10 | 2.87E+5 | 486.2 | 2.67E+5 | 3 432 | 7.58E+7 | 3.13E+4 | 6.92E+7 | 7.97E+5 | 1.98E+8 | 3.54E+6 | 1.04E+8 | 2.64E+7 |
实例 | MIMO系统 | |||||||||||
第1阶段 | 第2阶段 | 第3阶段 | ||||||||||
A | B | A | B | A | B | |||||||
均值 | 标准差 | 均值 | 标准差 | 均值 | 标准差 | 均值 | 标准差 | 均值 | 标准差 | 均值 | 标准差 | |
1 | 1.24E+5 | 310.1 | 1.13E+5 | 4 232 | 4.20E+7 | 1.85E+5 | 9.52E+6 | 1.25E+7 | 3.27E+8 | 3.59E+6 | 2.67E+7 | 5.44E+7 |
2 | 2.45E+5 | 674.9 | 2.24E+5 | 9 846 | 2.20E+8 | 5.06E+5 | 1.95E+8 | 7.33E+6 | 4.20E+8 | 6.03E+6 | 7.17E+7 | 7.81E+7 |
3 | 2.68E+5 | 918.2 | 1.97E+5 | 9.19E+4 | 1.89E+7 | 1.23E+5 | 0 | 0 | 1.22E+10 | 3.81E+7 | 9.38E+9 | 1.13E+9 |
4 | 1.63E+5 | 378.5 | 1.34E+5 | 4.56E+4 | 6.80E+7 | 1.35E+5 | 5.73E+7 | 2.70E+6 | 2.61E+9 | 1.25E+7 | 2.20E+9 | 1.77E+8 |
5 | 9.97E+5 | 1 899.0 | 9.50E+5 | 1.43E+4 | 5.36E+8 | 9.70E+5 | 5.09E+8 | 4.82E+6 | 2.40E+10 | 6.86E+7 | 2.17E+10 | 1.11E+9 |
6 | 7.21E+5 | 1 510.0 | 6.66E+5 | 1.53E+4 | 6.41E+8 | 4.70E+5 | 6.20E+8 | 8.05E+6 | 1.91E+10 | 1.24E+8 | 1.46E+10 | 1.34E+9 |
7 | 5.64E+5 | 1 126.0 | 5.26E+5 | 1.07E+4 | 5.02E+8 | 5.52E+5 | 4.76E+8 | 6.94E+6 | 1.53E+10 | 6.91E+7 | 1.31E+10 | 6.27E+8 |
8 | 1.30E+5 | 150.6 | 1.24E+5 | 2 206 | 2.84E+7 | 4.24E+4 | 1.95E+7 | 3.04E+6 | 1.04E+9 | 1.57E+7 | 1.01E+9 | 3.46E+7 |
9 | 5.45E+5 | 1 226.0 | 5.10E+5 | 7 034 | 1.35E+8 | 2.98E+5 | 1.09E+8 | 1.54E+7 | 1.48E+10 | 1.61E+7 | 1.39E+10 | 3.83E+8 |
10 | 1.29E+5 | 359.2 | 1.18E+5 | 2 678 | 2.13E+7 | 6.63E+4 | 5.53E+6 | 5.45E+6 | 6.36E+7 | 2.32E+6 | 2.26E+7 | 1.39E+7 |
Tab. 8 Hypervolume (mean and standard deviation) results of two algorithms in simple system
实例 | SISO系统 | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
第1阶段 | 第2阶段 | 第3阶段 | ||||||||||
A | B | A | B | A | B | |||||||
均值 | 标准差 | 均值 | 标准差 | 均值 | 标准差 | 均值 | 标准差 | 均值 | 标准差 | 均值 | 标准差 | |
1 | 2.63E+5 | 170.7 | 2.53E+5 | 3 011 | 1.10E+7 | 1.48E+5 | 0 | 0 | 1.80E+9 | 6.37E+6 | 1.12E+9 | 2.15E+8 |
2 | 2.49E+5 | 445.5 | 2.35E+5 | 6 283 | 1.16E+8 | 9.56E+4 | 1.08E+8 | 1.18E+6 | 1.09E+9 | 1.36E+7 | 9.99E+8 | 2.73E+7 |
