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

单目标概率约束规划的微种群免疫优化算法

李静 张仁崇 潘春燕 杨凯

李静,张仁崇,潘春燕,等. 单目标概率约束规划的微种群免疫优化算法[J]. 北京航空航天大学学报,2023,49(3):525-537 doi: 10.13700/j.bh.1001-5965.2021.0288
引用本文: 李静,张仁崇,潘春燕,等. 单目标概率约束规划的微种群免疫优化算法[J]. 北京航空航天大学学报,2023,49(3):525-537 doi: 10.13700/j.bh.1001-5965.2021.0288
LI J,ZHANG R C,PAN C Y,et al. Micro immune optimization algorithm for single objective probabilistic constrained programming[J]. Journal of Beijing University of Aeronautics and Astronautics,2023,49(3):525-537 (in Chinese) doi: 10.13700/j.bh.1001-5965.2021.0288
Citation: LI J,ZHANG R C,PAN C Y,et al. Micro immune optimization algorithm for single objective probabilistic constrained programming[J]. Journal of Beijing University of Aeronautics and Astronautics,2023,49(3):525-537 (in Chinese) doi: 10.13700/j.bh.1001-5965.2021.0288

单目标概率约束规划的微种群免疫优化算法

doi: 10.13700/j.bh.1001-5965.2021.0288
基金项目: 贵州省科技计划(黔科合基础[2020]1Y423, 黔科合基础[2019]1178);贵州省大数据应用工程研究中心(黔教合KY字[2017]022);贵州省教育厅青年科技人才成长项目(黔教合KY字[2018]276, 黔教合KY字[2018]429)
详细信息
    作者简介:

    李 静等:单目标概率约束规划的微种群免疫优化算法 13

    通讯作者:

    E-mail:zhangrenchong1990@163.com

  • 中图分类号: TP301.6

Micro immune optimization algorithm for single objective probabilistic constrained programming

Funds: Science and Technology Program of Guizhou Province of China (QKHJC [2020] 1Y423, QKHJC [2019] 1178); Project of Guizhou Big Data Application Engineering Research Center in Guizhou Province (QJHKY Zi [2017] 022); Youth Science and Technology Talent Development Project of Education Department in Guizhou Province (QJHKY Zi [2018] 276, QJHKY Zi [2018] 429)
More Information
  • 摘要:

    针对无先验随机分布信息的单目标概率约束规划,探讨了微种群免疫优化算法。算法设计中,受危险理论启发设计微种群免疫优化算法进化框架;借助估计值的误差幅度,提出2个方法分别估计概率值和目标值;依据个体间的优劣关系,划分群体为3个类型子群协同进化;构建生命周期模型,设计自适应的交叉与变异概率、变异策略,结合交叉算子促进子群信息有效交流,并沿不同方向协同进化。数值实验统计结果说明:所提算法拥有良好的搜索效率、搜索效果及降噪能力,具有一定的竞争力和应用潜力。

     

  • 图 1  μIOA-Ⅲ 的流程

    Figure 1.  Flowchart of μIOA-Ⅲ

    图 2  问题1的箱线图

    Figure 2.  Box plots for problem 1

    图 3  问题1的搜索曲线

    Figure 3.  Search curves for problem 1

    图 4  问题2的箱线图

    Figure 4.  Box plots for problem 2

    图 5  问题2的搜索曲线

    Figure 5.  Search curves for problem 2

    图 6  问题3的箱线图

    Figure 6.  Box plots for problem 3

    图 7  问题3的搜索曲线

    Figure 7.  Search curves for problem 3

    图 8  问题4的箱线图

    Figure 8.  Box plots for problem 4

    图 9  问题4的搜索曲线

    Figure 9.  Search curves for problem 4

    表  1  问题1的统计结果比较

    Table  1.   Comparison of statistical results for problem 1

    算法minmaxmeanSt.DevCIIAEFR/%AR/s
    SSGA-A1.88302.32352.21630.0784[2.2033,2.2294]0.0021833.30
    SSGA-B1.94482.34162.22210.0788[2.2090,2.2352]0.00212843.13
    FROFI2.16532.34492.27400.0378[2.2677,2.2802]0.0031786.52
    C2oDE1.91142.32222.18340.0890[2.1686,2.1982]0.00109420.78
    SPSO2.13342.35332.30270.0299[2.2978,2.3077]0.01144715.44
    GA2.20312.34662.30750.0249[2.3033,2.3116]0.00516720.18
    μIOA2.10242.30982.23830.0477[2.2304,2.2462]01000.84
    μIOA-Ⅱ2.15052.31912.26580.0319[2.2605,2.2711]01000.54
    μIOA-Ⅲ2.13222.31632.26140.0372[2.2552,2.2675]01000.49
    下载: 导出CSV

