非线性多目标概率优化问题的自适应采样免疫优化算法

doi:10.12263/DZXB.20200171

电子学报 ›› 2021, Vol. 49 ›› Issue (4): 647-660.DOI: 10.12263/DZXB.20200171

非线性多目标概率优化问题的自适应采样免疫优化算法

张仁崇¹, 潘春燕², 武星³, 杨坤¹

1. 贵州商学院计算机与信息工程学院, 贵州贵阳 550014;
2. 黔南民族师范学院数学与统计学院, 贵州都匀 558000;
3. 贵州商学院管理学院, 贵州贵阳 550014

收稿日期:2020-02-14 修回日期:2020-07-19 出版日期:2021-04-25
- 通讯作者:
- 张仁崇
- 作者简介:
- 潘春燕 女,1990年10月出生,贵州三都人.2017年在贵州民族大学获理学硕士学位.现为黔南民族师范学院数学与统计学院讲师,主要研究方向为数据挖掘.E-mail:chunyanpan666@163.com;武星男,1988年7月出生,安徽来安人.2014年在贵州大学获工程硕士学位.现为贵州商学院管理学院讲师,主要研究方向为物流与供应链管理.E-mail:wuxingjobmail@163.com;杨坤男,1987年11月出生,贵州织金人.2017年在贵州民族大学获理学硕士学位.现为贵州商学院计算机与信息工程学院讲师,主要研究方向为模式识别与图像处理.E-mail:kunflv@126.com
- 基金资助:
- 贵州省科技计划 (No.QKHJC[2020]1Y423）; 贵州省教育厅青年科技人才成长 (No.QJH KY Zi[2018]276，No.QJH KY Zi[2018]429，No.QJH KY Zi[2018]275，No.QJH KY Zi[2018]269）; 贵州省教育厅人文社科 (No.2018qn42）

Adaptive Sampling Immune Optimization Algorithm for Nonlinear Multi-Objective Probabilistic Optimization Problems

ZHANG Ren-chong¹, PAN Chun-yan², WU Xing³, YANG Kun¹

1. Computer and Information Engineering College, Guizhou University of Commerce, Guiyang, Guizhou 550014, China;
2. School of Mathematics and Statistics, Qiannan Normal University for Nationalities, Duyun, Guizhou 558000, China;
3. College of Management, Guizhou University of Commerce, Guiyang, Guizhou 550014, China

Received:2020-02-14 Revised:2020-07-19 Online:2021-04-25 Published:2021-04-25
- Corresponding author:
- ZHANG Ren-chong
- Supported by:
- Science and Technology Project of Guizhou Province (No.QKHJC[2020]1Y423); Youth Science & Technology Talents Development Project of Department of Education of Guizhou Province (No.QJHKYZi[2018]276, No.QJHKYZi[2018]429, No.QJHKYZi[2018]275, No.QJHKYZi[2018]269); Department of Education of the Guizhou Province, Humanities and Social Sciences (No.2018qn42)

摘要/Abstract

摘要： 针对噪声环境下非线性多目标概率优化问题，提出问题求解的自适应采样免疫优化算法.在算法设计中，基于克隆选择原理，设计小种群的算法进化框架；提出目标值估计法自适应确定个体的样本大小并估算其目标值；借助传统快速非支配排序法，种群被分割成多级非支配子群协同进化；设计动态交叉分布指数的模拟二进制交叉加强各子群之间的信息交流；设计动态变异分布指数的多项式变异、均匀变异，以及自适应变异概率平衡全局、局部探索.最后，借助3个理论测试问题、海铁联运能耗优化问题以及9个代表性的比较算法，数值实验结果表明，此算法寻优效率优势显著、搜索效果优越、稳定性好.

关键词: 多目标概率优化, 免疫优化, 随机模拟, 自适应采样, 海铁联运

Abstract: In this paper, an adaptive sampling immune optimization algorithm is proposed to solve the nonlinear multi-objective probabilistic optimization problem in noisy environments. In the whole design of the algorithm, we develop an evolutionary framework with small population inspired by the clonal selection principle. The approach for estimating objective value is designed by adaptively determining the sample size of an individual. The population is divided into multilevel non-dominated sub-populations for co-evolution by the traditional fast non-dominated sorting approach. The simulation binary crossover with dynamic crossover distribution index is designed to enhance the information exchanges among all sub-populations. Polynomial mutation and uniform mutation with dynamic mutation distribution index, and adaptive mutation probability are designed to enhance the capability of global and local exploration. Finally, based on three theoretical test questions, energy consumption optimization of sea-rail intermodal transportation and nine representative comparison algorithms, the numerical experiment results show that the algorithm has significant search efficiency, superior search effect and good stability.