3 | 8.10E+5 | 1 365.0 | 7.64E+5 | 8 732 | 4.96E+8 | 1.24E+6 | 4.41E+8 | 1.66E+7 | 1.75E+10 | 1.32E+8 | 1.40E+10 | 1.59E+9 |
4 | 2.87E+5 | 431.7 | 2.73E+5 | 2 938 | 1.75E+7 | 1.32E+5 | 3.73E+6 | 4.12E+6 | 1.03E+9 | 5.92E+6 | 6.61E+8 | 1.49E+8 |
5 | 4.74E+5 | 693.9 | 4.46E+5 | 5 022 | 1.11E+8 | 2.64E+5 | 8.33E+7 | 2.11E+7 | 1.16E+10 | 4.24E+7 | 8.61E+9 | 1.28E+9 |
6 | 6.51E+5 | 716.0 | 6.26E+5 | 9 515 | 1.47E+8 | 2.25E+5 | 1.06E+8 | 2.59E+7 | 1.14E+10 | 2.69E+7 | 1.01E+10 | 6.65E+8 |
7 | 3.38E+5 | 840.1 | 2.70E+5 | 9.38E+4 | 2.37E+8 | 6.34E+5 | 1.98E+8 | 1.60E+7 | 2.97E+10 | 1.20E+8 | 2.84E+10 | 5.76E+8 |
8 | 1.28E+5 | 232.7 | 1.07E+5 | 3.02E+4 | 1.04E+8 | 1.97E+5 | 9.29E+7 | 1.31E+6 | 3.96E+9 | 7.16E+6 | 3.68E+9 | 4.23E+7 |
9 | 3.53E+5 | 1 162.0 | 2.42E+5 | 1.36E+5 | 6.01E+8 | 1.00E+6 | 5.82E+8 | 7.31E+6 | 1.87E+10 | 6.28E+7 | 1.87E+10 | 6.78E+8 |
10 | 2.87E+5 | 486.2 | 2.67E+5 | 3 432 | 7.58E+7 | 3.13E+4 | 6.92E+7 | 7.97E+5 | 1.98E+8 | 3.54E+6 | 1.04E+8 | 2.64E+7 |
实例 | MIMO系统 | |||||||||||
第1阶段 | 第2阶段 | 第3阶段 | ||||||||||
A | B | A | B | A | B | |||||||
均值 | 标准差 | 均值 | 标准差 | 均值 | 标准差 | 均值 | 标准差 | 均值 | 标准差 | 均值 | 标准差 | |
1 | 1.24E+5 | 310.1 | 1.13E+5 | 4 232 | 4.20E+7 | 1.85E+5 | 9.52E+6 | 1.25E+7 | 3.27E+8 | 3.59E+6 | 2.67E+7 | 5.44E+7 |
2 | 2.45E+5 | 674.9 | 2.24E+5 | 9 846 | 2.20E+8 | 5.06E+5 | 1.95E+8 | 7.33E+6 | 4.20E+8 | 6.03E+6 | 7.17E+7 | 7.81E+7 |
3 | 2.68E+5 | 918.2 | 1.97E+5 | 9.19E+4 | 1.89E+7 | 1.23E+5 | 0 | 0 | 1.22E+10 | 3.81E+7 | 9.38E+9 | 1.13E+9 |
4 | 1.63E+5 | 378.5 | 1.34E+5 | 4.56E+4 | 6.80E+7 | 1.35E+5 | 5.73E+7 | 2.70E+6 | 2.61E+9 | 1.25E+7 | 2.20E+9 | 1.77E+8 |
5 | 9.97E+5 | 1 899.0 | 9.50E+5 | 1.43E+4 | 5.36E+8 | 9.70E+5 | 5.09E+8 | 4.82E+6 | 2.40E+10 | 6.86E+7 | 2.17E+10 | 1.11E+9 |
6 | 7.21E+5 | 1 510.0 | 6.66E+5 | 1.53E+4 | 6.41E+8 | 4.70E+5 | 6.20E+8 | 8.05E+6 | 1.91E+10 | 1.24E+8 | 1.46E+10 | 1.34E+9 |
7 | 5.64E+5 | 1 126.0 | 5.26E+5 | 1.07E+4 | 5.02E+8 | 5.52E+5 | 4.76E+8 | 6.94E+6 | 1.53E+10 | 6.91E+7 | 1.31E+10 | 6.27E+8 |
8 | 1.30E+5 | 150.6 | 1.24E+5 | 2 206 | 2.84E+7 | 4.24E+4 | 1.95E+7 | 3.04E+6 | 1.04E+9 | 1.57E+7 | 1.01E+9 | 3.46E+7 |