    表  2  问题2的统计结果比较

    Table  2.   Comparison of statistical results for problem 2

    算法minmaxmeanSt.DevCIIAEFR/%AR/s
    SSGA-A6.95418.59757.94010.3230[7.8864,7.9937]0.0027832.98
    SSGA-B6.88478.54687.93210.3354[7.8764,7.9878]0.0038792.98
    FROFI6.79698.54597.81940.3055[7.7687,7.8701]0.0005925.87
    C2oDE7.90638.59728.31850.1419[8.2950,8.3421]0.00248417.42
    SPSO7.29018.65598.06520.3424[8.0083,8.1220]0.0126619.01
    GA7.60298.62938.17290.2719[8.1277,8.2180]0.00576611.52
    μIOA7.31728.34277.97260.1607[7.9459,7.9993] 8.50×10−5991.08
    μIOA-Ⅱ7.29048.27797.96970.1590[7.9433,7.9961] 3.56×10−5990.91
    μIOA-Ⅲ7.63168.30928.02730.1504[8.0023,8.0523]0 1000.70
    下载: 导出CSV

    表  3  问题3的统计结果比较

    Table  3.   Comparison of statistical results for problem 3

    算法minmaxmeanSt.DevCIIAEFR/%AR/s
    SSGA-A30.768531.401030.98030.1120[30.9617,30.9989]0.0023742.83
    SSGA-B30.716931.328130.94840.1124[30.9297,30.9671]0.0025762.79
    FROFI30.715831.158530.94310.0877[30.9286,30.9577]0.0022765.88
    C2oDE30.704730.906230.79050.0404[30.7838,30.7972]0.00653917.51
    SPSO30.671631.445730.96330.1470[30.9389,30.9877]0.0107287.43
    GA30.753131.348431.04190.1194[31.0221,31.0617]0.0024836.88
    μIOA30.790531.499931.00480.1135[30.9860,31.0237]4.54×10−5990.72
    μIOA-Ⅱ30.821331.177730.97810.0782[30.9651,30.9911]01000.93
    μIOA-Ⅲ30.785731.132630.91850.0608[30.9084,30.9286]01000.75
    下载: 导出CSV

    表  4  问题4的统计结果比较

    Table  4.   Comparison of statistical results for problem 4

    算法minmaxmeanSt.DevCIIAEFR/%AR/s
    SSGA-A0.16400.16600.16520.0004[0.1651,0.1653]01006.25
    SSGA-B0.16360.16610.16520.0005[0.1651,0.1653]01006.20
    FROFI0.16370.16580.16500.0004[0.1650,0.1651]010013.16
    C2oDE0.16590.16640.16620.0001[0.1662,0.1663]010038.17
    SPSO0.16390.16630.16580.0004[0.1658,0.1659]010026.94
    GA0.16130.16550.16350.0008[0.1634,0.1637]010026.54
    μIOA0.16580.16650.16630.0001[0.1663,0.1663]01003.71
    μIOA-Ⅱ0.16540.16640.16600.0002[0.1660,0.1661]01002.09
    μIOA-Ⅲ0.16530.16640.16600.0002[0.1660,0.1661]01001.58
    下载: 导出CSV

    表  5  μIOA-Ⅲ在不同参数设置下求解问题2的统计结果比较

    Table  5.   Comparison of statistical results for solving problem 2 of μIA-Ⅲ in different parameter settings

    参数组合minmaxmeanSt.DevCIIAEFR/%AR/s
    N=4, M=10,W=57.38148.32257.9360.1779[7.9064,7.9654]01000.41
    N=5 , M=10, W=57.63198.37478.02290.1348[8.0005,8.0453]01000.60
    N=6, M=10, W=57.84668.34468.05790.1390[8.0348,8.0810]01000.88
    N=5, M=10, W=47.61218.31548.00740.1460[7.9832,8.0317]01000.60
    N=5, M=10, W=67.65358.33978.03080.1384[8.0078,8.0538]01000.63
    N=5, M=8, W=57.60798.30447.98430.1436[7.9604,8.0081]1.19×10−4990.43
    N=5, M=12, W=57.58528.34238.04220.1642[8.0150,8.0695]01000.79
    下载: 导出CSV
  • [1] CHEN Y, LI Y, SUN B, et al. A chance-constrained programming approach for a zinc hydrometallurgy blending problem under uncertainty[J]. Computers & Chemical Engineering, 2020, 140: 106893.
    [2] 卢福强, 陈伟东, 毕华玲, 等. 考虑随机需求和多种运输方式的第四方物流路径问题[J]. 计算机集成制造系统, 2020, 26(10): 2864-2876. doi: 10.13196/j.cims.2020.10.025

