《计算机应用》唯一官方网站 ›› 2022, Vol. 42 ›› Issue (5): 1367-1374.DOI: 10.11772/j.issn.1001-9081.2021030505
所属专题: 人工智能
收稿日期:
2021-04-02
修回日期:
2021-06-01
接受日期:
2021-06-02
发布日期:
2022-06-11
出版日期:
2022-05-10
通讯作者:
孟晗
作者简介:
孟晗(1996—),女,河南漯河人,硕士研究生,主要研究方向:系统工程、智能优化 menghan_usst@163.com基金资助:
Han MENG(), Liang MA, Yong LIU
Received:
2021-04-02
Revised:
2021-06-01
Accepted:
2021-06-02
Online:
2022-06-11
Published:
2022-05-10
Contact:
Han MENG
About author:
MENG Han, born in 1996,M. S. candidate. Her research interestsinclude system engineering,intelligent optimization.Supported by:
摘要:
针对简单人类学习优化(SHLO)算法寻优精度低和收敛慢的问题,提出了一种融合学习心理学的人类学习优化算法(LPHLO)。首先,结合学习心理学中的小组学习(TBL)理论引入TBL算子,从而在个体经验、社会经验的基础上,增加了小组经验来对个体学习状态进行控制,避免算法早熟收敛;然后,结合记忆编码理论提出了动态调参策略,从而实现个体信息、社会信息、团队信息的有效融合,更好地平衡了算法局部探索和全局开发的能力。选取典型的组合优化难题——背包问题中的两种算例,即单约束背包问题、多约束背包问题进行仿真实验,实验结果表明,所提LPHLO与基本的SHLO算法、遗传算法(GA)和二进制粒子群优化(BPSO)算法等算法相比,在寻优精度和收敛速度方面更具优势,具有更好的解决实际问题的能力。
中图分类号:
孟晗, 马良, 刘勇. 融合学习心理学的人类学习优化算法[J]. 计算机应用, 2022, 42(5): 1367-1374.
Han MENG, Liang MA, Yong LIU. Human learning optimization algorithm based on learning psychology[J]. Journal of Computer Applications, 2022, 42(5): 1367-1374.
问题类型 | 算法 | 最优值 | 平均值 | 最差值 | 标准差 | 问题类型 | 算法 | 最优值 | 平均值 | 最差值 | 标准差 |
---|---|---|---|---|---|---|---|---|---|---|---|
KP1.100 | BBA | 6 358 | 6 102 | 2 856 | 633.56 | KP2.100 | BBA | 6 172 | 5 895 | 2 353 | 686.45 |
BPSO | 6 546 | 6 523 | 6 507 | 9.07 | BPSO | 6 289 | 6 225 | 6 116 | 39.26 | ||
GA | 6 551 | 6 529 | 6 372 | 31.70 | GA | 6 379 | 6 368 | 6 338 | 10.39 | ||
SHLO | 6 551 | 6 551 | 6 550 | 0.50 | SHLO | 6 379 | 6 379 | 6 378 | 0.31 | ||
ASHLO | 6 551 | 6 551 | 6 550 | 0.49 | ASHLO | 6 379 | 6 379 | 6 378 | 0.31 | ||
LPHLO | 6 551 | 6 551 | 6 550 | 0.47 | LPHLO | 6 379 | 6 379 | 6 378 | 0.25 | ||
KP1.200 | BBA | 12 288 | 11 538 | 6 030 | 1 118.19 | KP2.200 | BBA | 12 419 | 11 558 | 5 965 | 1 170.37 |
BPSO | 14 595 | 14 550 | 14 527 | 14.26 | BPSO | 14 752 | 14 732 | 14 714 | 8.63 | ||
GA | 14 618 | 14 607 | 14 601 | 8.38 | GA | 14 761 | 14 761 | 14 758 | 0.55 | ||
SHLO | 14 617 | 14 602 | 14 597 | 4.19 | SHLO | 14 761 | 14 761 | 14 761 | 0 | ||
ASHLO | 14 618 | 14 604 | 14 599 | 6.35 | ASHLO | 14 761 | 14 761 | 14 761 | 0 | ||
LPHLO | 14 618 | 14 604 | 14 601 | 6.78 | LPHLO | 14 761 | 14 761 | 14 761 | 0 | ||
KP1.400 | BBA | 21 957 | 20 847 | 13 825 | 1 511.11 | KP2.400 | BBA | 22 702 | 21 363 | 13 147 | 1 736.72 |
BPSO | 25 464 | 25 350 | 25 304 | 35.80 | BPSO | 26 452 | 26 418 | 26 389 | 16.24 | ||
GA | 26 706 | 266 975 | 26 662 | 8.84 | GA | 27 589 | 27 578 | 27 565 | 7.68 | ||
