• ISSN 1006-3080
• CN 31-1691/TQ

 引用本文: 任静, 项月, 刘漫丹. 基于双模式更新五行环算法的多目标冷链配送[J]. 华东理工大学学报（自然科学版）. REN Jing, XIANG Yue, LIU Mandan. Multi-Objective Cold Chain Distribution Based on Dual-Mode Updated Five-Element Cycle Algorithm[J]. Journal of East China University of Science and Technology. doi: 10.14135/j.cnki.1006-3080.20211030001
 Citation: REN Jing, XIANG Yue, LIU Mandan. Multi-Objective Cold Chain Distribution Based on Dual-Mode Updated Five-Element Cycle Algorithm[J]. Journal of East China University of Science and Technology. • 中图分类号: TP273

## Multi-Objective Cold Chain Distribution Based on Dual-Mode Updated Five-Element Cycle Algorithm

• 摘要: 针对生产运输中广泛存在的冷链配送问题，建立了以配送成本最小化和顾客满意度最大化为目标函数的多目标冷链物流优化模型。基于五行环优化 (Five-Elements Cycle Optimization, FECO) 算法，提出了双模式更新个体的五行环优化算法(Five-Elements Cycle Optimization Algorithm of Dual-Mode Updating Individuals, FECO-DMUI)，并对多目标冷链物流模型进行求解。将FECO-DMUI算法与FECO算法、NSGA-II算法、鲸鱼优化算法和灰狼优化算法进行比较，结果验证了模型与算法的有效性，同时验证了FECO-DMUI算法在多目标冷链配送问题中能更加高效地获得路径优化的最优解集。

• 图  1  顾客满意度分析

Figure  1.  Customer satisfaction analysis

图  2  五行元素相生相克关系

Figure  2.  Five elements complement each other

图  3  编码与解码操作

Figure  3.  Encoding and decoding operations

图  4  交叉操作

Figure  4.  Cross operation

图  5  变异操作

Figure  5.  Mutation operation

图  6  个体的修复

Figure  6.  Individual repair

图  7  FECO-DMUI算法流程图

Figure  7.  Algorithm flowchart of FECO-DMUI

图  8  客户点分布图

Figure  8.  Customer point distribution map

图  9  路径规划图

Figure  9.  Path planning diagrams

图  10  最优解集分布图

Figure  10.  Optimal solution set distribution graph

表  1  客户点信息

Table  1.   Customer point information

 Number Coordinate/km Demand/kg Time window/min 0 (35,35)(41,49)(35,17)(55,45)(55,20)(15,30)(25,30)(20,50)(10,43)(55,60)(30,60)(20,65)(50,35) 0 (0,0,1000,1000) 1 10 (15,56,100,120) 2 7 (2,70,120,200) 3 13 (14,64,150,200) 4 19 (18,160,340,450) 5 26 (0,42,100,138) 6 3 (5,76,180,240) 7 5 (62,150,285,320) 8 9 (7,89,200,250) 9 16 (35,115,200,260) 10 16 (21,110,190,250) 11 12 (62,120,200,250) 12 19 (50,180,250,382) 13 (50,25) 23 (21,140,270,350) 14 (15,10) 20 (0,80,160,230) 15 (30,5) 8 (0,48,100,150) 16 (10,20) 19 (8,48,150,180) 17 (5,30) 2 (32,100,200,350) 18 (20,40) 12 (6,65,156,218) 19 (15,60) 17 (0,40,120,200) 20 (45,65) 9 (11,89,200,290) 21 (45,20) 11 (15,75,150,208) 22 (45,10) 18 (7,65,200,320) 23 (55,5) 29 (2,38,168,238) 24 (65,35) 3 (18,98,172,210) 25 (65,20) 6 (72,190,300,382)

表  2  优化模型参数取值

Table  2.   Optimize model parameter values

 $Q$ $h$ $e$ ${\mu _1}$ ${\mu _2}$ $s$ $p$ ${c_1}$ ${c_2}$ $\alpha$ $\beta$ 95 2 4.68 0.5 1 1.7 350 0.5 1 0.04 0.03

表  3  交叉概率比较实验

Table  3.   Crossover probability comparison experiment

 Pc HV 0.3 3.3872×1020 0.4 3.9753×1020 0.5 3.8035×1020 0.6 3.2997×1020 0.7 3.5151×1020 0.8 3.5615×1020 0.9 3.5504×1020

表  4  变异概率比较实验

Table  4.   Mutation probability comparison experiment

 ${p_m}$ HV 0.1 $3.7487 \times {10^{20}}$ 0.2 $3.9753 \times {10^{20}}$ 0.3 $2.9106 \times {10^{20}}$ 0.4 $2.8600 \times {10^{20}}$ 0.5 $1.5053 \times {10^{20}}$

表  5  尺度因子比较实验

Table  5.   Scale factor comparison experiment

 ${p_s}$ HV 0.2 $1.9892 \times {10^{19}}$ 0.4 $3.2433 \times {10^{19}}$ 0.6 $1.1541 \times {10^{20}}$ 0.8 $1.7562 \times {10^{20}}$ 1.0 $3.9753 \times {10^{20}}$ 1.2 $3.8134 \times {10^{20}}$ 1.4 $3.8636 \times {10^{20}}$ 1.6 $3.0664 \times {10^{20}}$ 1.8 $3.8636 \times {10^{20}}$

表  6  给定概率比较实验

Table  6.   Comparison experiment with given probability

 ${p_n}$ HV 0.1 $1.9569 \times {10^{20}}$ 0.2 $2.1576 \times {10^{20}}$ 0.3 $2.2579 \times {10^{20}}$ 0.4 $2.2579 \times {10^{20}}$ 0.5 $3.7130\times {10^{20}}$ 0.6 $2.3583 \times {10^{20}}$ 0.7 $3.1171 \times {10^{20}}$ 0.8 $3.8636 \times {10^{20}}$ 0.9 $3.9753 \times {10^{20}}$ 1.0 $2.3583 \times {10^{20}}$

表  7  5种算法的对比结果

Table  7.   Comparison results of five algorithms

 Algorithm HV Minimal delivery cost/CNY Maximum customer satisfaction Average minimum delivery cost/CNY Average maximum customer satisfaction FECO-DMUI 3.9753x1020 39861 0.9446 41082 0.9262 NSGA-II 1.7402x1020 36170 0.8467 41947 0.8157 FECO 7.4377x1019 44970 0.8397 44720 0.8570 GWO 2.2985x1020 41330 0.9343 42271 0.8928 WOA 1.6919x1020 43740 0.9043 43867 0.8542
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##### 出版历程
• 收稿日期:  2021-10-30
• 录用日期:  2022-03-16
• 网络出版日期:  2022-04-12

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