    LU F Q, CHEN W D, BI H L, et al. Fourth party logistics routing problem considering stochastic demand and multiple transportation modes[J]. Computer Integrated Manufacturing Systems, 2020, 26(10): 2864-2876(in Chinese). doi: 10.13196/j.cims.2020.10.025
    [3] LONG J, SUN Z, PARDALOS P M, et al. A robust dynamic scheduling approach based on release time series forecasting for the steelmaking-continuous casting production[J]. Applied Soft Computing, 2020, 92: 106271. doi: 10.1016/j.asoc.2020.106271
    [4] LONG J, SUN Z, HONG Y, et al. Robust dynamic scheduling with uncertain release time for the steelmaking-continuous casting production[C]//2018 International Conference on Sensing, Diagnostics, Prognostics, and Control. Piscataway: IEEE Press, 2018: 531-536.
    [5] SONG H, DONG M, HAN R, et al. Stochastic programming-based fault diagnosis in power systems under imperfect and incomplete information[J]. Energies, 2018, 11(10): 2565. doi: 10.3390/en11102565
    [6] HONG Z, ZHANG Q, GONG T, et al. Peak load regulation and cost optimization for microgrids by installing a heat storage tank and a portable energy system[J]. Applied Sciences, 2018, 8(4): 567. doi: 10.3390/app8040567
    [7] ZHANG H, HA M, ZHAO H, et al. Inexact multistage stochastic chance constrained programming model for water resources management under uncertainties[J]. Scientific Programming, 2017, 2017: 1-14.
    [8] AHMED S. Convex relaxations of chance constrained optimization problems[J]. Optimization Letters, 2014, 8(1): 1-12. doi: 10.1007/s11590-013-0624-7
    [9] SUN X L, BAI X D, ZHENG X J. A survey on probabilistically constrained optimization problems[J]. Operations Research Transactions, 2012, 16(3): 65-73.
    [10] 刘宝碇, 赵瑞清. 随机规划与模糊规划[M]. 北京: 清华大学出版社, 1998: 79-87.

    LIU B D, ZHAO R Q. Stochastic programming and fuzz programming[M]. Beijing: Tsinghua University Press, 1998: 79-87(in Chinese).
    [11] YANG L, YANG Z, LI G, et al. Optimal scheduling of an isolated microgrid with battery storage considering load and renewable generation uncertainties[J]. IEEE Transactions on Industrial Electronics, 2019, 66(2): 1565-1575. doi: 10.1109/TIE.2018.2840498
    [12] HOMEN-DE-MELLO T, BAYRAKSAN G. Monte Carlo sampling-based methods for stochastic optimization[J]. Surveys in Operations Research and Management Science, 2014, 19(1): 56-85. doi: 10.1016/j.sorms.2014.05.001
    [13] ZHANG Z H. Noisy immune optimization for chance-constrained programming problems[J]. Applied Mechanics and Materials, 2011, 48-49: 740-744. doi: 10.4028/www.scientific.net/AMM.48-49.740
    [14] ZHANG Z H, WANG L, LIAO M. Adaptive sampling immune algorithm solving joint chance-constrained programming[J]. Journal of Control Theory and Applications, 2013, 11(2): 237-246. doi: 10.1007/s11768-013-1186-z
    [15] YANG K, ZHANG Z H. Adaptive sampling detection based immune optimization approach and its application to chance constrained programming[M]//SUN H, YANG C Y, LIN C W, et al. Genetic and evolutionary computing. Berlin: Springer International Publishing, 2015: 19-28.
    [16] ZHANG Z H, LI L, ZHANG R C. Danger theory based micro immune optimization algorithm solving probabilistic constrained optimization[C]//2017 2nd IEEE International Conference on Computational Intelligence and Applications. Piscataway: IEEE Press, 2017: 103-107.
    [17] ZHANG Z H, ZHANG R C. Danger theory inspired micro-population immune optimization for probabilistic constrained programming[J]. Evolving Systems, 2020, 11(2): 333-348. doi: 10.1007/s12530-019-09277-6
    [18] 张著洪, 张仁崇. 求解概率优化问题的微种群免疫优化算法[J]. 北京航空航天大学学报, 2016, 42(9): 1785-1794. doi: 10.13700/j.bh.1001-5965.2015.0563

