2.765

2022影响因子

(CJCR)

  • 中文核心
  • EI
  • 中国科技核心
  • Scopus
  • CSCD
  • 英国科学文摘

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

基于问题性质的分布式低碳并行机调度算法研究

潘子肖 雷德明

潘子肖, 雷德明. 基于问题性质的分布式低碳并行机调度算法研究. 自动化学报, 2020, 46(11): 2427-2438 doi: 10.16383/j.aas.c180581
引用本文: 潘子肖, 雷德明. 基于问题性质的分布式低碳并行机调度算法研究. 自动化学报, 2020, 46(11): 2427-2438 doi: 10.16383/j.aas.c180581
Pan Zi-Xiao, Lei De-Ming. Research on property-based distributed low carbon parallel machines scheduling algorithm. Acta Automatica Sinica, 2020, 46(11): 2427-2438 doi: 10.16383/j.aas.c180581
Citation: Pan Zi-Xiao, Lei De-Ming. Research on property-based distributed low carbon parallel machines scheduling algorithm. Acta Automatica Sinica, 2020, 46(11): 2427-2438 doi: 10.16383/j.aas.c180581

基于问题性质的分布式低碳并行机调度算法研究

doi: 10.16383/j.aas.c180581
基金项目: 

国家自然科学基金 61573264

详细信息
    作者简介:

    潘子肖  清华大学控制科学与工程博士研究生.主要研究方向为智能系统优化与调度. E-mail: pzxwhut@126.com

    通讯作者:

    雷德明  武汉理工大学自动化学院教授.主要研究方向为智能系统优化与控制.本文通信作者. E-mail: deminglei11@163.com

Research on Property-based Distributed Low Carbon Parallel Machines Scheduling Algorithm

Funds: 

National Natural Science Foundation of China 61573264

More Information
    Author Bio:

    PAN Zi-Xiao  Ph. D. candidate in control theory and control engineering at Tsinghua University. His research interest covers manufacturing systems intelligent optimization and scheduling

    Corresponding author: LEI De-Ming  Professor at the School of Automation, Wuhan University of Technology. His research interest covers intelligent system optimization and control. Corresponding author of this paper
  • 摘要: 针对分布式低碳并行机调度问题(Distributed low carbon parallel machine scheduling problem, DLCPMSP), 由于该问题子问题众多, 为此, 首先将问题转换为扩展的低碳不相关并行机调度问题以降低子问题的数量; 然后提出了一种基于问题性质的非劣排序遗传算法-Ⅱ(Property-based non-dominated sorting genetic algorithm-Ⅱ, PNSGA-Ⅱ)以同时最优化总延迟时间和总能耗, 该算法运用针对问题特征的两种启发式算法初始化种群, 给出了问题的四种性质及证明, 提出了两种基于问题性质的局部搜索方法.运用大量实例进行了算法策略分析和对比实验, 结果分析表明, PNSGA-Ⅱ在求解DLCPMSP方面具有较强优势.
    Recommended by Associate Editor WU Zhou
    1)  本文责任编委  伍洲
  • 图  1  PNSGA-Ⅱ算法流程图

    Fig.  1  The flowchart of PNSGA-Ⅱ

    图  2  均值主效应图

    Fig.  2  Principal effect plot of mean

    图  3  6种算法关于四个实例的非劣解分布

    Fig.  3  Distribution of non-dominated solutions of six algorithms on four instances

    表  1  参数各水平取值

    Table  1  Factor levels of parameters

    参数水平
    1234
    $p_c$0.800.850.9095
    $p_m$0.000.050.100.15
    $N$6090120150
    下载: 导出CSV

    表  2  参数正交表及$DI_R$值

    Table  2  Orthogonal array and $DI_R$ value

    No.Factor$DI_R$
    $p_c$$p_m$$N$
    111120.94
    212213.42
    31336.012
    41446.519
    521219.85
    622113.82
    72346.721
    82436.000
    931311.89
    103248.126
    1133110.68
    123426.536
    1341411.13
    144238.531
    154328.199
    1644114.84
    下载: 导出CSV

