吉林大学学报(工学版) ›› 2025, Vol. 55 ›› Issue (7): 2464-2474.doi: 10.13229/j.cnki.jdxbgxb.20231086

• 通信与控制工程 • 上一篇    

非支配排序粒子群遗传算法解决车辆位置路由问题

刘琼昕1,2(),王甜甜2,王亚男2   

  1. 1.北京理工大学 北京市海量语言信息处理与云计算应用工程技术研究中心，北京 100081
    2.北京理工大学 计算机学院，北京 100081
  • 收稿日期:2023-12-26 出版日期:2025-07-01 发布日期:2025-09-12
  • 作者简介:刘琼昕（1972-），女，副教授，博士. 研究方向：人工智能. E-mail： summer@bit.edu.cn
  • 基金资助:
    国家自然科学基金项目(62072039)

Non-dominated sorted particle swarm genetic algorithm to solve vehicle location routing problems

Qiong-xin LIU1,2(),Tian-tian WANG2,Ya-nan WANG2   

  1. 1.Beijing Engineering Applications Research Center on High Volume Language Information Processing and Cloud Computing，Beijing Institute of Technology，Beijing 100081，China
    2.School of Computer Science and Technology，Beijing Institute of Technology，Beijing 100081，China
  • Received:2023-12-26 Online:2025-07-01 Published:2025-09-12

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摘要：

提出一种混合全局局部搜索的非支配排序粒子群遗传算法，该算法能够有效解决车辆位置路由问题。全局搜索使用粒子群和遗传算法以提高收敛速度，使用第三代非支配排序遗传算法挑选种群下一代个体以保留种群多样性。局部搜索策略针对优质和次优个体进行优化，以提高得到更优解的概率，对种群中后1/12个体打乱用户顺序，提高种群质量。使用开放标准数据集将本文算法与基准算法对比，结果表明本文算法在种群质量、多样性上均更优，能够为车辆位置路由问题提供有效的解决方案。

关键词: 计算机应用, 车辆位置路由问题, 第三代非支配排序遗传算法, 粒子群算法, 遗传算法

Abstract:

A non-dominated sorted particle swarm genetic algorithm with hybrid global-local search is proposed， by which the vehicle location routing problem can be effectively solved. Both particle swarm optimization and genetic algorithm operators are utilized in the global search to improve convergence speed. The non-dominated sorting genetic algorithm III is employed so that population diversity is maintained. The local search strategy is applied separately to superior and inferior individuals， by which the probability of obtaining better solutions is increased. Additionally， the user orders of the last 1/12 individuals in the population are shuffled so that the overall population quality is enhanced. The proposed algorithm is compared with benchmark algorithms by using the open standard dataset， and it is demonstrated that population quality and diversity are better provided， and an effective solution to the vehicle location routing problem can be supplied.

Key words: computer application, vehicle location routing problem, non-dominated sorting genetic algorithm III, particle swarm optimization algorithm, genetic algorithm

中图分类号: 

  • TP391

图1

解向量示意图"

图2

LRP解决方案"

图3

交叉和变异操作"

表1

KBSN实例中实验结果对比"

