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摘要: 对运输能力受限条件下的跨单元调度问题进行分析, 提出一种基于动态决策块和蚁群优化 (Ant colony optimization, ACO) 的超启发式方法, 同时解决跨单元生产调度和运输调度问题. 在传统超启发式方法的基础上, 采用动态决策块策略, 通过蚁群算法合理划分决策块, 并为决策块选择合适的规则. 实验表明, 采用动态决策块策略的超启发式方法比传统的超启发式方法具有更好的性能, 本文所提的方法在最小化加权延迟总和目标方面有较好的优化能力 并且具有较高的计算效率.Abstract: In this paper, the inter-cell scheduling problem with a transportation capacity constraint is analyzed. An ant colony optimization (ACO)-based hyper-heuristic with dynamic decision blocks is proposed, which selects appropriate heuristic rules for production and transportation simultaneously. On the basis of traditional hyper-heuristics, a dynamic decision block strategy is proposed, in which several entities are grouped into a decision block under the guidance of pheromones, and appropriate heuristic rules are selected for each decision block. Comparisons between the proposed method and other hyper-heuristics with different decision block strategies are conducted. Computational results show a satisfying performance of the proposed method in minimizing total weighted tardiness with less computational costs.
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图 2 General algorithm of DABH
Fig. 2 Representation of decision blocks whose size is 1
图 5 最小化TWT 目标下的双因子交互作用图
Fig. 5 In°uence of 2-factor interaction with respect to minimizing TWT
图 6 DABH 与不同决策块划分策略之间的Gap 比较
Fig. 6 Gap values between DABH and di®erent decision block strategies
表 1 生成算例属性值
Table 1 Attributes for generating test problems
算例产生参数 取值范围 工件数 U[5, 450] 机器数 U[6, 120] 单元数(小车数) U(3, 15] 每个单元内机器数 U[2, 6] 小车容量 U[2, 10] 工件权重 U(0, 1] 工序加工时间 U[1, 30] 单元间转移时间 U[6, 50] 
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表 2 DABH参数
Table 2 Parameters in DABH
参数 范围 ρ (0.01, 0.05, 0.2, 0.8) Q/τmax (0.01, 0.05, 0.2, 0.8)
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表 3 DABH 与静态决策块划分策略的性能比较
Table 3 Comparison between DABH and static decision block strategies
测试用例 TWT 运行时间(s) GapONE(%) GapALL(%) GapAVG(%) DABH DABH-ONE DABH-ALL DABH-AVG p5m6c3 0 0.0 0.0 0.0 1.8 - - - p15m8c3 0 0.0 10.5 0.0 4.5 - - - p20m11c3 0 0.0 15.5 0.0 5.6 - - - p40m13c5 1317.5 1320.3 3363.7 2224.9 28.2 0.2 155.3 68.9 p50m15c5 4463.4 4717.4 7292.8 5750.6 38.6 5.7 63.4 28.8 p60m16c5 7853.8 8183.2 10594.3 9416.9 48.9 4.2 34.9 19.9 p70m20c7 7966.6 9736.6 11216.2 9798.4 74.5 22.2 40.8 23.0 p80m21c7 16504.9 19385.3 19653.919 137.8 84.1 17.5 19.1 16.0 p90m21c7 8312.6 9853.9 11981.9 9554.0 98.9 18.5 44.1 14.9 p100m25c9 21774.826 339.4 25924.7 25197.7 93.3 21.0 19.1 15.7 p120m30c9 41868.645 104.2 47292.2 44605.0 145.2 7.7 13.0 6.5 p140m35c11 43255.4 47646.4 47523 47284.2 199 10.2 9.9 9.3 p160m40c11 53375.9 61828.7 56588.8 56262.8 232 15.8 6.0 5.4 p180m45c13 78761 86352.7 89622.8 83336.1 299.5 9.6 13.8 5.8 p200m50c15 110299.3 119319.6 119545.3 115330.3 323.3 8.2 8.4 4.6 p250m65c15 155422.9 167271.9 164193.1 164003.1 447.5 7.6 5.6 5.5 p300m75c15 232254.5 255936 247079.6 243052.9 514.5 10.2 6.4 4.6 p350m90c15 303144.1 334527.3 316700.5 314547.5 692.0 10.4 4.5 3.8 p400m100c15 378489.1 421689.9 406151.6 397148 798.5 11.4 7.3 4.9 p450m120c15 466779.7 535080.7 489769.7 486647.2 1187.9 14.6 4.9 4.3 平均值 11.5 26.8 14.2
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表 4 DABH 与DGBH 的性能比较
Table 4 Comparison between DABH and DGBH
测试用例 TWT 运行时间(s) GapDGBH(%) DABH DGBH p10m10 6865 7048.0 1.9 2.7 p20m10 26176 26686.8 4.0 2.0 p20m15 37625 39070.2 6.4 3.8 p20m20 23791.8 25214.8 9.3 6.0 p25m20 41136.7 44152.3 14.3 7.3 p25m24 62536.8 67871.5 18.9 8.5 p28m25 118555.2 123994.3 18.9 4.6 p32m25 147814.5 155273.5 25.8 5 p30m30 100600.2 105500 29.4 4.9 p40m25 207853.8 219031.5 32.2 5.4 平均值 5.0
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