    表  3  各参数平均$DI_R$

    Table  3  Average $DI_R$ of factors

    水平$p_c$$p_m$$N$
    111.7215.9515.07
    211.6010.9712.00
    39.3087.9038.108
    410.688.4748.124
    Delta2.4158.0506.962
    排秩312
    下载: 导出CSV

    表  4  种算法关于指标$DI_R$的对比

    Table  4  Comparisons of six algorithms on metric $DI_R$

    实例PNSGA-ⅡA1A2NSGA-ⅡSPEA2TIPG
    $2\times 10$1.0095.9893.75313.501.14729.95
    $2\times 20$0.2816.3763.3887.7964.38853.21
    $2\times 30$0.2976.2723.3619.4655.24047.96
    $2\times 40$0.7305.5591.7146.0744.89468.06
    $3\times 40$0.0746.5830.6767.4326.26963.24
    $4\times 40$0.1389.1223.64011.819.68275.89
    $2\times 50$0.9339.6062.0458.02412.7372.65
    $3\times 50$0.5754.5342.1599.2299.56782.67
    $4\times 50$0.0457.0532.2438.3497.63983.56
    $2\times 60$1.3529.8570.8979.0369.90573.18
    $3\times 60$0.8665.1661.6086.8617.68573.38
    $4\times 60$0.2578.6100.9449.48510.0977.30
    $2\times 80$1.8518.6160.8719.53914.0483.09
    $3\times 80$0.9328.2990.97910.0811.3084.17
    $4\times 80$1.01714.530.59416.1818.0698.23
    $5\times 80$0.59112.020.51211.7714.9191.74
    $2\times 100$1.6115.9171.9966.71410.7376.21
    $3\times 100$0.2346.3281.2957.72911.8483.59
    $4\times 100$0.0837.4401.07911.5315.1388.09
    $5\times 100$1.29913.470.56513.4617.3488.42
    $2\times 200$1.66421.422.19828.4836.18$-$
    $3\times 200$2.80839.371.55945.6956.06$-$
    $4\times 200$0.64033.891.88638.9648.04$-$
    $5\times 200$0.29134.633.11836.6554.36$-$
    均值0.81612.111.79514.3316.5574.73
    下载: 导出CSV

    表  5  6种算法关于指标$\rho $的结果对比

    Table  5  Comparisons of six algorithms on metric $\rho $

    实例PNSGA-ⅡA1A2NSGA-ⅡSPEA2TIPG
    $2\times 10$0.4440.1110.0000.0000.5560.000
    $2\times 20$0.5830.0210.3330.0210.0830.000
    $2\times 30$0.9750.0250.0000.0000.0120.000
    $2\times 40$0.8470.0200.0530.0670.0200.000
    $3\times 40$0.9100.0100.0800.0000.0100.000
    $4\times 40$0.7100.0110.2900.0000.0000.000
    $2\times 50$0.7180.1370.0760.0460.0310.000
    $3\times 50$0.8720.0320.1060.0000.0000.000
    $4\times 50$0.8960.0150.1040.0000.0000.000
    $2\times 60$0.8400.0240.0800.0320.0320.000
    $3\times 60$0.8220.0590.1290.0000.0000.000
    $4\times 60$0.7930.0090.1980.0000.0090.000
    $2\times 80$0.5510.0590.3240.0740.0000.000
    $3\times 80$0.6320.0080.3610.0000.0080.000
    $4\times 80$0.6460.0150.3540.0000.0000.000
    $5\times 80$0.6480.0140.3520.0000.0000.000
    $2\times 100$0.7590.0360.0150.1970.0000.000
    $3\times 100$0.9120.0540.0390.0000.0000.000
    $4\times 100$0.8970.0150.0880.0040.0000.000
    $5\times 100$0.4800.0100.5200.0000.0000.000
    $2\times 200$0.8530.0410.0860.0240.000$-$
    $3\times 200$0.7650.0080.2120.0190.000$-$
    $4\times 200$0.8520.0040.1480.0000.000$-$
    $5\times 200$0.9260.0050.0740.0000.000$-$
    均值0.7640.0310.1680.0200.0320.000
    下载: 导出CSV

