Multi-Objective Cold Chain Distribution Based on Dual-Mode Updated Five-Element Cycle Algorithm
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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。Abstract: With the development of the logistics industry, cold chain logistics have been studied by more and more scholarsas an important branch of the logistics industry. Because the waste of resources in cold chain logistics and distribution is a problem that cannot be underestimated, we use the optimization algorithm to solve the multi-objective optimization model to provide an effective distribution plan for solving the problem of resource waste in this paper. We establish a multi-objective cold chain logistics optimization model with minimizing distribution costs and maximizing customer satisfaction as the objective function in this paper. Customer satisfaction is reflected by the relationship between the delivery vehicle’s arrival time at the customer’s point and the customer’s specific time window; delivery costs are composed of transportation costs, cargo damage costs, cooling costs, and time penalty costs. We adopt the improved five-elements cycle optimization (FECO), which is the five-elements cycle optimization algorithm of dual-mode updating individuals (FECO-DMUI) for multi-objective cold chain logistics optimization model in this paper. The chain logistics optimization model is solved by FECO-DMUI algorithm and compared with FECO algorithm, NSGA-II, whale optimization algorithm and gray wolf optimization algorithm. The effectiveness of the model and algorithm is verified through specific examples, and the FECO-DMUI algorithm can be used to obtain the optimal solution set for path optimization more efficiently in the multi-objective cold chain distribution problem.
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Key words:
- dual mode /
- multi-objective optimization /
- cold chain logistics /
- route optimization /
- FECO algorithm
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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/CNYMaximum customer
satisfactionAverage minimum
delivery cost/CNYAverage maximum
customer satisfactionFECO-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 -
[1] CHEN J, XU S, CHEN H, et al. Research on optimization of food cold chain logistics distribution route based on internet of things[J]. Journal of Physics:Conference Series, 2020, 1544(1): 012086. doi: 10.1088/1742-6596/1544/1/012086 [2] WANG S, TAO F, SHI Y, et al. Optimization of vehicle routing problem with time windows for cold chain logistics based on carbon tax[J]. Sustainability, 2017, 9(5): 1-23. [3] GOVINDAN K, JAFARIAN A, KHODAVERDI R. Two-echelon multiple-vehicle location-routing problem with time windows for optimization of sustainable supply chain network of perishable food[J]. International Journal of Production Economics, 2014, 152: 9-28. doi: 10.1016/j.ijpe.2013.12.028 [4] CAOA E, GAOA R, LAI M. Research on the vehicle routing problem with interval demands[J]. Applied Mathematical Modelling, 2018, 54: 332-346. doi: 10.1016/j.apm.2017.09.050 [5] WANG X X, CAO W J. Research on optimization of distribution route for cold chain logistics cooperative distribution of fresh ecommerce based on price discount[J]. Journal of Physics:Conference Series, 2020, 1732(1): 012041. [6] GONG Y J, ZHANG J, HUANG R. Optimizing the vehicle routing problem with time windows: A discrete particle swarm optimization approach[J]. IEEE Transactions on Systems, Man and Cybernetics:Part C. Applications and Reviews, 2012, 42(2): 254-267. doi: 10.1109/TSMCC.2011.2148712 [7] WANG X P, WANG M, RUAN J, et al. The multi-objective optimization for perishable food distribution route considering temporal-spatial distance[J]. Procedia Computer Science, 2016, 96: 1211-1220. doi: 10.1016/j.procs.2016.08.165 [8] ZHAO B, GUI H, LI H, et al. Cold chain logistics path optimization via improved multi- objective ant colony algorithm[J]. IEEE Access, 2020, 8: 142977-142995. doi: 10.1109/ACCESS.2020.3013951 [9] CLAUDIA A, ELENA F. A two-phase solution algorithm for the flexible periodic vehicle routing problem[J]. Computers and Operations Research, 2018, 99: 27-37. doi: 10.1016/j.cor.2018.05.021 [10] CHEN L, LIU Y, ANDRE L. A multi-compartment vehicle routing problem in cold-chain distribution[J]. Computers and Operations Research, 2019, 111: 58-66. doi: 10.1016/j.cor.2019.06.001 [11] 刘漫丹. 一种新的启发式优化算法—五行环优化算法研究与分析[J]. 自动化学报, 2020, 46(5): 957-970. [12] DEB K, AGRAWAL S, PRATAP A, et al. A fast elitist Non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II [C]//Parallel Problem Solving from Nature PPSN VI. UK Springer, 2000: 849-858. [13] MIRJALILI S, LEWIS A. The whale optimization algorithm[J]. Advances in Engineering Software, 2016, 95: 51-67. doi: 10.1016/j.advengsoft.2016.01.008 [14] MIRJALILI S, MIRJALILI S M, LEWIS A. Grey wolf optimizer[J]. Advances in Engineering Software, 2014, 69: 46-61. doi: 10.1016/j.advengsoft.2013.12.007 [15] 李常敏, 陶颖, 彭显, 等. 基于顾客时间满意度的车辆路径问题[J]. 上海大学学报(自然科学版), 2020, 26(3): 472-480. [16] WEI J. Research on the cold chain logistics distribution system of agricultural products[J]. IOP Conference Series:Earth and Environmental Science, 2019, 237(5): 052050. [17] 梁承姬, 黄涛, 徐德洪, 等. 改进遗传算法求解带模糊时间窗冷链配送问题[J]. 广西大学学报(自然科学版), 2016, 41(3): 826-835. [18] LIU G, HU J, YU Y, et al. Vehicle routing problem in cold chain logistics: A joint distribution model with carbon trading mechanisms[J]. Resources, Conservation & Recycling, 2020, 156: 104715. [19] LIU M D. Five-elements cycle optimization algorithm for the travelling salesman problem[C]//2017 18th International Conference on Advanced Robotics(ICAR). Hong Kong, China: IEEE, 2017: 595-601. [20] 区月华. 某乳制品企业冷链配送物流车辆调度优化研究[D]. 广州: 华南理工大学, 2017. [21] XIONG C K, CHEN D F, LU D, et al. Path planning of multiple autonomous marine vehicles for adaptive sampling using Voronoi-based ant colony optimization[J]. Robotics & Autonomous Systems, 2019, 115: 90-103. [22] 邓丽君. 基于客户满意度的物流配送车辆调度优化模型与算法研究[D]. 北京: 北京交通大学, 2012. [23] ZITZLER E, THIELE L. Multi-objective evolutionary algorithms: A comparative case study and the strength Pareto approach[J]. IEEE Transactions on Evolutionary Computation, 1999, 3(4): 257-271. doi: 10.1109/4235.797969 -