算法实例车辆数量距离成本路线代价SM1SM2DM
HSNS-PSOGABar_8_2_X_NSrivastava86_8x23406.70928.545 97.9428.054122.190
Bar_12_2_X_NPerl83_12x22102.08141.5030.3370.42136.589
Bar_21_5_X_NGaskell67_21x53354.279144.4291.5131.930187.626
Bar_27_5_X_NMin92_27x51.62 587.950215.3467.5208.449983.118
Bar_32_5_X_NGaskell67_32x5_13598.918326.5541.6882.191326.516
Bar_36_5_X_NGaskell67_36x53646.198408.3391.5902.159132.189
Bar_50_5_X_NCh69_50x54891.776680.5382.0472.583201.946
Bar_55_15_X_NPerl83_55x157.667814.9431 008.5902.6283.588136.783
Bar_88_8_X_NDaskin95_88x83981.6192 211.7902.8393.666202.410
Bar_100_10_X_NCh69_100x105.82 720.4002 838.2803.9625.031230.094
NSGA-IIBar_8_2_X_NSrivastava86_8x23549.31531.4939.0448.071603.429
Bar_12_2_X_NPerl83_12x22168.88639.9313.6533.690208.700
Bar_21_5_X_NGaskell67_21x53.083504.445151.6431.8602.016178.333
Bar_27_5_X_NMin92_27x51.0024 769.868199.7829.1509.361385.335
Bar_32_5_X_NGaskell67_32x5_13.087964.129327.3942.3692.505101.066
Bar_36_5_X_NGaskell67_36x53.062890.955388.7321.6572.034103.409
Bar_50_5_X_NCh69_50x53.7231 424.860691.9346.3857.17776.333
Bar_55_15_X_NPerl83_55x158.4451 093.0831 095.7003.5123.99969.795
Bar_88_8_X_NDaskin95_88x83.4421 473.3012 210.2514.8255.29284.102
Bar_100_10_X_NCh69_100x105.7303 161.1422 876.1333.5994.723113.101
NSGA-II+PSOBar_8_2_X_NSrivastava86_8x23520.67731.12814.84014.818690.584
Bar_12_2_X_NPerl83_12x22153.56644.3221.0671.082254.661
Bar_21_5_X_NGaskell67_21x53.968435.416157.69877.50678.316340.150
Bar_27_5_X_NMin92_27x51.0024 551.351204.4918.0368.103260.896
Bar_32_5_X_NGaskell67_32x5_13784.149327.7032.8352.98278.992
Bar_36_5_X_NGaskell67_36x53.008831.141392.5851.2851.497153.438
Bar_50_5_X_NCh69_50x53.9631 421.524688.7834.3264.976412.546
Bar_55_15_X_NPerl83_55x158.0671 058.4331 078.5351.9792.62146.320
Bar_88_8_X_NDaskin95_88x831 318.6192 189.0868.7938.86653.580
Bar_100_10_X_NCh69_100x106.0153 092.1612 868.3686.6037.11891.082
NSGA-IIIBar_8_2_X_NSrivastava86_8x23523.65730.67310.85310.664467.230
Bar_12_2_X_NPerl83_12x22144.11340.0701.3271.40216.435 9
Bar_21_5_X_NGaskell67_21x53.1481.374158.1281.3041.767155.288
Bar_27_5_X_NMin92_27x51.85 133.620214.7114.5885.5141 426.190
Bar_32_5_X_NGaskell67_32x5_13.2912.400327.7392.4201.937111.288
Bar_36_5_X_NGaskell67_36x53.3862.456396.1621.4371.926143.357
Bar_50_5_X_NCh69_50x53.91 342.910689.4541.9832.556196.267
Bar_55_15_X_NPerl83_55x158.2351 074.4101 034.8802.3483.099105.374
Bar_88_8_X_NDaskin95_88x83.61 482.2302 235.7402.9563.864142.481
Bar_100_10_X_NCh69_100x105.8072 978.0002 914.2706.6146.77693.457
NSGA-III+PSOBar_8_2_X_NSrivastava86_8x23517.54430.55219.96620.031328.193
Bar_12_2_X_NPerl83_12x2296.85242.4720.6650.71011.827
Bar_21_5_X_NGaskell67_21x53.03423.300152.9141.4791.933106.731
Bar_27_5_X_NMin92_27x513 026.060207.4878.2267.794881.259
Bar_32_5_X_NGaskell67_32x5_13.5790.263308.1854.7424.293144.994
Bar_36_5_X_NGaskell67_36x53555.626387.8221.6672.196126.4
Bar_50_5_X_NCh69_50x53.91 221.680689.9701.9522.531171.18
Bar_55_15_X_NPerl83_55x158.7621 034.7691 076.8322.7633.65276.873
Bar_88_8_X_NDaskin95_88x83.51 577.8672 001.6724.7324.74565.432
Bar_100_10_X_NCh69_100x107.0033 040.7102 831.7902.1253.277100.654

表2

消融实验的实验结果"

算法实例车辆数量距离成本路线代价SM1SM2DM收敛迭代轮数

HSNS-

PSOGA

Bar_8_2_X_NSrivastava86_8x23406.70928.54597.9428.054122.19440.2
Bar_12_2_X_NPerl83_12x22102.08141.5030.3370.42136.589685.3
Bar_21_5_X_NGaskell67_21x53354.279144.4291.5131.930187.626622.7
Bar_27_5_X_NMin92_27x51.62587.95215.3467.5208.449983.118403.7
Bar_32_5_X_NGaskell67_32x5_13598.918326.5541.6882.191326.516820.4
Bar_36_5_X_NGaskell67_36x53646.198408.3391.5902.159132.189780.3
Bar_50_5_X_NCh69_50x54891.776680.5382.0472.583201.946810.4
Bar_55_15_X_NPerl83_55x157.667814.9431 008.592.6283.588136.783648.2
Bar_88_8_X_NDaskin95_88x83981.6192 211.792.8393.666202.41961.4
Bar_100_10_X_NCh69_100x105.82 720.402 838.283.9625.031230.094723.6