    表  6  6种算法关于指标$SP$的结果对比

    Table  6  Comparisons of six algorithms on metric $SP$

    实例PNSGA-ⅡA1A2NSGA-ⅡSPEA2TIPG
    $2\times 10$1.1273.2074.55414.682.7847.470
    $2\times 20$5.0677.4658.55411.716.24210.89
    $2\times 30$5.03613.7710.958.81614.2218.55
    $2\times 40$5.99111.068.5338.8438.17332.89
    $3\times 40$6.4778.19910.129.6246.82313.56
    $4\times 40$11.626.9397.77828.527.42313.82
    $2\times 50$10.946.34514.2613.6016.3221.35
    $3\times 50$7.4556.91713.6611.198.6419.448
    $4\times 50$8.0899.01427.5210.738.11424.12
    $2\times 60$6.58715.739.2648.06410.1714.75
    $3\times 60$9.44712.2717.7413.228.95713.86
    $4\times 60$20.6017.8110.1314.207.3109.080
    $2\times 80$13.9813.508.97710.196.92336.90
    $3\times 80$17.0216.838.46414.6710.7713.87
    $4\times 80$4.88117.2610.3417.977.76012.32
    $5\times 80$6.40112.1911.5417.1811.8419.29
    $2\times 100$11.7812.9217.6537.6838.74101.1
    $3\times 100$22.3819.9015.5014.3214.0015.60
    $4\times 100$10.3116.2712.0910.9320.6026.28
    $5\times 100$4.99710.2046.7512.727.56420.12
    $2\times 200$20.3722.1053.7216.0841.22$-$
    $3\times 200$8.38834.4018.1419.9825.37$-$
    $4\times 200$23.6836.7818.3723.0032.56$-$
    $5\times 200$24.1228.5920.1933.7411.76$-$
    均值11.1114.9916.0315.9013.9321.77
    下载: 导出CSV

    表  7  配对样本$t$-test

    Table  7  Paired-sample $t$-test

    $t$-test experiment$p-$值$\left(DI_R\right)$ $p-$值$\left(\rho \right)$$p-$值$\left(SP\right)$
    $t$-test (PNSGA-Ⅱ, A1)0.0000.0000.007
    $t$-test (PNSGA-Ⅱ, A2)0.0010.0000.048
    $t$-test (PNSGA-Ⅱ, NSGA-Ⅱ)0.0000.0000.005
    $t$-test (PNSGA-Ⅱ, SPEA2)0.0000.0000.148
    $t$-test (PNSGA-Ⅱ, TIPG)0.0000.0000.014
    下载: 导出CSV
  • [1] Cheng T C E, Sin C C S. A state-of-the-art review of parallel-machine scheduling research. European Journal of Operational Research, 1990, 47(3): 271-292
    [2] 王凌, 王晶晶, 吴楚格.绿色车间调度优化研究进展.控制与决策, 2018, 33(3): 385-391 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=kzyjc201803001