9 | 5.45E+5 | 1 226.0 | 5.10E+5 | 7 034 | 1.35E+8 | 2.98E+5 | 1.09E+8 | 1.54E+7 | 1.48E+10 | 1.61E+7 | 1.39E+10 | 3.83E+8 |
10 | 1.29E+5 | 359.2 | 1.18E+5 | 2 678 | 2.13E+7 | 6.63E+4 | 5.53E+6 | 5.45E+6 | 6.36E+7 | 2.32E+6 | 2.26E+7 | 1.39E+7 |
实例 | SISO系统 | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
第1阶段 | 第2阶段 | 第3阶段 | ||||||||||
A | B | A | B | A | B | |||||||
均值 | 标准差 | 均值 | 标准差 | 均值 | 标准差 | 均值 | 标准差 | 均值 | 标准差 | 均值 | 标准差 | |
1 | 1.27E+6 | 9 484 | 8.22E+5 | 4.72E+5 | 1.40E+9 | 1.22E+7 | 1.16E+9 | 5.13E+7 | 3.10E+10 | 3.50E+8 | 1.53E+10 | 8.34E+9 |
2 | 1.00E+6 | 5 149 | 5.42E+5 | 3.99E+5 | 6.02E+8 | 4.78E+6 | 5.49E+8 | 1.45E+7 | 3.79E+10 | 1.57E+8 | 2.22E+10 | 5.97E+9 |
3 | 2.08E+6 | 2.47E+4 | 2.80E+5 | 6.40E+5 | 8.23E+8 | 1.67E+7 | 3.46E+7 | 1.13E+8 | 1.10E+11 | 7.63E+8 | 1.86E+10 | 2.64E+10 |
4 | 1.41E+6 | 1.27E+4 | 0 | 0 | 8.47E+8 | 1.96E+7 | 2.70E+8 | 2.74E+8 | 2.04E+11 | 2.09E+9 | 7.55E+10 | 4.86E+10 |
5 | 1.62E+6 | 1.67E+4 | 5.31E+5 | 6.26E+5 | 6.66E+8 | 8.56E+6 | 5.67E+8 | 3.97E+7 | 1.50E+11 | 7.54E+8 | 1.03E+11 | 1.45E+10 |
6 | 8.39E+7 | 2.81E+7 | 6.26E+5 | 3.02E+5 | 5.55E+8 | 1.34E+7 | 3.70E+8 | 1.72E+8 | 9.38E+10 | 1.21E+9 | 6.95E+10 | 1.03E+10 |
7 | 7.18E+7 | 1.34E+7 | 5.72E+5 | 3.27E+5 | 9.70E+8 | 7.15E+6 | 8.88E+8 | 3.14E+7 | 1.12E+11 | 2.63E+9 | 9.63E+10 | 1.34E+10 |
8 | 5.67E+7 | 1.06E+7 | 4.60E+4 | 9.77E+4 | 6.00E+8 | 1.24E+7 | 1.64E+8 | 2.12E+8 | 2.12E+11 | 7.82E+8 | 1.67E+11 | 1.98E+10 |
9 | 3.91E+7 | 7.26E+6 | 1.99E+5 | 2.57E+5 | 1.87E+9 | 1.64E+6 | 1.80E+9 | 1.54E+7 | 1.52E+11 | 6.70E+8 | 1.18E+11 | 1.13E+10 |
10 | 1.14E+8 | 2.10E+7 | 2.18E+6 | 8.85E+5 | 1.36E+9 | 1.30E+7 | 1.06E+9 | 3.74E+8 | 1.79E+11 | 1.38E+9 | 1.40E+11 | 1.47E+10 |
实例 | MIMO系统 | |||||||||||
第1阶段 | 第2阶段 | 第3阶段 | ||||||||||
A | B | A | B | A | B | |||||||
均值 | 标准差 | 均值 | 标准差 | 均值 | 标准差 | 均值 | 标准差 | 均值 | 标准差 | 均值 | 标准差 | |
1 | 1.89E+5 | 1 526 | 9 079 | 3.49E+4 | 8.57E+7 | 6.90E+5 | 4.29E+7 | 1.58E+7 | 3.42E+9 | 1.26E+8 | 1.62E+8 | 4.13E+8 |
