Location-routing optimization for regular maritime cruise and emergency rescue system in remote islands
Article Text (Baidu Translation)
-
摘要: 为提高远海群岛的海上救助能力，研究了救助基地选址与救助船巡航路径的集成优化问题；考虑海上救助力量的覆盖范围和响应时间限制，建立了以基地建设、运营成本最小和救助时间最短为评价指标的双目标数学模型，优化了基地和海上值班点的选址及救助船的配置、巡航路径和巡航周期；根据研究问题所具有的选址数量可变、连续空间选址及选址与路径优化相互耦合等特征，设计了嵌入模糊C-均值聚类和模拟退火的非支配排序遗传算法NSGA-Ⅱ集成优化算法对模型进行求解；为验证模型及算法的有效性，选取中国南海南沙群岛的实地数据进行了案例分析。研究结果表明：相较于现有文献中的改进NSGA-Ⅱ及多目标模拟退火算法，本文算法在最优Pareto前沿解逼近度、解集分布均匀性、多样性及非劣解数量等关键性能指标上均具有显著优势，相关指标提升幅度为19.13%~960.00%；对海上常态巡航救助系统救助时间和总成本的影响因素进行敏感性分析，研究发现，在救助船配置相同的情况下，民船聚集分布较民船随机分布，平均救助时间降低61.50%，总成本降低18.38%，而民船数量对总成本和平均救助时间的影响较小；在相同聚集度下，不同远海岛屿分布和数量下Pareto前沿解明显重合，表明救助时间和总成本对远海岛屿分布和数量的变化均不敏感；而海上值班点数量对救助时间影响较大，当值班点数由5个增加到29个时，平均救助时间降低80.46%。Abstract: To enhance maritime rescue capabilities in remote islands, the integrated optimization problem of rescue base location and cruise routing for rescue ships was investigated. The coverage and response time limitations of maritime rescue forces were considered, and a bi-objective mathematical model was formulated to minimize base construction and operational costs while reducing rescue time. The location of the base and the maritime duty points, as well as the configuration, cruise routes, and cruise cycles of rescue ships, were optimized. Based on the characteristics of the problem, such as a variable number of locations, continuous spatial location, and the mutual coupling of location and route optimization, an NSGA-Ⅱ-based integrated optimization algorithm incorporating fuzzy C-means clustering and simulated annealing mechanisms was developed to solve the model. A case study based on field data from the Nansha Islands in the South China Sea was conducted to validate the effectiveness of the proposed model and algorithm. Experimental results demonstrate that, compared to the improved NSGA-Ⅱ and multi-objective simulated annealing algorithms from the literature, the proposed algorithm exhibits significant advantages in key performance indicators, including proximity to the optimal Pareto front, solution set uniformity and diversity, and number of non-dominated solutions, with performance improvements ranging from 19.13% to 960.00%. Sensitivity analysis of the factors affecting rescue time and total cost in the regular maritime cruise and rescue system reveals that, under the same configuration of rescue ships, a more concentrated distribution of civilian ships reduces average rescue time by 61.50% and total cost by 18.38% compared to a random distribution, while the number of civilian ships has a relatively small impact on total cost and average rescue time; for the same level of concentration, Pareto front solutions remain highly consistent across different distributions and numbers of remote islands, indicating that rescue time and total cost are insensitive to variations in island distribution and quantity. However, the number of maritime duty points has a significant impact on rescue time. When the duty point number increases from 5 to 29, the average rescue time decreases by 80.46%.