    Wang Ling, Wang Jing-Jing, Wu Chu-Ge. Advances in green shop scheduling and optimization. Control and Decision, 2018, 33(3): 385-391 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=kzyjc201803001
    [3] Li K, Zhang X, Leung J Y T, Yang S L. Parallel machine scheduling problems in green manufacturing industry. Journal of Manufacturing Systems, 2016, 38: 98-106 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=1b1d4c8bcc6bb0b76950e2d31d6daee2
    [4] Wang S J, Wang X D, Yu J B, Ma S, Liu M. Bi-objective identical parallel machine scheduling to minimize total energy consumption and makespan. Journal of Cleaner Production, 2018, 193: 424-440 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=eb7bc4ea618ba7c377ab7388475f30e3
    [5] Wu X Q, Che A D. A memetic differential evolution algorithm for energy-efficient parallel machine scheduling. Omega, 2019, 82: 155-165 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=a20a2c052677b71255873c01b1ffd8d8
    [6] Zheng X L, Wang L. A collaborative multiobjective fruit fly optimization algorithm for the resource constrained unrelated parallel machine green scheduling problem. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2018, 48(5): 790-800 http://ieeexplore.ieee.org/document/7605452
    [7] Liang P, Yang H D, Liu G S, Guo J H. An ant optimization model for unrelated parallel machine scheduling with energy consumption and total tardiness. Mathematical Problems in Engineering, 2015, 2015: Article No. 907034
    [8] Li Z T, Yang H D, Zhang S Q, Liu S Q. Unrelated parallel machine scheduling problem with energy and tardiness cost. The International Journal of Advanced Manufacturing Technology, 2016, 84(1): 213-226 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=c055c9d705e004ac44af028f54031ce3
    [9] Che A D, Zhang S B H, Wu X Q. Energy-conscious unrelated parallel machine scheduling under time-of-use electricity tariffs. Journal of Cleaner Production, 2017, 156: 688-697 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=d073310b588cea264bb80c94121662c0
    [10] 雷德明, 潘子肖, 张清勇.多目标低碳并行机调度研究.华中科技大学学报(自然科学版), 2018, 46(8): 104-109 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=hzlgdxxb201808020

    Lei De-Ming, Pan Zi-Xiao, Zhang Qing-Yong. Researches on multi-objective low carbon parallel machines scheduling. Journal of Huazhong University of Science and Technology (Natural Science Edition), 2018, 46(8): 104-109 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=hzlgdxxb201808020
    [11] Guo Z X, Ngai E W T, Yang C, Liang X D. An RFID-based intelligent decision support system architecture for production monitoring and scheduling in a distributed manufacturing environment. International Journal of Production Economics, 2015, 159: 16-28 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=df53b2567919bf7afc9a0e70cc824e01
    [12] Lee C K, Shen Y A, Yang T, Tang A L. An effective two-phase approach in solving a practical multi-site order scheduling problem. Journal of the Chinese Institute of Industrial Engineers, 2011, 28(7): 543-552 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=10.1080/10170669.2011.637579
    [13] Gnoni M G, Iavagnilio R, Mossa G, Mummolo G, Di Leva A. Production planning of a multi-site manufacturing system by hybrid modelling: A case study from the automotive industry. International Journal of Production Economics, 2003, 85(2): 251-262 http://www.sciencedirect.com/science/article/pii/S0925527303001130
    [14] Timpe C H, Kallrath J. Optimal planning in large multi-site production networks. European Journal of Operational Research, 2000, 126(2): 422-435 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=5bcdacd526ebaf6e7dbfd1e00c3c92c5
    [15] Behnamian J, Fatemi Ghomi S M T. A survey of multi-factory scheduling. Journal of Intelligent Manufacturing, 2016, 27(1): 231-249 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=e98c9e9ebb9852aba68e057b1b492b85
    [16] 王凌, 邓瑾, 王圣尧.分布式车间调度优化算法研究综述.控制与决策, 2016, 31(1): 1-11 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=kzyjc201601001

