非支配排序粒子群遗传算法解决车辆位置路由问题

doi:10.13229/j.cnki.jdxbgxb.20231086

摘要/Abstract

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

刘琼昕,王甜甜,王亚男. 非支配排序粒子群遗传算法解决车辆位置路由问题[J]. 吉林大学学报(工学版), 2025, 55(7): 2464-2474.

Qiong-xin LIU,Tian-tian WANG,Ya-nan WANG. Non-dominated sorted particle swarm genetic algorithm to solve vehicle location routing problems[J]. Journal of Jilin University(Engineering and Technology Edition), 2025, 55(7): 2464-2474.

图/表 6

图1

图2

图3

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	SM1	SM2	DM
HSNS-PSOGA	Bar_8_2_X_NSrivastava86_8x2	3	406.709	28.545 9	7.942	8.054	122.190
	Bar_12_2_X_NPerl83_12x2	2	102.081	41.503	0.337	0.421	36.589
	Bar_21_5_X_NGaskell67_21x5	3	354.279	144.429	1.513	1.930	187.626
	Bar_27_5_X_NMin92_27x5	1.6	2 587.950	215.346	7.520	8.449	983.118
	Bar_32_5_X_NGaskell67_32x5_1	3	598.918	326.554	1.688	2.191	326.516
	Bar_36_5_X_NGaskell67_36x5	3	646.198	408.339	1.590	2.159	132.189
	Bar_50_5_X_NCh69_50x5	4	891.776	680.538	2.047	2.583	201.946
	Bar_55_15_X_NPerl83_55x15	7.667	814.943	1 008.590	2.628	3.588	136.783
	Bar_88_8_X_NDaskin95_88x8	3	981.619	2 211.790	2.839	3.666	202.410
	Bar_100_10_X_NCh69_100x10	5.8	2 720.400	2 838.280	3.962	5.031	230.094
NSGA-II	Bar_8_2_X_NSrivastava86_8x2	3	549.315	31.493	9.044	8.071	603.429
	Bar_12_2_X_NPerl83_12x2	2	168.886	39.931	3.653	3.690	208.700
	Bar_21_5_X_NGaskell67_21x5	3.083	504.445	151.643	1.860	2.016	178.333
	Bar_27_5_X_NMin92_27x5	1.002	4 769.868	199.782	9.150	9.361	385.335
	Bar_32_5_X_NGaskell67_32x5_1	3.087	964.129	327.394	2.369	2.505	101.066
	Bar_36_5_X_NGaskell67_36x5	3.062	890.955	388.732	1.657	2.034	103.409
	Bar_50_5_X_NCh69_50x5	3.723	1 424.860	691.934	6.385	7.177	76.333
	Bar_55_15_X_NPerl83_55x15	8.445	1 093.083	1 095.700	3.512	3.999	69.795
	Bar_88_8_X_NDaskin95_88x8	3.442	1 473.301	2 210.251	4.825	5.292	84.102
	Bar_100_10_X_NCh69_100x10	5.730	3 161.142	2 876.133	3.599	4.723	113.101
NSGA-II+PSO	Bar_8_2_X_NSrivastava86_8x2	3	520.677	31.128	14.840	14.818	690.584
	Bar_12_2_X_NPerl83_12x2	2	153.566	44.322	1.067	1.082	254.661
	Bar_21_5_X_NGaskell67_21x5	3.968	435.416	157.698	77.506	78.316	340.150
	Bar_27_5_X_NMin92_27x5	1.002	4 551.351	204.491	8.036	8.103	260.896
	Bar_32_5_X_NGaskell67_32x5_1	3	784.149	327.703	2.835	2.982	78.992
	Bar_36_5_X_NGaskell67_36x5	3.008	831.141	392.585	1.285	1.497	153.438
	Bar_50_5_X_NCh69_50x5	3.963	1 421.524	688.783	4.326	4.976	412.546
	Bar_55_15_X_NPerl83_55x15	8.067	1 058.433	1 078.535	1.979	2.621	46.320
	Bar_88_8_X_NDaskin95_88x8	3	1 318.619	2 189.086	8.793	8.866	53.580
	Bar_100_10_X_NCh69_100x10	6.015	3 092.161	2 868.368	6.603	7.118	91.082
NSGA-III	Bar_8_2_X_NSrivastava86_8x2	3	523.657	30.673	10.853	10.664	467.230
	Bar_12_2_X_NPerl83_12x2	2	144.113	40.070	1.327	1.402	16.435 9
	Bar_21_5_X_NGaskell67_21x5	3.1	481.374	158.128	1.304	1.767	155.288
	Bar_27_5_X_NMin92_27x5	1.8	5 133.620	214.711	4.588	5.514	1 426.190
	Bar_32_5_X_NGaskell67_32x5_1	3.2	912.400	327.739	2.420	1.937	111.288
	Bar_36_5_X_NGaskell67_36x5	3.3	862.456	396.162	1.437	1.926	143.357
	Bar_50_5_X_NCh69_50x5	3.9	1 342.910	689.454	1.983	2.556	196.267
	Bar_55_15_X_NPerl83_55x15	8.235	1 074.410	1 034.880	2.348	3.099	105.374
	Bar_88_8_X_NDaskin95_88x8	3.6	1 482.230	2 235.740	2.956	3.864	142.481
	Bar_100_10_X_NCh69_100x10	5.807	2 978.000	2 914.270	6.614	6.776	93.457
NSGA-III+PSO	Bar_8_2_X_NSrivastava86_8x2	3	517.544	30.552	19.966	20.031	328.193
	Bar_12_2_X_NPerl83_12x2	2	96.852	42.472	0.665	0.710	11.827
	Bar_21_5_X_NGaskell67_21x5	3.03	423.300	152.914	1.479	1.933	106.731
	Bar_27_5_X_NMin92_27x5	1	3 026.060	207.487	8.226	7.794	881.259
	Bar_32_5_X_NGaskell67_32x5_1	3.5	790.263	308.185	4.742	4.293	144.994
	Bar_36_5_X_NGaskell67_36x5	3	555.626	387.822	1.667	2.196	126.4
	Bar_50_5_X_NCh69_50x5	3.9	1 221.680	689.970	1.952	2.531	171.18
	Bar_55_15_X_NPerl83_55x15	8.762	1 034.769	1 076.832	2.763	3.652	76.873
	Bar_88_8_X_NDaskin95_88x8	3.5	1 577.867	2 001.672	4.732	4.745	65.432
	Bar_100_10_X_NCh69_100x10	7.003	3 040.710	2 831.790	2.125	3.277	100.654