SHLO | 26 708 | 26 701 | 26 692 | 5.91 | SHLO | 27 588 | 27 586 | 27 573 | 2.78 | ||
ASHLO | 26 708 | 26 703 | 26 692 | 4.59 | ASHLO | 27 588 | 27 586 | 27 581 | 1.72 | ||
LPHLO | 26 708 | 26 704 | 26 693 | 4.97 | LPHLO | 27 589 | 27 586 | 27 583 | 1.09 | ||
KP1.600 | BBA | 30 793 | 29 613 | 19 949 | 1 995.92 | KP2.600 | BBA | 31 528 | 29 955 | 20 298 | 2 026.92 |
BPSO | 36 169 | 35 694 | 35 356 | 178.49 | BPSO | 38 024 | 37 955 | 37 900 | 27.83 | ||
GA | 39 537 | 39 521 | 39 497 | 9.20 | GA | 40 212 | 40 196 | 40 174 | 9.74 | ||
SHLO | 39 541 | 39 530 | 39 512 | 7.84 | SHLO | 40 218 | 40 208 | 40 193 | 6.07 | ||
ASHLO | 39 541 | 39 533 | 39 525 | 5.64 | ASHLO | 40 218 | 40 210 | 40 201 | 4.65 | ||
LPHLO | 39 541 | 39 538 | 39 529 | 3.30 | LPHLO | 40 219 | 40 213 | 40 206 | 3.26 | ||
KP1.800 | BBA | 41 234 | 38 493 | 26 759 | 2 477.93 | KP2.800 | BBA | 40 591 | 38 734 | 26 569 | 2 434.53 |
BPSO | 48 281 | 47 311 | 40 982 | 1 689.95 | BPSO | 49 612 | 49 547 | 49 494 | 32.12 | ||
GA | 52 812 | 52 786 | 52 762 | 12.57 | GA | 53 063 | 53 036 | 53 008 | 14.06 | ||
SHLO | 52 834 | 52 813 | 52 776 | 13.48 | SHLO | 53 085 | 53 075 | 53 052 | 6.30 | ||
ASHLO | 52 842 | 52 829 | 52 810 | 7.02 | ASHLO | 53 087 | 53 073 | 53 036 | 10.49 | ||
LPHLO | 52 843 | 52 837 | 52 816 | 5.74 | LPHLO | 53 088 | 53 081 | 53 069 | 4.62 | ||
KP1.1000 | BBA | 50 637 | 47 908 | 33 923 | 2 909.28 | KP2.1000 | BBA | 49 809 | 47 374 | 33 431 | 3 004.26 |
BPSO | 63 204 | 62 971 | 62 776 | 96.42 | BPSO | 60 142 | 59 818 | 59 476 | 166.92 | ||
GA | 68 092 | 68 058 | 68 023 | 16.61 | GA | 65 572 | 65 541 | 65 509 | 14.13 | ||
SHLO | 68 121 | 68 112 | 68 093 | 6.47 | SHLO | 65 614 | 65 605 | 65 581 | 7.72 | ||
ASHLO | 68 121 | 68 115 | 68 106 | 3.67 | ASHLO | 65 615 | 65 610 | 65 606 | 2.88 | ||
LPHLO | 68 121 | 68 116 | 68 106 | 3.17 | LPHLO | 65 616 | 65 613 | 65 606 | 3.39 | ||
KP1.1200 | BBA | 57 795 | 55 614 | 41 638 | 2 868.58 | KP2.1200 | BBA | 58 356 | 56 143 | 41 655 | 3 098.39 |
BPSO | 85 039 | 84 913 | 84 775 | 69.94 | BPSO | 84 606 | 84 407 | 84 259 | 103.61 | ||
GA | 86 755 | 86 715 | 86 684 | 16.49 | GA | 86 747 | 86 714 | 86 688 | 17.31 | ||
SHLO | 86 774 | 86 756 | 86 743 | 14.20 | SHLO | 86 788 | 86 768 | 86 737 | 11.90 | ||
ASHLO | 86 784 | 86 766 | 86 744 | 12.23 | ASHLO | 86 789 | 86 774 | 86 763 | 10.53 | ||
LPHLO | 86 788 | 86 767 | 86 744 | 10.60 | LPHLO | 86 790 | 86 778 | 86 764 | 10.28 | ||
KP1.1500 | BBA | 72 594 | 69 367 | 52 228 | 3 559.44 | KP2.1500 | BBA | 71 846 | 69 584 | 52 150 | 3 695.93 |