    Wang Ling, Deng Jin, Wand Sheng-Yao. Survey on optimization algorithms for distributed shop scheduling. Control and Decision, 2016, 31(1): 1-11 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=kzyjc201601001
    [17] Chen Z L, Pundoor G. Order assignment and scheduling in a supply chain. Operations Research, 2006, 54(3): 555-572 http://dl.acm.org/citation.cfm?id=1246577
    [18] Terrazas-Moreno S, Grossmann I E. A multiscale decomposition method for the optimal planning and scheduling of multi-site continuous multiproduct plants. Chemical Engineering Science, 2011, 66(19): 4307-4318 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=52e76902534a683e4ca757e03e50bc3a
    [19] Behnamian J, Fatemi Ghomi S M T. The heterogeneous multi-factory production network scheduling with adaptive communication policy and parallel machine. Information Sciences, 2013, 219: 181-196 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=283e7956c2449a0f11d78199dee4914f
    [20] Behnamian J. Decomposition based hybrid VNS-TS algorithm for distributed parallel factories scheduling with virtual corporation. Computers & Operations Research, 2014, 52: 181-191 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=f25e3e0042841ec15565128b12cd35e5
    [21] Behnamian J, Fatemi Ghomi S M T. Minimizing cost-related objective in synchronous scheduling of parallel factories in the virtual production network. Applied Soft Computing, 2015, 29: 221-232 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=f9cebf0fa53df4bc4f147bc6748eff9e
    [22] Deb K, Agrawal S, Pratap A, Meyarivan T. A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-Ⅱ. In: Proceedings of the 6th International Conference on Parallel Problem Solving From Nature. Paris, France: Springer, 2000. 849-858
    [23] Wang Y, Zhang J, Assogba K, Liu Y, Xu M Z, Wang Y H. Collaboration and transportation resource sharing in multiple centers vehicle routing optimization with delivery and pickup. Knowledge-Based Systems, 2018, 160: 296-310 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=3715dbf73dfa30fc4a3c51ec5813aaec
    [24] Vahdani B, Veysmoradi D, Shekari N, Mousavi S M. Multi-objective, multi-period location-routing model to distribute relief after earthquake by considering emergency roadway repair. Neural Computing and Applications, 2018, 30(3): 835-854 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=7e2dfdf089a6235c7258ca4f74ab5d18
    [25] Nedjati A, Izbirak G, Arkat J. Bi-objective covering tour location routing problem with replenishment at intermediate depots: Formulation and meta-heuristics. Computers & Industrial Engineering, 2017, 110: 191-206 http://www.sciencedirect.com/science/article/pii/S0360835217302565
    [26] Camara M V O, Ribeiro G M, Tosta M D C R. A pareto optimal study for the multi-objective oil platform location problem with NSGA-Ⅱ. Journal of Petroleum Science and Engineering, 2018, 169: 258-268 http://www.sciencedirect.com/science/article/pii/S0920410518304297
    [27] Sun Y, Lin F H, Xu H T. Multi-objective optimization of resource scheduling in fog computing using an improved NSGA-Ⅱ. Wireless Personal Communications, 2018, 102(2): 1369-1385 doi: 10.1007/s11277-017-5200-5
    [28] Afzalirad M, Rezaeian J. A realistic variant of bi-objective unrelated parallel machine scheduling problem: NSGA-Ⅱ and MOACO approaches. Applied Soft Computing, 2017, 50: 109-123
    [29] Sofia A S, GaneshKumar P. Multi-objective task scheduling to minimize energy consumption and makespan of cloud computing using NSGA-Ⅱ. Journal of Network and Systems Management, 2018, 26(2): 463-485 doi: 10.1007/s10922-017-9425-0
    [30] Wang H F, Fu Y P, Huang M, Huang G O, Wang J W. A NSGA-Ⅱ based memetic algorithm for multiobjective parallel flowshop scheduling problem. Computers & Industrial Engineering, 2017, 113: 185-194
    [31] Yang Y, Cao L C, Wang C C, Zhou Q, Jiang P. Multi-objective process parameters optimization of hot-wire laser welding using ensemble of metamodels and NSGA-Ⅱ. Robotics and Computer-Integrated Manufacturing, 2018, 53: 141-152 http://www.zhangqiaokeyan.com/academic-journal-foreign_other_thesis/0204112722649.html
    [32] Wang S, Ali S, Yue T, Liaaen M. Integrating weight assignment strategies with NSGA-Ⅱ for supporting user preference multiobjective optimization. IEEE Transactions on Evolutionary Computation, 2018, 22(3): 378-393 http://ieeexplore.ieee.org/document/8123878
    [33] 陈志旺, 白锌, 杨七, 黄兴旺, 李国强.区间多目标优化中决策空间约束、支配及同序解筛选策略.自动化学报, 2015, 41(12): 2115-2124 doi: 10.16383/j.aas.2015.c150218