表1

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	SM1	SM2	DM	收敛迭代轮数
HSNS- PSOGA	Bar_8_2_X_NSrivastava86_8x2	3	406.709	28.5459	7.942	8.054	122.19	440.2
	Bar_12_2_X_NPerl83_12x2	2	102.081	41.503	0.337	0.421	36.589	685.3
	Bar_21_5_X_NGaskell67_21x5	3	354.279	144.429	1.513	1.930	187.626	622.7
	Bar_27_5_X_NMin92_27x5	1.6	2587.95	215.346	7.520	8.449	983.118	403.7
	Bar_32_5_X_NGaskell67_32x5_1	3	598.918	326.554	1.688	2.191	326.516	820.4
	Bar_36_5_X_NGaskell67_36x5	3	646.198	408.339	1.590	2.159	132.189	780.3
	Bar_50_5_X_NCh69_50x5	4	891.776	680.538	2.047	2.583	201.946	810.4
	Bar_55_15_X_NPerl83_55x15	7.667	814.943	1 008.59	2.628	3.588	136.783	648.2
	Bar_88_8_X_NDaskin95_88x8	3	981.619	2 211.79	2.839	3.666	202.41	961.4
	Bar_100_10_X_NCh69_100x10	5.8	2 720.40	2 838.28	3.962	5.031	230.094	723.6
本文算法- PSO	Bar_8_2_X_NSrivastava86_8x2	3	424.673	28.699	3.882	4.11	128.052	693.6
	Bar_12_2_X_NPerl83_12x2	2	134.434	40.072	1.212	1.404	131.233	782.4
	Bar_21_5_X_NGaskell67_21x5	3.3	444.420	152.287	1.905	2.552	137.681	805.8
	Bar_27_5_X_NMin92_27x5	1.1	4 767.980	238.801	6.195	26.466	529.600	598.3
	Bar_32_5_X_NGaskell67_32x5_1	3.1	856.442	318.987	3.894	4.497	189.016	1065.36
	Bar_36_5_X_NGaskell67_36x5	3	785.541	417.356	3.090	4.076	319.632	875.4
	Bar_50_5_X_NCh69_50x5	4.2	1 249.310	690.010	3.505	4.725	196.947	991.3
	Bar_55_15_X_NPerl83_55x15	7.5	865.433	1 071.002	4.055	5.332	130.369	805.3
	Bar_88_8_X_NDaskin95_88x8	2.8	1 273.020	2 170.120	5.616	7.062	165.368	1 075.2
	Bar_100_10_X_NCh69_100x10	5.8	2 814.230	2 840.560	6.548	7.957	205.378	883.5
本文算法- GA	Bar_8_2_X_NSrivastava86_8x2	3	415.404	28.107	2.132	2.628	112.328	470.7
	Bar_12_2_X_NPerl83_12x2	2	113.156	40.094	0.539	0.728	45.548	709.4
	Bar_21_5_X_NGaskell67_21x5	3.5	458.437	150.533	1.785	2.358	162.030	620.6
	Bar_27_5_X_NMin92_27x5	2.2	2 767.620	220.468	12.165	12.979	1 037.520	503.4
	Bar_32_5_X_NGaskell67_32x5_1	3.4	646.538	334.773	2.471	3.096	312.291	728.4
	Bar_36_5_X_NGaskell67_36x5	3.1	682.457	417.378	2.398	2.528	138.824	794.2
	Bar_50_5_X_NCh69_50x5	4	1 174.530	697.699	4.625	5.699	36.472	860.4
	Bar_55_15_X_NPerl83_55x15	8.1	1 193.840	1 060.510	3.250	4.240	94.164 2	890.2
	Bar_88_8_X_NDaskin95_88x8	3.5	415.404	28.107	2.132	2.628	112.328	982.6
	Bar_100_10_X_NCh69_100x10	7.2	113.156	40.094	0.539	0.728	45.548	750.3