-
Key words:
- waterway transportation /
- remote island /
- multi-objective programming /
- location /
- maritime rescue /
- regular cruise /
- routing
-
图 10 船舶点随机-聚集Pareto前沿解集对比
Figure 10. Comparison of ship point ramdom-aggregation Pareto front solution set
图 11 岛屿随机-聚集Pareto前沿解集对比
Figure 11. Comparison of solution set of ramdom-aggregate Pareto front of islands and reefs
图 12 不同救助船数Pareto前沿解集对比
Figure 12. Comparison of Pareto front solution sets for different numbers of rescue ships
图 13 不同最大巡航时间Pareto前沿解集对比
Figure 13. Comparison of Pareto front solution sets for different maximum cruise times
图 14 不同救助时间阈值Pareto前沿解集对比
Figure 14. Comparison of Pareto front solution sets for different rescue time thresholds
图 15 不同救助船速Pareto前沿解集对比
Figure 15. Comparison of Pareto front solution sets for different rescue vessel speeds
表 1 南沙主要岛屿位置
Table 1. Locations of the main islands in Nansha
岛屿 名称 经纬度 直角坐标/n mile 1 华阳岛 (112.86 °E，8.85 °N) (6 784.16，534.59) 2 赤瓜岛 (114.30 °E，9.72 °N) (6 870.31，586.87) 3 渚碧岛 (114.06 °E，10.91 °N) (6 855.99，659.98) 4 永暑岛 (112.96 °E，9.62 °N) (6 790.17，580.77) 5 美济岛 (115.54 °E，9.90 °N) (6 944.95，598.05) 6 东门岛 (114.50 °E，9.91 °N) (6 882.49，598.64) 7 南熏岛 (114.20 °E，10.22 °N) (6 864.30，617.38) 
下载: 导出CSV
表 2 大型救助船相关参数
Table 2. Parameters of large rescue vessels
参数 数值 巡航航速/kn 20 救助航速/kn 30 船舶造价/万元 10 000 船舶运营费/(万元·d-1) 1.2 每n mile航行成本/万元 0.01
下载: 导出CSV
表 3 海上值班点坐标(解1)
Table 3. Coordinates of offshore duty points (solution 1)
海上值班点 直角坐标/n mile 1# (6 890.98，589.22) 2# (6 766.87，518.20) 3# (6 965.93，596.61) 4# (6 653.79，479.43) 5# (6 669.46，603.78)
下载: 导出CSV
表 4 海上值班点坐标(解2)
Table 4. Coordinates of offshore duty points (solution 2)
海上值班点 直角坐标/n mile 海上值班点 直角坐标/n mile 1# (6 743.55，514.80) 16# (6 665.66，464.56) 2# (6 608.36，528.10) 17# (6 802.11，516.96) 3# (6 625.81，584.29) 18# (6 666.21，524.78) 4# (6 619.99，462.17) 19# (6 988.66，586.25) 5# (6 767.10，530.09) 20# (6 809.43，586.05) 6# (6 713.58，512.25) 21# (6 957.35，644.35) 7# (6 764.11，512.32) 22# (6 960.59，584.12) 8# (6 784.34，515.72) 23# (6 748.11，528.88) 9# (6 711.60，591.88) 24# (6 646.80，524.40) 10# (6 881.67，581.47) 25# (67 14.47，530.36) 11# (6 901.09，593.35) 26# (6 903.50，519.77) 12# (6 745.6，463.80) 27# (6 755.56，589.13) 13# (6 657.05，646.20) 28# (6 925.20，585.17) 14# (6 777.55，645.45) 29# (6 794.43，532.11) 15# (6 905.43，692.30)
下载: 导出CSV
表 5 海上值班点坐标(解3)
Table 5. Coordinates of offshore duty points (solution 3)