BPSO | 97 948 | 97 741 | 97 510 | 124.33 | BPSO | 98 357 | 98 029 | 97 657 | 165.64 | ||
GA | 104 228 | 104 140 | 104 045 | 42.81 | GA | 104 267 | 104 201 | 104 078 | 45.16 | ||
SHLO | 104 418 | 104 404 | 104 373 | 10.26 | SHLO | 104 503 | 104 492 | 104 475 | 8.67 | ||
ASHLO | 104 418 | 104 408 | 104 392 | 5.90 | ASHLO | 104 503 | 104 494 | 104 472 | 7.73 | ||
LPHLO | 104 423 | 104 415 | 104 404 | 5.62 | LPHLO | 104 508 | 104 498 | 104 490 | 5.50 | ||
KP1.2000 | BBA | 93 760 | 90 467 | 70 368 | 4 323.94 | KP2.2000 | BBA | 93 262 | 89 666 | 69 685 | 4 167.92 |
BPSO | 120 324 | 106 576 | 101 924 | 6 359.24 | BPSO | 123 392 | 122 914 | 122 720 | 190.03 | ||
GA | 133 073 | 132 909 | 132 678 | 92.64 | GA | 133 818 | 133 700 | 133 487 | 77.90 | ||
SHLO | 133 776 | 133 761 | 133 748 | 7.06 | SHLO | 134 549 | 134 537 | 134 516 | 8.24 | ||
ASHLO | 133 775 | 133 765 | 133 752 | 6.43 | ASHLO | 134 551 | 134 543 | 134 517 | 7.29 | ||
LPHLO | 133 778 | 133 772 | 133 755 | 5.74 | LPHLO | 134 554 | 134 549 | 134 541 | 3.38 | ||
KP1.3000 | BBA | 134 038 | 130 121 | 106 456 | 5 026.56 | KP2.3000 | BBA | 133 705 | 130 430 | 106 494 | 4 857.61 |
BPSO | 148 807 | 147 167 | 144 189 | 1 346.99 | BPSO | 149 919 | 144 638 | 134 607 | 5 378.50 | ||
GA | 176 621 | 176 287 | 175 923 | 175.54 | GA | 175 900 | 175 579 | 175 251 | 155.99 | ||
SHLO | 179 266 | 179 252 | 179 232 | 8.61 | SHLO | 178 580 | 178 556 | 178 530 | 12.78 | ||
ASHLO | 179 270 | 179 254 | 179 229 | 10.37 | ASHLO | 178 581 | 178 565 | 178 544 | 9.20 | ||
LPHLO | 179 280 | 179 271 | 179 264 | 4.12 | LPHLO | 178 593 | 178 586 | 178 575 | 4.31 |
表1 单约束背包问题的结果对比
Tab. 1 Comparison of results on 0-1KPs
问题类型 | 算法 | 最优值 | 平均值 | 最差值 | 标准差 | 问题类型 | 算法 | 最优值 | 平均值 | 最差值 | 标准差 |
---|---|---|---|---|---|---|---|---|---|---|---|
KP1.100 | BBA | 6 358 | 6 102 | 2 856 | 633.56 | KP2.100 | BBA | 6 172 | 5 895 | 2 353 | 686.45 |
BPSO | 6 546 | 6 523 | 6 507 | 9.07 | BPSO | 6 289 | 6 225 | 6 116 | 39.26 | ||
GA | 6 551 | 6 529 | 6 372 | 31.70 | GA | 6 379 | 6 368 | 6 338 | 10.39 | ||
SHLO | 6 551 | 6 551 | 6 550 | 0.50 | SHLO | 6 379 | 6 379 | 6 378 | 0.31 | ||
ASHLO | 6 551 | 6 551 | 6 550 | 0.49 | ASHLO | 6 379 | 6 379 | 6 378 | 0.31 | ||
LPHLO | 6 551 | 6 551 | 6 550 | 0.47 | LPHLO | 6 379 | 6 379 | 6 378 | 0.25 | ||
KP1.200 | BBA | 12 288 | 11 538 | 6 030 | 1 118.19 | KP2.200 | BBA | 12 419 | 11 558 | 5 965 | 1 170.37 |
BPSO | 14 595 | 14 550 | 14 527 | 14.26 | BPSO | 14 752 | 14 732 | 14 714 | 8.63 | ||
GA | 14 618 | 14 607 | 14 601 | 8.38 | GA | 14 761 | 14 761 | 14 758 | 0.55 | ||