本文算法-聚合函数选择优质个体局部搜索	Bar_8_2_X_NSrivastava86_8x2	3	418.357	29.357	1.935	2.178	150.371	450.2
	Bar_12_2_X_NPerl83_12x2	2	102.680	43.672	0.877	1.172	31.357	688.4
	Bar_21_5_X_NGaskell67_21x5	3.4	339.256	157.278	2.263	2.836	195.378	601.3
	Bar_27_5_X_NMin92_27x5	3	3 209.465	238.468	33.826	34.372	610.291	490.3
	Bar_32_5_X_NGaskell67_32x5_1	3.1	600.764	310.235	9.725	11.367	180.267	710.6
	Bar_36_5_X_NGaskell67_36x5	3	576.367	385.283	2.168	2.856	169.356	785.3
	Bar_50_5_X_NCh69_50x5	4.3	1 017.267	705.384	2.518	3.278	210.372	830.6
	Bar_55_15_X_NPerl83_55x15	7	791.689	1 096.257	3.382	4.368	120.783	857.3
	Bar_88_8_X_NDaskin95_88x8	3.2	1 093.835	2 218.392	3.628	4.473	158.367	952.6
	Bar_100_10_X_NCh69_100x10	6.6	2 890.457	2 867.463	6.720	7.798	228.493	737.9
本文算法-次优个体局部搜索	Bar_8_2_X_NSrivastava86_8x2	3.3	411.267	31.725	2.718	3.029	197.346	452.7
	Bar_12_2_X_NPerl83_12x2	2	93.250	43.710	0.562	0.774	35.782	679.5
	Bar_21_5_X_NGaskell67_21x5	3	402.679	143.591	2.162	2.676	185.618	590.6
	Bar_27_5_X_NMin92_27x5	2.3	3 434.716	315.625	25.862	13.095	929.623	458.2
	Bar_32_5_X_NGaskell67_32x5_1	3	667.418	320.634	2.371	3.205	219.512	699.3
	Bar_36_5_X_NGaskell67_36x5	3.2	671.783	401.729	2.320	2.848	147.641	778.3
	Bar_50_5_X_NCh69_50x5	4	1 315.367	680.523	2.693	3.396	174.719	849.5
	Bar_55_15_X_NPerl83_55x15	7	970.392	1 010.670	2.631	4.736	79.230	862.9
	Bar_88_8_X_NDaskin95_88x8	4.3	1 525.381	2 220.420	2.465	3.482	200.183	928.4
	Bar_100_10_X_NCh69_100x10	7.4	2 956.491	2 926.380	6.117	7.729	203.714	730.5
本文算法-对种群中后1/12个体进行局部搜索	Bar_8_2_X_NSrivastava86_8x2	3	406.709	28.545 9	7.983	8.182	122.190	442.8
	Bar_12_2_X_NPerl83_12x2	2	96.413	42.174 8	1.258	1.390	293.196	673.6
	Bar_21_5_X_NGaskell67_21x5	3	378.831	146.445	1.805	2.322	262.696	524.8
	Bar_27_5_X_NMin92_27x5	2	3 113.850	219.381	10.116	10.844	635.685	444.9
	Bar_32_5_X_NGaskell67_32x5_1	3	741.388	310.122	10.320	11.116	145.673	844.4
	Bar_36_5_X_NGaskell67_36x5	3	653.843	390.472	2.142	2.705	201.434	695.5
	Bar_50_5_X_NCh69_50x5	3.5	965.022	702.648	4.999	5.924	357.133	862.6
	Bar_55_15_X_NPerl83_55x15	7.667	934.004	993.711	4.656	5.882	111.279	643.7
	Bar_88_8_X_NDaskin95_88x8	3	1 293.360	2 208.900	6.230	7.875	209.230	986.1
	Bar_100_10_X_NCh69_100x10	5.25	2 744.040	2 776.480	8.974	10.039	325.476	877.2