海上值班点 直角坐标/n mile 海上值班点 直角坐标/n mile 1# (6 924.31，586.02) 14# (6 766.16，530.12) 2# (6 986.99，593.33) 15# (6 752.23，515.51) 3# (6 783.14，517.44) 16# (6 877.78，578.08) 4# (6 905.09，693.78) 17# (6 900.93，579.15) 5# (6 902.61，518.10) 18# (6 734.66，597.06) 6# (6 986.22，578.52) 19# (6 711.75，524.00) 7# (6 666.98，464.91) 20# (6 629.02，584.73) 8# (6 891.75，643.93) 21# (6 657.50，525.01) 9# (6 960.90，644.85) 22# (6 954.35，582.38) 10# (6 611.70，528.11) 23# (6 741.58，527.37) 11# (6 889.02，594.45) 24# (6 799.11，525.00) 12# (6 803.23，589.39) 25# (6 663.04，646.84) 13# (6 749.20，464.30) 26# (6 620.31，462.56)
下载: 导出CSV
表 6 基于性价比法选取推荐解
Table 6. Selection of recommended solutions based on the price-performance method
海上值
班点TA/h C/109元 kT kC δT δC εT εC ωT ωC Δω 1# 1.05 4.22 -5.65×105 -1.77×10-6 -5.39×105 -4.20×10-12 5.27×10-2 2.37×10-4 9.96×10-1 4.48×10-3 9.91×10-1 2# 1.10 3.91 -1.12×106 -1.18×10-6 -1.01×106 -3.03×10-12 9.92×10-2 1.71×10-4 9.98×10-1 1.72×10-3 9.97×10-1 3# 1.12 3.64 -9.30×105 -2.91×10-6 -8.32×105 -7.99×10-12 8.14×10-2 4.52×10-4 9.94×10-1 5.52×10-3 9.89×10-1 4# 1.14 3.59 -2.86×105 -3.93×10-6 -2.50×105 -1.09×10-12 2.44×10-2 6.18×10-4 9.75×10-1 2.46×10-2 9.51×10-1 5# 1.20 3.40 -3.71×105 -2.70×10-6 -3.10×105 -7.95×10-12 3.03×10-2 4.49×10-4 9.85×10-1 1.46×10-2 9.71×10-1 6# 1.20 3.38 -5.41×105 -2.08×10-6 -4.51×105 -6.14×10-12 4.41×10-2 3.47×10-4 9.92×10-1 7.81×10-3 9.84×10-1 7# 1.20 3.36 -4.14×105 -5.35×10-6 -3.44×105 -1.59×10-11 3.37×10-2 9.01×10-4 9.74×10-1 2.60×10-2 9.48×10-1 8# 1.21 3.34 -2.02×105 -6.34×10-6 -1.67×105 -1.89×10-11 1.63×10-2 1.07×10-3 9.38×10-1 6.15×10-2 8.77×10-1 9# 1.22 3.34 -2.92×105 -3.42×10-6 -2.40×105 -1.03×10-11 2.35×10-2 5.80×10-4 9.76×10-1 2.41×10-2 9.52×10-1 10# 1.29 3.12 -6.49×105 -2.24×10-6 -5.04×105 -7.16×10-12 4.93×10-2 4.05×10-4 9.92×10-1 8.15×10-3 9.84×10-1 11# 1.30 3.03 -6.05×105 -3.02×10-6 -4.66×105 -9.98×10-12 4.56×10-2 5.64×10-4 9.88×10-1 1.22×10-2 9.76×10-1 12# 1.40 2.83 -1.12×105 -2.12×10-5 -8.04×104 -7.50×10-11 7.86×10-3 4.24×10-3 6.50×10-1 3.50×10-1 3.00×10-1 13# 1.43 2.82 -1.11×105 -2.13×10-5 -7.75×104 -7.54×10-11 7.58×10-3 4.26×10-3 6.40×10-1 3.60×10-1 2.80×10-1 14# 1.44 2.80 -3.00×105 -3.80×10-6 -2.08×105 -1.35×10-11 2.04×10-2 7.66×10-4 9.64×10-1 3.63×10-2 9.27×10-1 15# 1.45 2.75 -2.91×105 -4.04×10-6 -2.01×105 -1.47×10-11 1.96×10-2 8.29×10-4 9.59×10-1 4.06×10-2 9.19×10-1 16# 1.53 2.61 -1.52×105 -6.80×10-6 -9.92×104 -2.60×10-11 9.70×10-3 1.47×10-3 8.68×10-1 1.32×10-1 7.37×10-1 17# 1.56 2.58 -2.31×106 -4.11×10-6 -1.48×106 -1.59×10-11 1.45×10-1 9.01×10-4 9.94×10-1 6.17×10-3 9.88×10-1 18# 1.56 2.52 -2.29×106 -6.73×10-6 -1.47×106 -2.67×10-11 1.44×10-1 1.51×10-3 9.90×10-1 1.04×10-2 9.79×10-1 19# 1.58 2.51 -5.35×104 -2.25×10-5 -3.38×104 -8.98×10-11 3.30×10-3 5.08×10-3 3.94×10-1 6.06×10-1 2.12×10-1 20# 1.63 2.49 -7.29×105 -1.62×10-5 -4.48×105 -6.51×10-11 4.38×10-2 3.68×10-3 9.23×10-1 7.75×10-2 8.45×10-1 21# 1.64 