Hybrid-genetic-heuristic algorithm of vehicle routing problem with hard time-windows
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摘要: 为了提高物流配送效率, 建立了集货和配送一体化的带硬时间窗的车辆路线问题的数学模型, 提出了混合遗传启发式算法, 并对模型进行了求解。采用改进节约法与随机法相结合的手段构造了初始解群体以增加解的多样性, 对遗传算法中较优的一部分染色体进行了禁忌搜索以使搜索更容易跳出局部最优, 同时加快搜索初期的搜索速度。仿真计算结果表明: 混合遗传启发式算法具有更好的适应性, 采用改进交叉算子使解的精度提高11.0%;在宽时间窗情形下采用倒位变异可使解的精度提高11.6%。Abstract: In order to improve the efficiency of logistics distribution, a mathematic model of vehicle routing problem with pickups, deliveries and hard time-windows was set up, and a hybrid-genetic-heuristic algorithm is designed to solve the model.In the algorithm, improved C-W method and random producing method were used to produce the initial group of solutions to increase its varieties, and the tabu search was used for some better chromosomes of genetic algorithm to avoid local optimization and increase search beginning speed.Simulation result shows that the algorithm has better adaptability, the solution's precision is improved by 11.0% when improved cross operator is used, and the solution's precision is improved by 11.6% when reversed variation tactic is used under big time-windows condition.
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表 1 客户点的数据
Table 1. Data of customers
客户编号 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 横坐标 3.8 15.2 18.6 11.9 10.2 5.3 0.6 6.1 7.6 16.0 15.3 1.6 9.0 5.4 7.8 18.6 14.5 15.0 9.8 1.4 纵坐标 5.5 10.9 12.9 8.2 9.5 9.6 9.9 15.0 19.2 15.7 15.2 14.7 9.2 13.3 10.0 7.8 5.3 18.7 5.0 6.9 需求量 0.8 0.6 0.4 1.6 0.8 0.6 1.9 1.3 1.8 1.8 0.4 1.6 1.1 1.6 1.0 0.8 1.4 1.2 0.4 1.4 供应量 0.5 1.6 0.7 0.3 0.6 1.4 1.7 1.0 0.9 1.9 1.0 1.8 1.4 0.4 1.8 1.8 0.8 0.2 0.5 1.0 需求时间窗开始时间 8.8 2.4 0.1 9.8 9.6 0.3 5.9 1.7 0.6 9.8 4.7 7.0 0.1 0.1 9.0 7.4 0.5 8.3 5.7 3.0 需求时间窗结束时间 14.6 8.1 4.9 14.1 13.8 6.0 11.6 7.5 5.2 13.9 10.3 12.4 5.0 4.7 14.7 12.5 5.6 13.0 10.9 7.5 供应时间窗开始时间 6.0 8.0 6.8 0.6 1.7 5.6 8.0 4.5 4.9 6.1 7.1 4.0 2.9 5.1 8.1 6.7 3.6 0.0 1.1 2.9 供应时间窗结束时间 14.6 13.8 12.3 5.0 6.3 10.4 12.6 8.5 10.3 12.0 11.8 9.8 7.1 9.8 13.9 11.6 9.4 5.8 6.1 7.0 
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表 2 模拟结果比较
Table 2. Comparison of simulation results
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表 3 交叉算子试验结果
Table 3. Test results of cross operators
交叉算子 混合时间窗路线数/总行驶距离 紧时间窗路线数/总行驶距离 宽时间窗路线数/总行驶距离 HX1HX2 66/176 940.075 7 111/251 362.548 8 47/126 274.646 0 HX1MX2 66/193 535.022 0 108/263 366.992 2 48/166 841.772 5 MX1MX2 66/216 610.693 4 107/289 610.864 3 46/195 677.844 2 HX2MX1 70/176 957.214 4 107/286 066.259 8 43/198 448.999 0 IHMX 66/170 081.359 9 111/244 100.268 6 44/116 302.868 7
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表 4 变异概率试验结果
Table 4. Test results of variation probabilities
变异概率 混合时间窗路线数/总行驶距离 紧时间窗路线数/总行驶距离 宽时间窗路线数/总行驶距离 0.06 68/171 408.374 0 110/250 938.183 6 46/123 548.486 3 0.08 65/174 855.969 2 108/254 082.104 5 45/126 925.695 8 0.10 67/171 397.619 6 111/252 154.370 1 47/122 479.370 1 0.12 65/172 942.968 8 111/245 038.916 0 43/125 140.105 3 适应性变异概率 66/170 081.359 9 111/244 100.268 6 44/116 302.868 7
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表 5 变异算子试验结果
Table 5. Test results of variation operators
变异算子 混合时间窗路线数/总行驶距离 紧时间窗路线数/总行驶距离 宽时间窗路线数/总行驶距离 三次对换变异 66/185 320.520 0 110/247 271.362 3 47/131 613.531 6 倒位变异 66/170 081.359 9 111/244 100.268 6 44/116 302.868 7
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