本文算法-

PSO

Bar_8_2_X_NSrivastava86_8x23424.67328.6993.8824.11128.052693.6
Bar_12_2_X_NPerl83_12x22134.43440.0721.2121.404131.233782.4
Bar_21_5_X_NGaskell67_21x53.3444.420152.2871.9052.552137.681805.8
Bar_27_5_X_NMin92_27x51.14 767.980238.8016.19526.466529.600598.3
Bar_32_5_X_NGaskell67_32x5_13.1856.442318.9873.8944.497189.0161065.36
Bar_36_5_X_NGaskell67_36x53785.541417.3563.0904.076319.632875.4
Bar_50_5_X_NCh69_50x54.21 249.310690.0103.5054.725196.947991.3
Bar_55_15_X_NPerl83_55x157.5865.4331 071.0024.0555.332130.369805.3
Bar_88_8_X_NDaskin95_88x82.81 273.0202 170.1205.6167.062165.3681 075.2
Bar_100_10_X_NCh69_100x105.82 814.2302 840.5606.5487.957205.378883.5

本文算法-

GA

Bar_8_2_X_NSrivastava86_8x23415.40428.1072.1322.628112.328470.7
Bar_12_2_X_NPerl83_12x22113.15640.0940.5390.72845.548709.4
Bar_21_5_X_NGaskell67_21x53.5458.437150.5331.7852.358162.030620.6
Bar_27_5_X_NMin92_27x52.22 767.620220.46812.16512.9791 037.520503.4
Bar_32_5_X_NGaskell67_32x5_13.4646.538334.7732.4713.096312.291728.4
Bar_36_5_X_NGaskell67_36x53.1682.457417.3782.3982.528138.824794.2
Bar_50_5_X_NCh69_50x541 174.530697.6994.6255.69936.472860.4
Bar_55_15_X_NPerl83_55x158.11 193.8401 060.5103.2504.24094.164 2890.2
Bar_88_8_X_NDaskin95_88x83.5415.40428.1072.1322.628112.328982.6
Bar_100_10_X_NCh69_100x107.2113.15640.0940.5390.72845.548750.3
本文算法-聚合函数选择优质个体局部搜索Bar_8_2_X_NSrivastava86_8x23418.35729.3571.9352.178150.371450.2
Bar_12_2_X_NPerl83_12x22102.68043.6720.8771.17231.357688.4
Bar_21_5_X_NGaskell67_21x53.4339.256157.2782.2632.836195.378601.3
Bar_27_5_X_NMin92_27x533 209.465238.46833.82634.372610.291490.3
Bar_32_5_X_NGaskell67_32x5_13.1600.764310.2359.72511.367180.267710.6
Bar_36_5_X_NGaskell67_36x53576.367385.2832.1682.856169.356785.3
Bar_50_5_X_NCh69_50x54.31 017.267705.3842.5183.278210.372830.6
Bar_55_15_X_NPerl83_55x157791.6891 096.2573.3824.368120.783857.3
Bar_88_8_X_NDaskin95_88x83.21 093.8352 218.3923.6284.473158.367952.6
Bar_100_10_X_NCh69_100x106.62 890.4572 867.4636.7207.798228.493737.9
本文算法-次优个体局部搜索Bar_8_2_X_NSrivastava86_8x23.3411.26731.7252.7183.029197.346452.7
Bar_12_2_X_NPerl83_12x2293.25043.7100.5620.77435.782679.5
Bar_21_5_X_NGaskell67_21x53402.679143.5912.1622.676185.618590.6
Bar_27_5_X_NMin92_27x52.33 434.716315.62525.86213.095929.623458.2
Bar_32_5_X_NGaskell67_32x5_13667.418320.6342.3713.205219.512699.3
Bar_36_5_X_NGaskell67_36x53.2671.783401.7292.3202.848147.641778.3
Bar_50_5_X_NCh69_50x541 315.367680.5232.6933.396174.719849.5
Bar_55_15_X_NPerl83_55x157970.3921 010.6702.6314.73679.230862.9
Bar_88_8_X_NDaskin95_88x84.31 525.3812 220.4202.4653.482200.183928.4
Bar_100_10_X_NCh69_100x107.42 956.4912 926.3806.1177.729203.714730.5
本文算法-对种群中后1/12个体进行局部搜索Bar_8_2_X_NSrivastava86_8x23406.70928.545 97.9838.182122.190442.8
Bar_12_2_X_NPerl83_12x2296.41342.174 81.2581.390293.196673.6
Bar_21_5_X_NGaskell67_21x53378.831146.4451.8052.322262.696524.8
Bar_27_5_X_NMin92_27x523 113.850219.38110.11610.844635.685444.9
Bar_32_5_X_NGaskell67_32x5_13741.388310.12210.32011.116145.673844.4
Bar_36_5_X_NGaskell67_36x53653.843390.4722.1422.705201.434695.5
Bar_50_5_X_NCh69_50x53.5965.022702.6484.9995.924357.133862.6
Bar_55_15_X_NPerl83_55x157.667934.004993.7114.6565.882111.279643.7
Bar_88_8_X_NDaskin95_88x831 293.3602 208.9006.2307.875209.230986.1
Bar_100_10_X_NCh69_100x105.252 744.0402 776.4808.97410.039325.476877.2