2.29 -7.34×105 -1.24×10-5 -4.47×105 -5.44×10-11 4.37×10-2 3.07×10-3 9.34×10-1 6.57×10-2 8.69×10-1 22# 1.66 2.28 -1.04×105 -1.51×10-5 -6.26×104 -6.62×10-11 6.13×10-3 3.74×10-3 6.21×10-1 3.79×10-1 2.41×10-1 23# 1.84 1.99 -8.85×104 -5.34×10-5 -4.82×104 -2.68×10-10 4.72×10-3 1.52×10-2 2.37×10-1 7.63×10-1 5.25×10-1 24# 1.90 1.98 -2.50×104 -6.29×10-5 -1.31×104 -3.17×10-10 1.29×10-3 1.79×10-2 6.70×10-2 9.33×10-1 8.66×10-1 25# 1.94 1.97 -1.61×105 -1.42×10-5 -8.30×104 -7.23×10-11 8.12×10-3 4.08×10-3 6.65×10-1 3.35×10-1 3.30×10-1 26# 2.04 1.70 -1.44×105 -7.25×10-5 -7.09×104 -4.27×10-10 6.94×10-3 2.42×10-2 2.23×10-1 7.77×10-1 5.54×10-1 27# 2.10 1.69 -2.01×104 -8.59×10-5 -9.57×103 -5.07×10-10 9.36×10-4 2.87×10-2 3.16×10-2 9.68×10-1 9.37×10-1 28# 2.15 1.68 -7.82×104 -1.92×10-5 -3.64×104 -1.14×10-10 3.56×10-3 6.47×10-3 3.55×10-1 6.45×10-1 2.91×10-1 29# 2.16 1.66 -7.08×104 -3.13×10-5 -3.28×104 -1.88×10-10 3.21×10-3 1.06×10-2 2.32×10-1 7.68×10-1 5.37×10-1 30# 2.24 1.65 -1.47×105 -2.91×10-5 -6.55×104 -1.76×10-10 6.41×10-3 9.97×10-3 3.91×10-1 6.09×10-1 2.18×10-1 31# 2.34 1.38 -1.39×105 -1.50×10-4 -5.96×104 -1.09×10-9 5.83×10-3 6.15×10-2 8.65×10-2 9.13×10-1 8.27×10-1 32# 2.50 1.38 -2.06×104 -1.62×10-4 -8.23×103 -1.18×10-9 8.05×10-4 6.64×10-2 1.20×10-2 9.88×10-1 9.76×10-1 33# 2.59 1.34 -8.17×104 -1.72×10-5 -3.16×104 -1.28×10-10 3.09×10-3 7.22×10-3 3.00×10-1 7.00×10-1 4.01×10-1 34# 2.84 1.03 -7.66×104 -2.20×10-5 -2.70×104 -2.14×10-10 2.64×10-3 1.21×10-2 1.80×10-1 8.20×10-1 6.41×10-1 35# 2.91 1.01 -2.10×104 -5.30×10-5 -7.23×103 -5.23×10-10 7.07×10-4 2.96×10-2 2.34×10-2 9.77×10-1 9.53×10-1 36# 4.95 0.72 -1.15×104 -9.25×10-5 -2.32×103 -1.29×10-9 2.27×10-4 7.26×10-2 3.12×10-3 9.97×10-1 9.94×10-1 37# 5.04 0.71 -5.42×103 -2.88×10-4 -1.08×103 -4.05×10-9 1.05×10-4 2.29×10-1 4.60×10-4 1.00 9.99×10-1 38# 5.36 0.70 -2.17×103 -4.61×10-4 -4.04×1022 -6.54×10-9 3.96×10-5 3.70×10-1 1.07×10-4 1.00 1.00
下载: 导出CSV
表 7 算法对比(9组算例平均值)
Table 7. Algorithm comparison (average values of 9 sets of examples)
算例 指标 本文算法 NSGA-Ⅱ 改进NSGA-Ⅱ MOSA MOPSO MODE 本文算法较其他算法改进幅度/% NSGA-Ⅱ 改进NSGA-Ⅱ MOSA MOPSO MODE 岛屿数为3，船舶点数为1 000 σ 5 106 15 404 13 757 16 563 23 427 27 366 66.85 62.88 69.17 78.20 81.34 Δ 9 735 18 253 15 997 19 241 26 824 23 148 46.67 39.14 49.40 63.71 57.94 θ 48 9 16 11 17 8 433.33 200.00 336.36 182.35 500.00 t/s 421.77 528.46 1 811.72 854.12 758.83 252.58 20.19 76.72 50.62 44.42 岛屿数为7，船舶点数为3 000 σ 5 539 18 536 11 859 17 083 32 905 15 955 70.12 53.29 67.58 83.17 65.28 Δ 8 302 19 955 16 099 19 235 25 270 21 826 58.40 48.43 56.84 67.15 61.96 θ 58 8 14 9 13 9 625.00 314.29 544.44 346.15 544.44 t/s 580.38 1 560.51 1 877.42 1 708.25 2 043.81 278.04 62.81 69.09 