SHLO | 14 617 | 14 602 | 14 597 | 4.19 | SHLO | 14 761 | 14 761 | 14 761 | 0 | ||
ASHLO | 14 618 | 14 604 | 14 599 | 6.35 | ASHLO | 14 761 | 14 761 | 14 761 | 0 | ||
LPHLO | 14 618 | 14 604 | 14 601 | 6.78 | LPHLO | 14 761 | 14 761 | 14 761 | 0 | ||
KP1.400 | BBA | 21 957 | 20 847 | 13 825 | 1 511.11 | KP2.400 | BBA | 22 702 | 21 363 | 13 147 | 1 736.72 |
BPSO | 25 464 | 25 350 | 25 304 | 35.80 | BPSO | 26 452 | 26 418 | 26 389 | 16.24 | ||
GA | 26 706 | 266 975 | 26 662 | 8.84 | GA | 27 589 | 27 578 | 27 565 | 7.68 | ||
SHLO | 26 708 | 26 701 | 26 692 | 5.91 | SHLO | 27 588 | 27 586 | 27 573 | 2.78 | ||
ASHLO | 26 708 | 26 703 | 26 692 | 4.59 | ASHLO | 27 588 | 27 586 | 27 581 | 1.72 | ||
LPHLO | 26 708 | 26 704 | 26 693 | 4.97 | LPHLO | 27 589 | 27 586 | 27 583 | 1.09 | ||
KP1.600 | BBA | 30 793 | 29 613 | 19 949 | 1 995.92 | KP2.600 | BBA | 31 528 | 29 955 | 20 298 | 2 026.92 |
BPSO | 36 169 | 35 694 | 35 356 | 178.49 | BPSO | 38 024 | 37 955 | 37 900 | 27.83 | ||
GA | 39 537 | 39 521 | 39 497 | 9.20 | GA | 40 212 | 40 196 | 40 174 | 9.74 | ||
SHLO | 39 541 | 39 530 | 39 512 | 7.84 | SHLO | 40 218 | 40 208 | 40 193 | 6.07 | ||
ASHLO | 39 541 | 39 533 | 39 525 | 5.64 | ASHLO | 40 218 | 40 210 | 40 201 | 4.65 | ||
LPHLO | 39 541 | 39 538 | 39 529 | 3.30 | LPHLO | 40 219 | 40 213 | 40 206 | 3.26 | ||
KP1.800 | BBA | 41 234 | 38 493 | 26 759 | 2 477.93 | KP2.800 | BBA | 40 591 | 38 734 | 26 569 | 2 434.53 |
BPSO | 48 281 | 47 311 | 40 982 | 1 689.95 | BPSO | 49 612 | 49 547 | 49 494 | 32.12 | ||
GA | 52 812 | 52 786 | 52 762 | 12.57 | GA | 53 063 | 53 036 | 53 008 | 14.06 | ||
SHLO | 52 834 | 52 813 | 52 776 | 13.48 | SHLO | 53 085 | 53 075 | 53 052 | 6.30 | ||
ASHLO | 52 842 | 52 829 | 52 810 | 7.02 | ASHLO | 53 087 | 53 073 | 53 036 | 10.49 | ||
LPHLO | 52 843 | 52 837 | 52 816 | 5.74 | LPHLO | 53 088 | 53 081 | 53 069 | 4.62 | ||
KP1.1000 | BBA | 50 637 | 47 908 | 33 923 | 2 909.28 | KP2.1000 | BBA | 49 809 | 47 374 | 33 431 | 3 004.26 |
BPSO | 63 204 | 62 971 | 62 776 | 96.42 | BPSO | 60 142 | 59 818 | 59 476 | 166.92 | ||
GA | 68 092 | 68 058 | 68 023 | 16.61 | GA | 65 572 | 65 541 | 65 509 | 14.13 | ||
SHLO | 68 121 | 68 112 | 68 093 | 6.47 | SHLO | 65 614 | 65 605 | 65 581 | 7.72 | ||
ASHLO | 68 121 | 68 115 | 68 106 | 3.67 | ASHLO | 65 615 | 65 610 | 65 606 | 2.88 | ||
LPHLO | 68 121 | 68 116 | 68 106 | 3.17 | LPHLO | 65 616 | 65 613 | 65 606 | 3.39 | ||
KP1.1200 | BBA | 57 795 | 55 614 | 41 638 | 2 868.58 | KP2.1200 | BBA | 58 356 | 56 143 | 41 655 | 3 098.39 |
BPSO | 85 039 | 84 913 | 84 775 | 69.94 | BPSO | 84 606 | 84 407 | 84 259 | 103.61 | ||