    ZHANG Z H, ZHANG R C. Micro immune optimization algorithm for solving probabilistic optimization problems[J]. Journal of Beijing University of Aeronautics and Astronautics, 2016, 42(9): 1785-1794(in Chinese). doi: 10.13700/j.bh.1001-5965.2015.0563
    [19] 张仁崇, 张著洪. 非线性多目标概率约束规划免疫优化算法[J]. 北京航空航天大学学报, 2020, 46(5): 900-914. doi: 10.13700/j.bh.1001-5965.2019.0350

    ZHANG R C, ZHANG Z H. Immune optimization algorithm for nonlinear multi-objective probabilistic constrained programming[J]. Journal of Beijing University of Aeronautics and Astronautics, 2020, 46(5): 900-914(in Chinese). doi: 10.13700/j.bh.1001-5965.2019.0350
    [20] 张仁崇, 潘春燕, 武星, 等. 非线性多目标概率优化问题的自适应采样免疫优化算法[J]. 电子学报, 2021, 49(4): 647-660. doi: 10.12263/DZXB.20200171

    ZHANG R C, PAN C Y, WU X, et al. Adaptive sampling immune optimization algorithm for nonlinear multi-objective probabilistic optimization problems[J]. Acta Electronica Sinica, 2021, 49(4): 647-660(in Chinese). doi: 10.12263/DZXB.20200171
    [21] LIU B D. Theory and practice of uncertain programming[M]. 3rd ed. Berlin: Springer International Publishing, 2009: 50-53.
    [22] 沈依婷, 张菁, 武鹏, 等. 含电动汽车的配电网双重不确定性网架规划方法[J]. 中国电力, 2020, 53(4): 139-146.

    SHEN Y T, ZHANG J, WU P, et al. Bi-uncertainty network frame planning method for distribution network with electric vehicles[J]. Electric Power, 2020, 53(4): 139-146(in Chinese).
    [23] XIAO N. An algorithm for solving stochastic chance-constrained programming problem[J]. Advanced Materials Research, 2014, 912: 1138-1141.
    [24] HUANG D, XIE L, WU Z. Dynamic economic dispatch for microgrid based on the chance-constrained programming[J]. Journal of Electrical Engineering & Technology, 2017, 12(3): 1064-1072.
    [25] 李鹏, 蔡永青, 韩肖清, 等. 计及随机模糊双重不确定性的交直流混合微网优化运行[J]. 高电压技术, 2020, 46(7): 2269-2279. doi: 10.13336/j.1003-6520.hve.20200619001

    LI P, CAI Y Q, HAN X Q, et al. Optimization operation of AC/DC hybrid microgrid considering random fuzzy double uncertainties[J]. High Voltage Engineering, 2020, 46(7): 2269-2279(in Chinese). doi: 10.13336/j.1003-6520.hve.20200619001
    [26] 德格吉日夫, 谭忠富, 李梦露, 等. 考虑不确定性的风储电站参与电力现货市场竞价策略[J]. 电网技术, 2019, 43(8): 2799-2807. doi: 10.13335/j.1000-3673.pst.2019.0547

    DE G J R F, TAN Z F, LI M L, et al. Bidding strategy of wind-storage power plant participation in electricity spot market considering uncertainty[J]. Power System Technology, 2019, 43(8): 2799-2807(in Chinese). doi: 10.13335/j.1000-3673.pst.2019.0547
    [27] 马丽叶, 王志强, 陆肖宇, 等. 基于机会约束规划的风-火-蓄联合系统优化调度[J]. 电网技术, 2019, 43(9): 3311-3320.