66.02 71.60 岛屿数为11，船舶点数为5 000 σ 4 063 18 490 13 501 16 775 13 655 43 109 78.03 69.91 75.78 70.25 90.58 Δ 9 290 18 885 17 380 18 136 13 651 27 252 50.81 46.55 48.78 31.95 65.91 θ 50 9 13 9 17 7 455.56 284.62 455.56 194.12 614.29 t/s 1 109.39 3 157.76 1 728.34 2 942.94 3 137.14 373.08 64.87 35.81 62.30 64.64 岛屿数为15，船舶点数为7 000 σ 6 970 14 916 14 213 12 607 15 203 20 439 53.27 50.96 44.71 54.15 65.90 Δ 8 632 17 594 16 532 15 576 16 992 19 090 50.94 47.79 44.58 49.20 54.78 θ 54 9 19 10 24 7 500.00 184.21 440.00 125.00 671.43 t/s 818.62 2 646.42 2 170.87 3 258.06 3 033.71 383.74 69.07 62.29 74.87 73.02 岛屿数为20，船舶点数为10 000 σ 4 212 16 621 18 309 10 251 12 992 17 604 74.66 76.99 58.91 67.58 76.07 Δ 7 809 17 053 17 603 14 734 17 446 18 128 54.21 55.64 47.00 55.24 56.92 θ 53 13 9 11 6 5 307.69 488.89 381.82 783.33 960.00 t/s 877.83 2 612.4 1 632.67 3 191.55 2 897.77 362.97 66.40 46.23 72.50 69.71 岛屿数为30，船舶点数为15 000 σ 7 181 14 388 17 766 13 249 37 682 17 582 50.09 59.58 45.80 80.94 59.16 Δ 8 744 21 974 17 544 16 948 18 811 18 777 60.21 50.16 48.41 53.52 53.43 θ 55 13 9 13 7 9 323.08 511.11 323.08 685.71 511.11 t/s 802.42 2 568.75 1 671.23 3 323.89 3 108.95 344.89 68.76 51.99 75.86 74.19 岛屿数为40，船舶点数为20 000 σ 7 555 18 469 15 424 11 675 43 702 13 175 59.09 51.02 35.29 82.71 42.66 Δ 12 764 17 317 18 516 15 783 22 773 16 860 26.29 31.07 19.13 43.95 24.29 θ 33 7 6 13 10 8 371.43 450.00 153.85 230.00 312.50 t/s 718.67 3 075.71 2 135.56 3 294.99 3 323.84 375.97 76.63 66.35 78.19 78.38
下载: 导出CSV
-
[1] 李猛. 海上救助站及其动态值班点选址数学模型研究[C]//中国航海学会. 中国航海学会2005年度学术交流会优秀论文集. 北京, 2005: 143-144.LI Meng. Mathematical modeling study on the location of maritime rescue stations and dynamic duty points[C]//Chinese Institute of Navigation. Proceedings of the 2005 Annual Academic Exchange Conference of the China Institute of navigation. Beijing: Chinese Institute of Navigation, 2005: 143-144. [2] 陶夏妍. 救助动态值班点设置数学模型及应用的研究[J]. 珠江水运, 2016(23): 69-71.TAO Xia-yan. Research on the mathematical model and application of the setup of maritime rescue duty points[J]. Pearl River Water Transport, 2016(23): 69-71. [3] MA Q D, ZHANG D Z, WAN C F, et al. Multi-objective emergency resources allocation optimization for maritime search and rescue considering accident black-spots[J]. Ocean Engineering, 2022, 261: 112178. doi: 10.1016/j.oceaneng.2022.112178 [4] 王翊萱, 王诺, 高忠印, 等. 面向远海岛屿的救助基地选址优化模型及其算法[J]. 运筹与管理, 2022, 31(8): 45-50.WANG Yi-xuan, WANG Nuo, GAO Zhong-yin, et al. Models and algorithms for site selection of rescue bases in the islands in the far sea[J]. Operations Research and Management Science, 2022, 31(8): 45-50. [5] WEI L, LI Y B, XU J H, et al. Unmanned aerial vehicle maritime cruise base site selection strategy research in the Bohai Sea[J]. Applied Mechanics and Materials, 2015, 724: 378-382. doi: 10.4028/www.scientific.net/AMM.724.378 [6] 吴嘉鑫, 范厚明, 刘鹏程, 等. 