2 | 2.35E+6 | 1.23E+4 | 1.87E+6 | 6.02E+5 | 1.73E+9 | 1.62E+7 | 8.63E+8 | 7.27E+8 | 1.77E+10 | 7.02E+8 | 3.01E+9 | 4.03E+9 |
3 | 3.65E+6 | 2.41E+4 | 1.57E+6 | 1.54E+6 | 3.45E+8 | 7.84E+6 | 5.41E+6 | 2.96E+7 | 3.60E+10 | 4.69E+9 | 3.47E+9 | 9.67E+9 |
4 | 3.03E+5 | 3 423 | 1.22E+5 | 9.71E+4 | 1.04E+7 | 7.04E+5 | 0 | 0 | 2.25E+9 | 1.55E+8 | 7.18E+6 | 3.09E+7 |
5 | 1.47E+6 | 1.04E+4 | 1.06E+6 | 4.92E+5 | 1.39E+8 | 1.53E+7 | 4.43E+6 | 1.21E+7 | 2.67E+10 | 6.95E+8 | 1.09E+10 | 6.16E+9 |
6 | 3.28E+6 | 2.19E+4 | 3.05E+6 | 1.14E+5 | 1.46E+9 | 6.92E+6 | 1.37E+9 | 1.79E+7 | 1.57E+11 | 5.72E+8 | 1.32E+11 | 9.16E+9 |
7 | 1.74E+6 | 1.52E+4 | 6.19E+5 | 7.07E+5 | 1.27E+9 | 9.29E+6 | 4.34E+8 | 5.20E+8 | 5.03E+10 | 1.20E+9 | 2.33E+10 | 1.16E+10 |
8 | 2.63E+6 | 1.96E+4 | 2.72E+5 | 7.08E+5 | 3.92E+9 | 3.30E+7 | 2.94E+9 | 1.22E+9 | 2.67E+11 | 1.50E+9 | 1.84E+11 | 1.98E+10 |
9 | 1.90E+6 | 1.63E+4 | 9.76E+5 | 7.78E+5 | 3.58E+8 | 5.49E+6 | 4.32E+7 | 9.10E+7 | 9.16E+10 | 1.94E+9 | 5.70E+10 | 1.54E+10 |
10 | 2.89E+6 | 1.99E+4 | 1.67E+6 | 1.23E+6 | 1.21E+9 | 7.46E+6 | 1.11E+9 | 2.66E+7 | 4.95E+10 | 1.59E+9 | 1.13E+9 | 3.89E+9 |
Tab. 9 Hypervolume (mean and standard deviation) results of two algorithms in complex system
实例 | SISO系统 | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
第1阶段 | 第2阶段 | 第3阶段 | ||||||||||
A | B | A | B | A | B | |||||||
均值 | 标准差 | 均值 | 标准差 | 均值 | 标准差 | 均值 | 标准差 | 均值 | 标准差 | 均值 | 标准差 | |
1 | 1.27E+6 | 9 484 | 8.22E+5 | 4.72E+5 | 1.40E+9 | 1.22E+7 | 1.16E+9 | 5.13E+7 | 3.10E+10 | 3.50E+8 | 1.53E+10 | 8.34E+9 |
2 | 1.00E+6 | 5 149 | 5.42E+5 | 3.99E+5 | 6.02E+8 | 4.78E+6 | 5.49E+8 | 1.45E+7 | 3.79E+10 | 1.57E+8 | 2.22E+10 | 5.97E+9 |
3 | 2.08E+6 | 2.47E+4 | 2.80E+5 | 6.40E+5 | 8.23E+8 | 1.67E+7 | 3.46E+7 | 1.13E+8 | 1.10E+11 | 7.63E+8 | 1.86E+10 | 2.64E+10 |
4 | 1.41E+6 | 1.27E+4 | 0 | 0 | 8.47E+8 | 1.96E+7 | 2.70E+8 | 2.74E+8 | 2.04E+11 | 2.09E+9 | 7.55E+10 | 4.86E+10 |
5 | 1.62E+6 | 1.67E+4 | 5.31E+5 | 6.26E+5 | 6.66E+8 | 8.56E+6 | 5.67E+8 | 3.97E+7 | 1.50E+11 | 7.54E+8 | 1.03E+11 | 1.45E+10 |