表3

不同比例参数实验结果"

打乱比例实例车辆数量距离成本路线代价SM1SM2DM

HSNS-

PSOGA

（1/12）

Bar_8_2_X_NSrivastava86_8x23406.70928.54597.9428.054122.190
Bar_12_2_X_NPerl83_12x22102.08141.5030.3370.42136.589
Bar_21_5_X_NGaskell67_21x53354.279144.4291.3031.930187.626
Bar_27_5_X_NMin92_27x51.62 587.950215.34612.1137.1491 321.410
Bar_32_5_X_NGaskell67_32x5_13598.918326.5541.6882.077326.516
Bar_36_5_X_NGaskell67_36x53646.198385.7451.5902.159132.189
Bar_50_5_X_NCh69_50x54852.713680.5382.0472.583201.946
Bar_55_15_X_NPerl83_55x157.667814.9431 008.5903.8633.588136.783
Bar_88_8_X_NDaskin95_88x83981.6192 211.7902.8393.666212.046
Bar_100_10_X_NCh69_100x105.82 720.402 838.2803.9625.031235.119
对后1/6个体进行用户顺序打乱Bar_8_2_X_NSrivastava86_8x23410.57730.6741.7132.071126.398
Bar_12_2_X_NPerl83_12x22105.76144.1270.5660.77118.861
Bar_21_5_X_NGaskell67_21x53349.005152.0292.8023.436221.036
Bar_27_5_X_NMin92_27x52.12 710.487162.78311.7258.763207.452
Bar_32_5_X_NGaskell67_32x5_13.7576.728316.9271.6282.925154.925
Bar_36_5_X_NGaskell67_36x53.1701.673390.7561.7832.578139.634
Bar_50_5_X_NCh69_50x54847.735698.2472.8522.477251.706
Bar_55_15_X_NPerl83_55x157.8881.7431 109.4683.9473.833129.672
Bar_88_8_X_NDaskin95_88x83.51 007.3652 389.7541.7452.478201.467
Bar_100_10_X_NCh69_100x107.13 002.3843 005.4784.8255.732169.567
对后1/24个体进行用户顺序打乱Bar_8_2_X_NSrivastava86_8x23445.36125.062 41.8502.43882.934
Bar_12_2_X_NPerl83_12x22103.15041.0940.6190.82730.531
Bar_21_5_X_NGaskell67_21x53375.711154.2322.0321.738117.057
Bar_27_5_X_NMin92_27x51.83 303.970207.18012.7556.8011 262.670
Bar_32_5_X_NGaskell67_32x5_13546.247316.3841.7712.237166.391
Bar_36_5_X_NGaskell67_36x53.6659.582420.7451.7262.064189.634
Bar_50_5_X_NCh69_50x54901.182691.0122.6023.249190.523
Bar_55_15_X_NPerl83_55x157.3900.4261 101.3103.8014.673120.781
Bar_88_8_X_NDaskin95_88x841 144.6402 207.7104.1525.149411.740
Bar_100_10_X_NCh69_100x107.53 010.9902 847.8306.6598.208232.554
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