北部海域海上专业救助值班点布置及力量配置[J]. 上海海事大学学报, 2019, 40(2): 29-35, 94.WU Jia-xin, FAN Hou-ming, LIU Peng-cheng, et al. Duty point layout and resource configuration of maritime specialized rescue in northern sea area of China[J]. Journal of Shanghai Maritime University, 2019, 40(2): 29-35, 94. [7] CAI L C, WU Y W, ZHU S Y, et al. Bi-level programming enabled design of an intelligent maritime search and rescue system[J]. Advanced Engineering Informatics, 2020, 46: 101194. doi: 10.1016/j.aei.2020.101194 [8] KARATAS M. A dynamic multi-objective location-allocation model for search and rescue assets[J]. European Journal of Operational Research, 2021, 288(2): 620-633. doi: 10.1016/j.ejor.2020.06.003 [9] XIONG W T, VAN GELDER P H A J M, YANG K W. A decision support method for design and operationalization of search and rescue in maritime emergency[J]. Ocean Engineering, 2020, 207: 107399. doi: 10.1016/j.oceaneng.2020.107399 [10] AKBARI A, PELOT R, EISELT H A. A modular capacitated multi-objective model for locating maritime search and rescue vessels[J]. Annals of Operations Research, 2018, 267(1): 3-28. [11] LI X W, GAO M, KANG Z, et al. Collaborative search and rescue based on swarm of H-MASSs using consensus theory[J]. Ocean Engineering, 2023, 278: 114426. doi: 10.1016/j.oceaneng.2023.114426 [12] ZHOU X, CHENG L, MIN K F, et al. A framework for assessing the capability of maritime search and rescue in the South China Sea[J]. International Journal of Disaster Risk Reduction, 2020, 47: 101568. doi: 10.1016/j.ijdrr.2020.101568 [13] KARATAS M, RAZI N, GUNAL M M. An ILP and simulation model to optimize search and rescue helicopter operations[J]. Journal of the Operational Research Society, 2017, 68(11): 1335-1351. doi: 10.1057/s41274-016-0154-7 [14] 严梦迪, 王海红. 改进NSGA-Ⅱ算法的海上搜救调度方法[J]. 计算机系统应用, 2023, 32(8): 244-249.YAN Meng-di, WANG Hai-hong. Maritime search and rescue dispatching method based on improved NSGA-Ⅱ algorithm[J]. Computer Systems and Applications, 2023, 32(8): 244-249. [15] 石绍宸, 吴文周, 张鹏, 等. 南沙海域搜救可达性评估[J]. 热带地理, 2024, 44(11): 2015-2024.SHI Shao-chen, WU Wen-zhou, ZHANG Peng, et al. Search and rescue accessibility assessment in the Nansha Sea[J]. Tropical Geography, 2024, 44(11): 2015-2024. [16] 孙艺松, 胡海军, 李乐, 等. 基于改进蚁群算法的海上目标搜索路径规划[J]. 传感器与微系统, 2024, 43(10): 160-164.SUN Yi-song, HU Hai-jun, LI Le, et al. Maritime target search path planning based on improved ant colony algorithm[J]. Transducer and Microsystem Technologies, 2024, 43(10): 160-164. [17] 罗修波, 黄咸康, 薛丹, 等. 