6 | 8.39E+7 | 2.81E+7 | 6.26E+5 | 3.02E+5 | 5.55E+8 | 1.34E+7 | 3.70E+8 | 1.72E+8 | 9.38E+10 | 1.21E+9 | 6.95E+10 | 1.03E+10 |
7 | 7.18E+7 | 1.34E+7 | 5.72E+5 | 3.27E+5 | 9.70E+8 | 7.15E+6 | 8.88E+8 | 3.14E+7 | 1.12E+11 | 2.63E+9 | 9.63E+10 | 1.34E+10 |
8 | 5.67E+7 | 1.06E+7 | 4.60E+4 | 9.77E+4 | 6.00E+8 | 1.24E+7 | 1.64E+8 | 2.12E+8 | 2.12E+11 | 7.82E+8 | 1.67E+11 | 1.98E+10 |
9 | 3.91E+7 | 7.26E+6 | 1.99E+5 | 2.57E+5 | 1.87E+9 | 1.64E+6 | 1.80E+9 | 1.54E+7 | 1.52E+11 | 6.70E+8 | 1.18E+11 | 1.13E+10 |
10 | 1.14E+8 | 2.10E+7 | 2.18E+6 | 8.85E+5 | 1.36E+9 | 1.30E+7 | 1.06E+9 | 3.74E+8 | 1.79E+11 | 1.38E+9 | 1.40E+11 | 1.47E+10 |
实例 | MIMO系统 | |||||||||||
第1阶段 | 第2阶段 | 第3阶段 | ||||||||||
A | B | A | B | A | B | |||||||
均值 | 标准差 | 均值 | 标准差 | 均值 | 标准差 | 均值 | 标准差 | 均值 | 标准差 | 均值 | 标准差 | |
1 | 1.89E+5 | 1 526 | 9 079 | 3.49E+4 | 8.57E+7 | 6.90E+5 | 4.29E+7 | 1.58E+7 | 3.42E+9 | 1.26E+8 | 1.62E+8 | 4.13E+8 |
2 | 2.35E+6 | 1.23E+4 | 1.87E+6 | 6.02E+5 | 1.73E+9 | 1.62E+7 | 8.63E+8 | 7.27E+8 | 1.77E+10 | 7.02E+8 | 3.01E+9 | 4.03E+9 |
3 | 3.65E+6 | 2.41E+4 | 1.57E+6 | 1.54E+6 | 3.45E+8 | 7.84E+6 | 5.41E+6 | 2.96E+7 | 3.60E+10 | 4.69E+9 | 3.47E+9 | 9.67E+9 |
4 | 3.03E+5 | 3 423 | 1.22E+5 | 9.71E+4 | 1.04E+7 | 7.04E+5 | 0 | 0 | 2.25E+9 | 1.55E+8 | 7.18E+6 | 3.09E+7 |
5 | 1.47E+6 | 1.04E+4 | 1.06E+6 | 4.92E+5 | 1.39E+8 | 1.53E+7 | 4.43E+6 | 1.21E+7 | 2.67E+10 | 6.95E+8 | 1.09E+10 | 6.16E+9 |
6 | 3.28E+6 | 2.19E+4 | 3.05E+6 | 1.14E+5 | 1.46E+9 | 6.92E+6 | 1.37E+9 | 1.79E+7 | 1.57E+11 | 5.72E+8 | 1.32E+11 | 9.16E+9 |
7 | 1.74E+6 | 1.52E+4 | 6.19E+5 | 7.07E+5 | 1.27E+9 | 9.29E+6 | 4.34E+8 | 5.20E+8 | 5.03E+10 | 1.20E+9 | 2.33E+10 | 1.16E+10 |
8 | 2.63E+6 | 1.96E+4 | 2.72E+5 | 7.08E+5 | 3.92E+9 | 3.30E+7 | 2.94E+9 | 1.22E+9 | 2.67E+11 | 1.50E+9 | 1.84E+11 | 1.98E+10 |
9 | 1.90E+6 | 1.63E+4 | 9.76E+5 | 7.78E+5 | 3.58E+8 | 5.49E+6 | 4.32E+7 | 9.10E+7 | 9.16E+10 | 1.94E+9 | 5.70E+10 | 1.54E+10 |
10 | 2.89E+6 | 1.99E+4 | 1.67E+6 | 1.23E+6 | 1.21E+9 | 7.46E+6 | 1.11E+9 | 2.66E+7 | 4.95E+10 | 1.59E+9 | 1.13E+9 | 3.89E+9 |
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