    MA L Y, WANG Z Q, LU X Y, et al. Optimal scheduling of combined wind-thermo-storage system based on chance constrained programming[J]. Power System Technology, 2019, 43(9): 3311-3320(in Chinese).
    [28] ZHAO Q, YANG R, DUAN F. An immune clonal hybrid algorithm for solving stochastic chance-constrained programming[J]. Journal of Computational Information Systems, 2012, 8(20): 8295-8302.
    [29] 韩畅, 梁博淼, 林振智, 等. 防灾应急电源优化调度的机会约束规划方法[J]. 电力自动化设备, 2018, 38(3): 147-154. doi: 10.16081/j.issn.1006-6047.2018.03.020

    HAN C, LIANG B M, LIN Z Z, et al. Chance-constrained programming method for optimal scheduling of emergency power source[J]. Electric Power Automation Equipment, 2018, 38(3): 147-154(in Chinese). doi: 10.16081/j.issn.1006-6047.2018.03.020
    [30] 贾伯岩, 马天祥, 张智远, 等. 计及不确定性的含分布式发电并网的配电网故障区段定位方法[J]. 电力系统保护与控制, 2020, 48(14): 35-42. doi: 10.19783/j.cnki.pspc.191002

    JIA B Y, MA T X, ZHANG Z Y, et al. Fault section location method for distribution networks with distributed generation and grid connection considering uncertainty[J]. Power System Protection and Control, 2020, 48(14): 35-42(in Chinese). doi: 10.19783/j.cnki.pspc.191002
    [31] 茆诗松, 程依明, 濮晓龙, 等. 概率论与数理统计教程[M]. 北京: 高等教育出版社, 2004: 226-237.

    MAO S S, CHENG Y M, PU X L, et al. Probability theory and mathematical statistics course[M]. Beijing: Higher Education Press, 2004: 226-237(Chinese).
    [32] MATZINGER P. Tolerance, danger, and the extended family[J]. Annual Review of Immunology, 1994, 12(1): 991-1045. doi: 10.1146/annurev.iy.12.040194.005015
    [33] POOJARI C A, VARGHESE B. Genetic algorithm based technique for solving chance constrained problems[J]. European Journal of Operational Research, 2008, 185(3): 1128-1154. doi: 10.1016/j.ejor.2006.06.045
    [34] WANG Y, WANG B C, LI H X, et al. Incorporating objective function information into the feasibility rule for constrained evolutionary optimization[J]. IEEE Transactions on Cybernetics, 2016, 46(12): 2938-2952. doi: 10.1109/TCYB.2015.2493239
    [35] WANG B C, LI H X, LI J P, et al. Composite differential evolution for constrained evolutionary optimization[J]. IEEE Transactions on Systems Man and Cybernetics Systems, 2018, 49(7): 1482-1495.
    [36] SALEHINEJAD H, RAHNAMAYAN S, TIZHOOSH H R. Micro-differential evolution: diversity enhancement and a comparative study[J]. Applied Soft Computing, 2017, 52: 812-833. doi: 10.1016/j.asoc.2016.09.042
    [37] YASUI T, SUGISAKA J, HIRAYAMA K. Structural optimization of silica-based 2×2 multimode interference coupler using a real-coded micro-genetic algorithm[J]. Progress in Electromagnetics Research, 2017, 55: 169-178. doi: 10.2528/PIERM17012204
    [38] CAMERO A, ARELLANO-VERDEJO J, ALBA E. Road map partitioning for routing by using a micro steady state evolutionary algorithm[J]. Engineering Applications of Artificial Intelligence, 2018, 71: 155-165. doi: 10.1016/j.engappai.2018.02.016
    [39] VARGHESE B, POOJARI C A. Genetic algorithm based technique for solving chance constrained problems arising in risk management[R]. CARISMA Technical Report, 2004: 1-49.
    [40] 程晓娟, 韩庆兰, 全春光. 不确定条件下机械产品设计方案费效权衡优化[J]. 计算机集成制造系统, 2015, 21(8): 1988-1994. doi: 10.13196/j.cims.2015.08.003

    CHENG X J, HAN Q L, QUAN C G. Cost-effective trade-off of mechanical product design scheme under uncertainty[J]. Computer Integrated Manufacturing System, 2015, 21(8): 1988-1994(in Chinese). doi: 10.13196/j.cims.2015.08.003
  • 加载中
图(9) / 表(5)
计量
  • 文章访问数:  351
  • HTML全文浏览量:  87
  • PDF下载量:  33
  • 被引次数: 0
出版历程
  • 收稿日期:  2021-06-02
  • 录用日期:  2021-09-24
  • 网络出版日期:  2021-10-12
  • 整期出版日期:  2023-03-30

目录

    /

    返回文章
    返回
    常见问答