基于蚁群算法的双救生艇海上搜救路径策略研究[J]. 航海技术, 2022(5): 58-61.LUO Xiu-bo, HUANG Xian-kang, XUE Dan, et al. Research on dual lifeboat maritime search and rescue path strategy based on ant colony algorithm[J]. Marine Technology, 2022(5): 58-61. [18] YOO S L, KIM K I. Maritime accidents-based optimal rescue ship location using dynamic programming and particle swarm optimisation algorithm[J]. Journal of Navigation, 2024, 77(4): 543-558. doi: 10.1017/S0373463324000365 [19] 陈磊, 夏倩雯, 陈斯伊, 等. 基于无人机的应急物资配送设施选址及路径优化研究[J]. 科技与创新, 2025(16): 61-63.CHEN Lei, XIA Qian-wen, CHEN Si-yi, et al. Research on location selection and route optimization for emergency supply delivery using drones[J]. Technology and Innovation, 2025(16): 61-63. [20] 李慧芳, 胡大伟, 陈希琼, 等. 考虑碳排放的混合轴辐式多式联运网络枢纽扩增选址-路径问题[J]. 交通运输工程学报, 2022, 22(4): 306-321. doi: 10.19818/j.cnki.1671-1637.2022.04.024 LI Hui-fang, HU Da-wei, CHEN Xi-qiong, et al. Expanding hub location-routing problem for hybrid hub-and-spoke multimodal transport network considering carbon emissions[J]. Journal of Traffic and Transportation Engineering, 2022, 22(4): 306-321. doi: 10.19818/j.cnki.1671-1637.2022.04.024 [21] 汤兆平, 秦进, 孙剑萍. 基于非概率可靠性的铁路应急设施选址-路径鲁棒优化[J]. 中国管理科学, 2022, 30(9): 206-216.TANG Zhao-ping, QIN Jin, SUN Jian-ping. Robust optimization for railway emergency location-routing based on non-probabilistic reliability[J]. Chinese Journal of Management Science, 2022, 30(9): 206-216. [22] 丁肇炜, 杨建华, 王艾, 等. 面向突发事件的安保巡逻选址-路径优化研究[J]. 运筹与管理, 2021, 30(8): 1-6.DING Zhao-wei, YANG Jian-hua, WANG Ai, et al. Study on site location-routing optimization of security patrol in emergencies[J]. Operations Research and Management Science, 2021, 30(8): 1-6. [23] 郭放, 黄志红, 黄卫来. 考虑前置仓选址与服务策略的同时取送货车辆路径问题研究[J]. 系统工程理论与实践, 2021, 41(4): 962-978.GUO Fang, HUANG Zhi-hong, HUANG Wei-lai. Integrated sustainable planning of fast-pick area network and vehicle routing with simultaneous delivery and pick-up[J]. Systems Engineering — Theory & Practice, 2021, 41(4): 962-978. [24] ZHANG L Y, LU J, YANG Z L. Optimal scheduling of emergency resources for major maritime oil spills considering time-varying demand and transportation networks[J]. European Journal of Operational Research, 2021, 293(2): 529-546. doi: 10.1016/j.ejor.2020.12.040 [25] 马昌喜, 石褚巍, 杜波. 轴辐式应急救援网络规划[J]. 