表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	SM1	SM2	DM
HSNS- PSOGA （1/12）	Bar_8_2_X_NSrivastava86_8x2	3	406.709	28.5459	7.942	8.054	122.190
	Bar_12_2_X_NPerl83_12x2	2	102.081	41.503	0.337	0.421	36.589
	Bar_21_5_X_NGaskell67_21x5	3	354.279	144.429	1.303	1.930	187.626
	Bar_27_5_X_NMin92_27x5	1.6	2 587.950	215.346	12.113	7.149	1 321.410
	Bar_32_5_X_NGaskell67_32x5_1	3	598.918	326.554	1.688	2.077	326.516
	Bar_36_5_X_NGaskell67_36x5	3	646.198	385.745	1.590	2.159	132.189
	Bar_50_5_X_NCh69_50x5	4	852.713	680.538	2.047	2.583	201.946
	Bar_55_15_X_NPerl83_55x15	7.667	814.943	1 008.590	3.863	3.588	136.783
	Bar_88_8_X_NDaskin95_88x8	3	981.619	2 211.790	2.839	3.666	212.046
	Bar_100_10_X_NCh69_100x10	5.8	2 720.40	2 838.280	3.962	5.031	235.119
对后1/6个体进行用户顺序打乱	Bar_8_2_X_NSrivastava86_8x2	3	410.577	30.674	1.713	2.071	126.398
	Bar_12_2_X_NPerl83_12x2	2	105.761	44.127	0.566	0.771	18.861
	Bar_21_5_X_NGaskell67_21x5	3	349.005	152.029	2.802	3.436	221.036
	Bar_27_5_X_NMin92_27x5	2.1	2 710.487	162.783	11.725	8.763	207.452
	Bar_32_5_X_NGaskell67_32x5_1	3.7	576.728	316.927	1.628	2.925	154.925
	Bar_36_5_X_NGaskell67_36x5	3.1	701.673	390.756	1.783	2.578	139.634
	Bar_50_5_X_NCh69_50x5	4	847.735	698.247	2.852	2.477	251.706
	Bar_55_15_X_NPerl83_55x15	7.8	881.743	1 109.468	3.947	3.833	129.672
	Bar_88_8_X_NDaskin95_88x8	3.5	1 007.365	2 389.754	1.745	2.478	201.467
	Bar_100_10_X_NCh69_100x10	7.1	3 002.384	3 005.478	4.825	5.732	169.567
对后1/24个体进行用户顺序打乱	Bar_8_2_X_NSrivastava86_8x2	3	445.361	25.062 4	1.850	2.438	82.934
	Bar_12_2_X_NPerl83_12x2	2	103.150	41.094	0.619	0.827	30.531
	Bar_21_5_X_NGaskell67_21x5	3	375.711	154.232	2.032	1.738	117.057
	Bar_27_5_X_NMin92_27x5	1.8	3 303.970	207.180	12.755	6.801	1 262.670
	Bar_32_5_X_NGaskell67_32x5_1	3	546.247	316.384	1.771	2.237	166.391
	Bar_36_5_X_NGaskell67_36x5	3.6	659.582	420.745	1.726	2.064	189.634
	Bar_50_5_X_NCh69_50x5	4	901.182	691.012	2.602	3.249	190.523
	Bar_55_15_X_NPerl83_55x15	7.3	900.426	1 101.310	3.801	4.673	120.781
	Bar_88_8_X_NDaskin95_88x8	4	1 144.640	2 207.710	4.152	5.149	411.740
	Bar_100_10_X_NCh69_100x10	7.5	3 010.990	2 847.830	6.659	8.208	232.554

表3

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