GA | 86 755 | 86 715 | 86 684 | 16.49 | GA | 86 747 | 86 714 | 86 688 | 17.31 | ||
SHLO | 86 774 | 86 756 | 86 743 | 14.20 | SHLO | 86 788 | 86 768 | 86 737 | 11.90 | ||
ASHLO | 86 784 | 86 766 | 86 744 | 12.23 | ASHLO | 86 789 | 86 774 | 86 763 | 10.53 | ||
LPHLO | 86 788 | 86 767 | 86 744 | 10.60 | LPHLO | 86 790 | 86 778 | 86 764 | 10.28 | ||
KP1.1500 | BBA | 72 594 | 69 367 | 52 228 | 3 559.44 | KP2.1500 | BBA | 71 846 | 69 584 | 52 150 | 3 695.93 |
BPSO | 97 948 | 97 741 | 97 510 | 124.33 | BPSO | 98 357 | 98 029 | 97 657 | 165.64 | ||
GA | 104 228 | 104 140 | 104 045 | 42.81 | GA | 104 267 | 104 201 | 104 078 | 45.16 | ||
SHLO | 104 418 | 104 404 | 104 373 | 10.26 | SHLO | 104 503 | 104 492 | 104 475 | 8.67 | ||
ASHLO | 104 418 | 104 408 | 104 392 | 5.90 | ASHLO | 104 503 | 104 494 | 104 472 | 7.73 | ||
LPHLO | 104 423 | 104 415 | 104 404 | 5.62 | LPHLO | 104 508 | 104 498 | 104 490 | 5.50 | ||
KP1.2000 | BBA | 93 760 | 90 467 | 70 368 | 4 323.94 | KP2.2000 | BBA | 93 262 | 89 666 | 69 685 | 4 167.92 |
BPSO | 120 324 | 106 576 | 101 924 | 6 359.24 | BPSO | 123 392 | 122 914 | 122 720 | 190.03 | ||
GA | 133 073 | 132 909 | 132 678 | 92.64 | GA | 133 818 | 133 700 | 133 487 | 77.90 | ||
SHLO | 133 776 | 133 761 | 133 748 | 7.06 | SHLO | 134 549 | 134 537 | 134 516 | 8.24 | ||
ASHLO | 133 775 | 133 765 | 133 752 | 6.43 | ASHLO | 134 551 | 134 543 | 134 517 | 7.29 | ||
LPHLO | 133 778 | 133 772 | 133 755 | 5.74 | LPHLO | 134 554 | 134 549 | 134 541 | 3.38 | ||
KP1.3000 | BBA | 134 038 | 130 121 | 106 456 | 5 026.56 | KP2.3000 | BBA | 133 705 | 130 430 | 106 494 | 4 857.61 |
BPSO | 148 807 | 147 167 | 144 189 | 1 346.99 | BPSO | 149 919 | 144 638 | 134 607 | 5 378.50 | ||
GA | 176 621 | 176 287 | 175 923 | 175.54 | GA | 175 900 | 175 579 | 175 251 | 155.99 | ||
SHLO | 179 266 | 179 252 | 179 232 | 8.61 | SHLO | 178 580 | 178 556 | 178 530 | 12.78 | ||
ASHLO | 179 270 | 179 254 | 179 229 | 10.37 | ASHLO | 178 581 | 178 565 | 178 544 | 9.20 | ||
LPHLO | 179 280 | 179 271 | 179 264 | 4.12 | LPHLO | 178 593 | 178 586 | 178 575 | 4.31 |
问题类型 | 已知最优值 | BBA | BPSO | GA | SHLO | ASHLO | LPHLO | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
最优值 | 平均值 | 最优值 | 平均值 | 最优值 | 平均值 | 最优值 | 平均值 | 最优值 | 平均值 | 最优值 | 平均值 | ||
5.100.00 | 24 381 | 21 969 | 21 201 | 22 163 | 20 303 | 23 657 | 23 105 | 24 381 | 24 190 | 24 312 | 24 220 | 24 381 | 24 241 |
5.100.04 | 23 991 | 21 313 | 20 793 | 22 020 | 20 949 | 23 527 | 23 076 | 23 947 | 23 812 | 23 959 | 23 830 | 23 991 | 23 897 |
