Bi-level programming model of decision optimization of reconstruction and expansion for highway network
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摘要: 针对公路网改扩建问题, 在决策优化过程中, 考虑了技术、资金、环境保护以及运营效率等因素。以路网系统的最小交通量为上层模型目标函数, 以最小走行时间为下层模型目标函数, 以路段服务水平、土地占用状况、建设投资等为约束条件, 构建了公路网改扩建决策优化双层规划模型。采用遗传算法求解模型, 并通过济青北线的实例数据进行实证分析。计算结果表明: 济青北线济南—淄博段、淄博—青州段、青州—潍坊段的扩建优化指数分别为2.15、4.09、3.54, 新建优化指数分别为1.87、3.09、2.73, 相同路段的扩建优化指数均高于新建优化指数, 与实际相符。可见, 模型有效。Abstract: Aiming at the reconstruction and expansion problems of highway network, the factors such as technique, fund, environmental protection and operation efficiency were considered during the decision optimization process. The minimum traffuc volume of highway network system was taken as the objective function of upper-level model, the minimum trip time was taken as the objective function of lower-level model, the service level of road section, land occupancy status and construction investment were taken as constraint conditions, and a bi-level programming model of decision optimization of reconstruction and expansion for highway network was set up. Genetic algorithm was used to solve the model, and empirical analysis was carried out by using the example data of Northern Jiqing Highway. Calculation result shows that the expansion optimization indexes of Jinan-Zibo section, Zibo-Qingzhou section and Qingzhou-Weifang section for Northern Jiqing Highway are 2.15, 4.09 and 3.54 respectively, while the newly-built optimization indexes of the road sections are 1.87, 3.09 and 2.73 respectively. The expansion optimization index is higher than the newly-built optimization index for each road section, which is close to actual experience, so the model is effective.
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表 1 高速公路年平均日交通量
Table 1. Annual average daily traffic volumes of highway
设计速度/(km·h-1) 交通量/(103 pcu·d-1) 四车道 六车道 八车道 120 40~55 55~80 80~100 100 35~50 50~70 70~90 80 25~45 55~60 60~80 
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表 2 一级公路年平均日交通量
Table 2. Annual average daily traffic volumes of first-class highway
设计速度/(km·h-1) 交通量/(103 pcu·d-1) 四车道 六车道 100 27~30 30~55 80 20~27 27~45 60 15~25 25~35
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表 3 其他公路年平均日交通量
Table 3. Annual average daily traffic volumes of other highways
公路等级 速度/(km·h-1) 年平均日交通量/(103 pcu·d-1) 二级 40~80 5~15 三级 30~40 2~6 四级 20 < 2
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表 4 城市节点之间交通量
Table 4. Traffic volumes among city nodes pcu·d-1
线路走向 自西向东 自东向西 总计 济南—淄博—青州—潍坊—青岛 5 974 5 969 11 943 济南—淄博—青州—潍坊—烟台 11 529 6 689 18 218 济南—淄博—青州—潍坊 5 376 7 835 13 210 济南—淄博—青州—潍坊—威海 8 322 6 633 14 955 德州—济南—淄博—青州—潍坊—青岛 5 509 8 154 13 662 德州—济南—淄博—青州—潍坊—烟台 9 180 6 317 15 498 德州—济南—淄博—青州—潍坊 2 604 4 428 7 032 德州—济南—淄博—青州—潍坊—威海 5 753 6 132 11 885 聊城—济南—淄博—青州—潍坊—青岛 5 717 6 525 12 242 聊城—济南—淄博—青州—潍坊—烟台 9 498 4 948 14 446 聊城—济南—淄博—青州—潍坊 2 883 4 947 7 830 聊城—济南—淄博—青州—威海 7 254 5 216 12 470 菏泽—济南—淄博—青州—潍坊—青岛 6 482 5 062 11 544 菏泽—济南—淄博—青州—潍坊—烟台 12 771 3 440 16 212 菏泽—济南—淄博—青州—潍坊 2 731 3 162 5 893 菏泽—济南—淄博—青州—潍坊—威海 9 033 2 657 11 690 滨州—淄博—青州—潍坊—青岛 5 913 6 790 12 702 泰安—淄博—青州—潍坊 2 202 3 686 5 888 莱芜—淄博—青州—潍坊 1 791 3 525 5 316 菏泽—济南—淄博 3 466 1 468 4 934 聊城—济南—淄博 4 315 2 501 6 817 德州—济南—淄博 3 595 2 615 6 210 济南—淄博 4 849 3 132 7 981
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表 5 优化方案
Table 5. Optimization schemes
济青北线 年平均日交通量/103pcu 年平均月交通量/103pcu 年高峰月交通量/103pcu 四车道月通行能力/103pcu 六车道月通行能力/103pcu 八车道月通行能力/103pcu 当量交通量/103pcu 扩建 新建 济南—淄博 90 2 693 2 908 1 650 2 400 3 000 1 258 八车道 四车道 淄博—青州 89 2 668 2 882 1 650 2 400 3 000 1 232 八车道 四车道 青州—潍坊 89 2 668 2 882 1 650 2 400 3 000 1 232 八车道 四车道 潍坊—青岛 25 744 804 1 650 2 400 3 000 -846 否 否
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表 6 方案1计算结果
Table 6. Calculation result of scheme 1
济青北线 建设成本/(万元·km-1) 运输成本/[元·(pcu·km)-1] 年平均日交通量/103pcu 运输成本/万元 土地成本/万元 里程/km 优化前路网效率 优化后路网效率 优化指数 济南—淄博 2 940 2.91 90 26.12 707 92.8 1.63 0.90 2.15 淄博—青州 2 940 2.91 89 25.89 707 48.5 1.62 0.89 4.09 青州—潍坊 2 940 2.91 89 25.88 707 55.9 1.62 0.89 3.54 潍坊—青岛 2 940 2.91 25 7.22 707
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表 7 方案2计算结果
Table 7. Calculation result of scheme 2
济青北线 建设成本/(万元·km-1) 运输成本/[元·(pcu·km)-1] 年平均日交通量/103pcu 运输成本/万元 土地成本/万元 里程/km 优化前路网效率 优化后路网效率 优化指数 济南—淄博 4 200 2.91 90 26.12 1 010 75 1.63 0.90 1.87 淄博—青州 4 200 2.91 89 25.89 1 010 45 1.62 0.89 3.09 青州—潍坊 4 200 2.91 89 25.88 1 010 51 1.62 0.89 2.73 潍坊—青岛 4 200 2.91 25 7.22 1 010
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