    Chen Zhi-Wang, Bai Xin, Yang Qi, Huang Xing-Wang, Li Guo-Qiang. Strategy of constraint, dominance and screening solutions with same sequence in decision space for interval multi-objective optimization. Acta Automatica Sinica, 2015, 41(12): 2115-2124 doi: 10.16383/j.aas.2015.c150218
    [34] 乔俊飞, 韩改堂, 周红标.基于知识的污水生化处理过程智能优化方法.自动化学报, 2017, 43(6): 1038-1046 doi: 10.16383/j.aas.2017.c170088

    Qiao Jun-Fei, Han Gai-Tang, Zhou Hong-Biao. Knowledge-based intelligent optimal control for wastewater biochemical treatment process. Acta Automatica Sinica, 2017, 43(6): 1038-1046 doi: 10.16383/j.aas.2017.c170088
    [35] Wang J J, Wang L. A knowledge-based cooperative algorithm for energy-efficient scheduling of distributed flow-shop. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2020, 50(5): 1805-1819
    [36] Wang L, Zheng X L. A knowledge-guided multi-objective fruit fly optimization algorithm for the multi-skill resource constrained project scheduling problem. Swarm and Evolutionary Computation, 2018, 38: 54-63 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=4d6268ff7cda6f1d66bebc9b2ce848ee
    [37] Karimi H, Rahmati S H A, Zandieh M. An efficient knowledge-based algorithm for the flexible job shop scheduling problem. Knowledge-Based Systems, 2012, 36: 236-244 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=c36d7e479c958023975a2ee40f793983
    [38] Gao J Q, He G X, Wang Y S. A new parallel genetic algorithm for solving multiobjective scheduling problems subjected to special process constraint. The International Journal of Advanced Manufacturing Technology, 2009, 43(1-2): 151-160 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=5bd04960a3def4f838355a47fc3ba1d8
    [39] Knowles J, Corne D. On metrics for comparing nondominated sets. In: Proceedings of the 2002 Congress on Evolutionary Computation. Honolulu, USA: IEEE, 2002. 711-716
    [40] Lei D M. Pareto archive particle swarm optimization for multi-objective fuzzy job shop scheduling problems. The International Journal of Advanced Manufacturing Technology, 2008, 37(1-2): 157-165 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=2fc7730d349fa83780e3e8c9e79c6c13
    [41] Wang L, Wang S Y, Zheng X L. A hybrid estimation of distribution algorithm for unrelated parallel machine scheduling with sequence-dependent setup times. IEEE/CAA Journal of Automatica Sinica, 2016, 3(3): 235-246
    [42] Zitzler E, Laumanns M, Thiele L. SPEA2: Improving the strength Pareto evolutionary algorithm. In: Proceedings of Evolutionary Methods for Design, Optimization and Control with Applications to Industrial Problems. Lausanne, Switzerland, 2001. 95-100
    [43] Lin S W, Ying K C, Wu W J, Chiang Y I. Multi-objective unrelated parallel machine scheduling: A Tabu-enhanced iterated Pareto greedy algorithm. International Journal of Production Research, 2016, 54(4): 1110-1121
  • 加载中
图(3) / 表(7)
计量
  • 文章访问数:  1563
  • HTML全文浏览量:  156
  • PDF下载量:  126
  • 被引次数: 0
出版历程
  • 收稿日期:  2018-08-31
  • 录用日期:  2018-11-09
  • 刊出日期:  2020-11-24

目录

    /

    返回文章
    返回