5.100.06 | 25 591 | 22 488 | 21 800 | 22 788 | 21 833 | 24 915 | 24 363 | 25 591 | 25 376 | 25 591 | 25 359 | 25 591 | 25 444 |
5.100.08 | 24 216 | 21 574 | 20 850 | 22 445 | 20 884 | 23 737 | 23 038 | 24 204 | 24 028 | 24 204 | 24 088 | 24 216 | 24 136 |
5.100.11 | 42 545 | 40 048 | 39 626 | 40 224 | 39 354 | 42 204 | 41 570 | 42 470 | 42 360 | 42 545 | 42 405 | 42 545 | 42 427 |
5.100.14 | 42 218 | 39 914 | 39 310 | 40 193 | 38 932 | 41 902 | 41 312 | 42 218 | 42 073 | 42 218 | 42 065 | 42 218 | 42 124 |
5.100.16 | 42 009 | 39 338 | 39 018 | 39 487 | 38 655 | 41 677 | 41 061 | 41 980 | 41 846 | 41 980 | 41 841 | 42 009 | 41 910 |
5.100.19 | 44 554 | 42 124 | 41 584 | 42 363 | 41 216 | 44 328 | 43 558 | 44 529 | 44 432 | 44 554 | 44 448 | 44 554 | 44 479 |
5.100.20 | 59 822 | 57 572 | 57 077 | 57 929 | 57 036 | 59 503 | 58 904 | 59 822 | 59 709 | 59 799 | 59 710 | 59 822 | 59 776 |
5.100.21 | 62 081 | 59 912 | 59 285 | 60 438 | 59 409 | 61 756 | 61 264 | 61 983 | 61 923 | 62 081 | 61 923 | 62 081 | 61 970 |
5.100.22 | 59 802 | 57 805 | 56 987 | 57 961 | 57 143 | 59 596 | 59 167 | 59 760 | 59 678 | 59 802 | 59 702 | 59 802 | 59 717 |
5.100.24 | 61 091 | 59 338 | 58 126 | 58 928 | 58 017 | 60 869 | 60 451 | 61 055 | 60 993 | 61 079 | 61 002 | 61 091 | 61 023 |
5.100.26 | 61 538 | 59 547 | 58 773 | 59 765 | 58 880 | 61 266 | 60 757 | 61 519 | 61 400 | 61 538 | 61 400 | 61 538 | 61 450 |
5.100.28 | 59 453 | 56 993 | 56 591 | 57 498 | 56 465 | 59 105 | 58 658 | 59 453 | 59 286 | 59 453 | 59 309 | 59 453 | 59 352 |
5.100.29 | 59 965 | 57 953 | 57 150 | 58 185 | 57 011 | 59 432 | 59 126 | 59 960 | 59 864 | 59 960 | 59 885 | 59 965 | 59 914 |
10.100.00 | 23 064 | 20 018 | 19 439 | 20 327 | 19 223 | 22 518 | 21 999 | 22 981 | 22 834 | 23 055 | 22 860 | 23 064 | 22 941 |
10.100.01 | 22 801 | 19 997 | 19 099 | 20 308 | 19 342 | 22 175 | 21 545 | 22 731 | 22 431 | 22 731 | 22 453 | 22 801 | 22 569 |
10.100.04 | 22 751 | 19 838 | 19 165 | 20 772 | 19 356 | 22 180 | 21 629 | 22 534 | 22 367 | 22 624 | 22 429 | 22 751 | 22 491 |
10.100.06 | 21 875 | 18 899 | 18 233 | 19 232 | 18 275 | 21 265 | 20 800 | 21 771 | 21 635 | 21 821 | 21 648 | 21 875 | 21 688 |
10.100.07 | 22 635 | 19 833 | 19 030 | 20 207 | 19 347 | 22 360 | 21 423 | 22 476 | 22 294 | 22 551 | 22 322 | 22 635 | 22 387 |
10.100.09 | 22 702 | 19 667 | 19 059 | 20 742 | 19 340 | 22 235 | 21 500 | 22 702 | 22 313 | 22 486 | 22 338 | 22 702 | 22 424 |
10.100.12 | 42 401 | 39 918 | 39 315 | 40 141 | 38 890 | 41 875 | 41 191 | 42 311 | 42 165 | 42 318 | 42 190 | 42 401 | 42 264 |