交通运输工程学报, 2023, 23(3): 198-208. doi: 10.19818/j.cnki.1671-1637.2023.03.015 MA Chang-xi, SHI Chu-wei, DU Bo. Hub-and-spoke emergency rescue network planning[J]. Journal of Traffic and Transportation Engineering, 2023, 23(3): 198-208. doi: 10.19818/j.cnki.1671-1637.2023.03.015 [26] NIU Y Y, XU C, LIAO S B, et al. Multi-objective location-routing optimization based on machine learning for green municipal waste management[J]. Waste Management, 2024, 181: 157-167. doi: 10.1016/j.wasman.2024.04.001 [27] GUO F, WANG Z J, HUANG Z H, et al. Robust optimization of microhub network and mixed service strategy for a multidepot location-routing problem[J]. Computers & Industrial Engineering, 2024, 190: 110070. [28] CHO S W, PARK H J, LEE H, et al. Coverage path planning for multiple unmanned aerial vehicles in maritime search and rescue operations[J]. Computers & Industrial Engineering, 2021, 161: 107612. [29] 郑夏, 马良. 考虑灾后分区的应急物资LRP问题研究[J]. 运筹与管理, 2020, 29(11): 66-77.ZHENG Xia, MA Liang. Research on emergency material LRP problem considering post-disaster zoning[J]. Operations Research and Management Science, 2020, 29(11): 66-77. [30] HU Y Z, WANG M, GUO X H, et al. Pre-occurrence location-allocation-configuration of maritime emergency resources considering shipborne unmanned aerial vehicle (UAV)[J]. Omega, 2025, 131: 103231. doi: 10.1016/j.omega.2024.103231 [31] WANG C, PENG Z X, XU W Q, et al. Robust bi-level optimization for maritime emergency materials distribution in uncertain decision-making environments[J]. Mathematics, 2023, 11(19): 4140. doi: 10.3390/math11194140 [32] PRODHON C, PRINS C. A survey of recent research on location-routing problems[J]. European Journal of Operational Research, 2014, 238(1): 1-17. doi: 10.1016/j.ejor.2014.01.005 [33] 王诺, 吴迪, 黄祺, 等. 选择Pareto非劣解最优方案的量化方法: 性价比法[J]. 系统工程理论与实践, 2018, 38(3): 725-733.WANG Nuo, WU Di, HUANG Qi, et al. A quantitative method to select the best option from Pareto non-dominated solutions: Cost performance method[J]. Systems Engineering — Theory & Practice, 2018, 38(3): 725-733. [34] RAYAT F, MUSAVI M, BOZORGI-AMIRI A. Bi-objective reliable location-inventory-routing problem with partial backordering under disruption risks: A modified AMOSA approach[J]. Applied Soft Computing, 2017, 59: 622-643. doi: 10.1016/j.asoc.2017.06.036 [35] DEB K, AGRAWAL S, PRATAP A, et al. A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-Ⅱ[C]//Springer. Proceedings of the International Conference on Parallel Problem Solving from Nature PPSN Ⅵ. Berlin: Springer, 2000: 849-858. [36] SCHOTT J R. Fault-tolerant design using single and multicriteria genetic algorithm optimization[D]. Ohio: Air Force Institute of Technology, 1995. [37] VAN VELDHUIZEN D A, LAMONT G B. On measuring multiobjective evolutionary algorithm performance[C]//IEEE. Proceedings of the 2000 Congress on Evolutionary Computation. New York: IEEE, 2002: 204-211. -
图(15) / 表(7)
计量
- 文章访问数: 102
- HTML全文浏览量: 46
- PDF下载量: 16
- 被引次数: 0