10.100.15 | 42 995 | 40 510 | 39 859 | 40 480 | 39 437 | 42 497 | 42 029 | 42 917 | 42 705 | 42 995 | 42 736 | 42 995 | 42 815 |
10.100.18 | 42 212 | 39 862 | 39 051 | 39 819 | 38 609 | 41 604 | 41 104 | 42 153 | 42 003 | 42 212 | 42 017 | 42 212 | 42 071 |
10.100.20 | 57 375 | 55 214 | 54 402 | 55 428 | 54 456 | 56 977 | 56 568 | 57 375 | 57 183 | 57 353 | 57 185 | 57 375 | 57 231 |
10.100.22 | 58 391 | 56 701 | 55 718 | 56 776 | 55 704 | 57 920 | 57 544 | 58 391 | 58 192 | 58 391 | 58 201 | 58 391 | 58 243 |
10.100.23 | 61 966 | 60 039 | 59 150 | 60 039 | 59 068 | 61 698 | 61 222 | 61 966 | 61 773 | 61 875 | 61 765 | 61 966 | 61 823 |
10.100.25 | 61 437 | 59 204 | 58 533 | 59 257 | 58 357 | 60 912 | 60 440 | 61 336 | 61 162 | 61 336 | 61 188 | 61 437 | 61 233 |
10.100.27 | 59 391 | 56 804 | 56 358 | 57 102 | 56 257 | 59 236 | 58 511 | 59 391 | 59 224 | 59 366 | 59 247 | 59 391 | 59 271 |
10.100.29 | 60 633 | 58 083 | 57 384 | 58 290 | 57 356 | 60 482 | 60 132 | 60 633 | 60 562 | 60 633 | 60 567 | 60 633 | 60 581 |
表2 多约束背包问题的结果对比
Tab. 2 Comparison of results on MKPs
问题类型 | 已知最优值 | BBA | BPSO | GA | SHLO | ASHLO | LPHLO | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
最优值 | 平均值 | 最优值 | 平均值 | 最优值 | 平均值 | 最优值 | 平均值 | 最优值 | 平均值 | 最优值 | 平均值 | ||
5.100.00 | 24 381 | 21 969 | 21 201 | 22 163 | 20 303 | 23 657 | 23 105 | 24 381 | 24 190 | 24 312 | 24 220 | 24 381 | 24 241 |
5.100.04 | 23 991 | 21 313 | 20 793 | 22 020 | 20 949 | 23 527 | 23 076 | 23 947 | 23 812 | 23 959 | 23 830 | 23 991 | 23 897 |
5.100.06 | 25 591 | 22 488 | 21 800 | 22 788 | 21 833 | 24 915 | 24 363 | 25 591 | 25 376 | 25 591 | 25 359 | 25 591 | 25 444 |
5.100.08 | 24 216 | 21 574 | 20 850 | 22 445 | 20 884 | 23 737 | 23 038 | 24 204 | 24 028 | 24 204 | 24 088 | 24 216 | 24 136 |
5.100.11 | 42 545 | 40 048 | 39 626 | 40 224 | 39 354 | 42 204 | 41 570 | 42 470 | 42 360 | 42 545 | 42 405 | 42 545 | 42 427 |
5.100.14 | 42 218 | 39 914 | 39 310 | 40 193 | 38 932 | 41 902 | 41 312 | 42 218 | 42 073 | 42 218 | 42 065 | 42 218 | 42 124 |
5.100.16 | 42 009 | 39 338 | 39 018 | 39 487 | 38 655 | 41 677 | 41 061 | 41 980 | 41 846 | 41 980 | 41 841 | 42 009 | 41 910 |
5.100.19 | 44 554 | 42 124 | 41 584 | 42 363 | 41 216 | 44 328 | 43 558 | 44 529 | 44 432 | 44 554 | 44 448 | 44 554 | 44 479 |
5.100.20 | 59 822 | 57 572 | 57 077 | 57 929 | 57 036 | 59 503 | 58 904 | 59 822 | 59 709 | 59 799 | 59 710 | 59 822 | 59 776 |
5.100.21 | 62 081 | 59 912 | 59 285 | 60 438 | 59 409 | 61 756 | 61 264 | 61 983 | 61 923 | 62 081 | 61 923 | 62 081 | 61 970 |
5.100.22 | 59 802 | 57 805 | 56 987 | 57 961 | 57 143 | 59 596 | 59 167 | 59 760 | 59 678 | 59 802 | 59 702 | 59 802 | 59 717 |
5.100.24 | 61 091 | 59 338 | 58 126 | 58 928 | 58 017 | 60 869 | 60 451 | 61 055 | 60 993 | 61 079 | 61 002 | 61 091 | 61 023 |
5.100.26 | 61 538 | 59 547 | 58 773 | 59 765 | 58 880 | 61 266 | 60 757 | 61 519 | 61 400 | 61 538 | 61 400 | 61 538 | 61 450 |
5.100.28 | 59 453 | 56 993 | 56 591 | 57 498 | 56 465 | 59 105 | 58 658 | 59 453 | 59 286 | 59 453 | 59 309 | 59 453 | 59 352 |
5.100.29 | 59 965 | 57 953 | 57 150 | 58 185 | 57 011 | 59 432 | 59 126 | 59 960 | 59 864 | 59 960 | 59 885 | 59 965 | 59 914 |
10.100.00 | 23 064 | 20 018 | 19 439 | 20 327 | 19 223 | 22 518 | 21 999 | 22 981 | 22 834 | 23 055 | 22 860 | 23 064 | 22 941 |
10.100.01 | 22 801 | 19 997 | 19 099 | 20 308 | 19 342 | 22 175 | 21 545 | 22 731 | 22 431 | 22 731 | 22 453 | 22 801 | 22 569 |
10.100.04 | 22 751 | 19 838 | 19 165 | 20 772 | 19 356 | 22 180 | 21 629 | 22 534 | 22 367 | 22 624 | 22 429 | 22 751 | 22 491 |
10.100.06 | 21 875 | 18 899 | 18 233 | 19 232 | 18 275 | 21 265 | 20 800 | 21 771 | 21 635 | 21 821 | 21 648 | 21 875 | 21 688 |
10.100.07 | 22 635 | 19 833 | 19 030 | 20 207 | 19 347 | 22 360 | 21 423 | 22 476 | 22 294 | 22 551 | 22 322 | 22 635 | 22 387 |
10.100.09 | 22 702 | 19 667 | 19 059 | 20 742 | 19 340 | 22 235 | 21 500 | 22 702 | 22 313 | 22 486 | 22 338 | 22 702 | 22 424 |
10.100.12 | 42 401 | 39 918 | 39 315 | 40 141 | 38 890 | 41 875 | 41 191 | 42 311 | 42 165 | 42 318 | 42 190 | 42 401 | 42 264 |
10.100.15 | 42 995 | 40 510 | 39 859 | 40 480 | 39 437 | 42 497 | 42 029 | 42 917 | 42 705 | 42 995 | 42 736 | 42 995 | 42 815 |
10.100.18 | 42 212 | 39 862 | 39 051 | 39 819 | 38 609 | 41 604 | 41 104 | 42 153 | 42 003 | 42 212 | 42 017 | 42 212 | 42 071 |
10.100.20 | 57 375 | 55 214 | 54 402 | 55 428 | 54 456 | 56 977 | 56 568 | 57 375 | 57 183 | 57 353 | 57 185 | 57 375 | 57 231 |
10.100.22 | 58 391 | 56 701 | 55 718 | 56 776 | 55 704 | 57 920 | 57 544 | 58 391 | 58 192 | 58 391 | 58 201 | 58 391 | 58 243 |
10.100.23 | 61 966 | 60 039 | 59 150 | 60 039 | 59 068 | 61 698 | 61 222 | 61 966 | 61 773 | 61 875 | 61 765 | 61 966 | 61 823 |
10.100.25 | 61 437 | 59 204 | 58 533 | 59 257 | 58 357 | 60 912 | 60 440 | 61 336 | 61 162 | 61 336 | 61 188 | 61 437 | 61 233 |
10.100.27 | 59 391 | 56 804 | 56 358 | 57 102 | 56 257 | 59 236 | 58 511 | 59 391 | 59 224 | 59 366 | 59 247 | 59 391 | 59 271 |
10.100.29 | 60 633 | 58 083 | 57 384 | 58 290 | 57 356 | 60 482 | 60 132 | 60 633 | 60 562 | 60 633 | 60 567 | 60 633 | 60 581 |
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