Key words: multi-objective probabilistic optimization, immune optimization, stochastic simulation, adaptive sampling, sea-rail intermodal transportation

中图分类号:

TP301.6

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.

ZHANG Ren-chong, PAN Chun-yan, WU Xing, et al. Adaptive Sampling Immune Optimization Algorithm for Nonlinear Multi-Objective Probabilistic Optimization Problems[J]. Acta Electronica Sinica, 2021, 49(4): 647-660.

参考文献

[1] 纪昌明,李克飞,张验科,等.基于机会约束的水库调度随机多目标决策模型[J].电力系统保护与控制,2012(19):36-40. JI Chang-ming,LI Ke-fei,ZHANG Yan-ke,et al.Stochastic multi-objective decision-making model of the reservoir operation based on chance-constrained programming[J].Power System Protection and Control,2012(19):36-40.(in Chinese)
[2] 李晓娜.不确定环境下城市需水量预测及多水源联合供水调度研究[D].邯郸:河北工程大学,2018. LI Xiao-na.Study on urban water demand forecast and multiple water sources optimization allocation under uncertainty[D].Handan:Hebei University of Engineering,2018.(in Chinese)
[3] 张国新,王瑜,沈田双.空降地面作战突破点决策模型[J].火力与指挥控制,2010,35(11):54-57. ZHANG Guo-xin,WANG Yu,SHEN Tian-shuang.A study on breakthrough point decision model of airborne ground operation[J].Fire Control & Command Control,2010,35(11):54-57.(in Chinese)
[4] 李卓环,陈艺璇,余涛,等.考虑大气污染时空分布的风火联合系统多目标优化调度[J].电力系统自动化,2019,43(14):126-139. LI Zhuo-huan,CHEN Yi-xuan,YU Tao,et al.Multi-objective optimization dispatching for wind-thermal power joint system considering temporal and spatial distribution of air pollutants[J].Automation of Electric Power Systems,2019,43(14):126-139.(in Chinese)
[5] 吕凯,唐昊,王珂,等.计及源荷双侧不确定性的跨区互联电网源网荷协同调度[J].电力系统自动化,2019,43(22):38-51,150. LV Kai,TANG Hao,WANG Ke,et al.Coordinated dispatching of source-grid-load for inter-regional power grid considering uncertainties of both source and load sides[J].Automation of Electric Power Systems,2019,43(22):38-51,150.(in Chinese)
[6] 裴文杰,汪沨,谭阳红,等.含光伏分布式电源配电网的电动汽车充电站机会约束规划[J].电力系统及其自动化学报,2017,29(6):45-52. PEI Wen-jie,WANG Feng,TAN Yang-hong,et al.Chance-constrained programming for electric vehicle charging stations in distribution network containing photovoltaic distributed generations[J].Proceedings of the CSU-EPSA,2017,29(6):45-52.(in Chinese)
[7] 杨新宇,胡业发.不确定环境下复杂产品维护、维修和大修服务资源调度优化[J].浙江大学学报(工学版),2019,53(05):852-861. YANG Xin-yu,HU Ye-fa.Maintenance,repair and overhaul/operations service resource scheduling optimization for complex products in uncertain environment[J].Journal of Zhejiang University(Engineering Science),2019,53(05):852-861.(in Chinese)
[8] 李整.基于粒子群优化算法的机组组合问题的研究[D].北京:华北电力大学(北京),2016. LI Zheng.Unit commitment via particle swarm optimization algorithm[D].Beijing:North China Electric Power University(Beijing),2016.(in Chinese)
[9] ZHANG Z H.Noisy immune optimization for chance-constrained programming problems[J].Applied Mechanics and Materials,2011,48:740-744.
[10] YANG K,ZHANG Z H,LU J X.Adaptive racing ranking-based immune optimization approach solving multi-objective expected value programming[J].Soft Computing,2017.1-20.
[11] 杨凯,张著洪.基于免疫优化的单目标多模态期望值规划[J].西南交通大学学报,2014,49(6):1061-1067. YANG Kai,ZHANG Zhu-hong.A single-objective multi-modal expected value programming based on immune optimization[J].Journal of Southwest Jiaotong University,2014,49(6):1061-1067.(in Chinese)
[12] 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.
[13] YANG K,ZHANG Z H.Adaptive sampling detection based immune optimization approach and its application to chance constrained programming[A].Genetic and Evolutionary Computing[C].Berlin:Springer,2015.19-28.
[14] ZHANG Z H,YANG K,ZHANG D M.Sample bound estimate based chance-constrained immune optimization and its applications[J].International Journal of Automation and Computing,2016,13(5):468-479.
[15] ZHANG Z H,ZHANG R C.Danger theory inspired micro-population immune optimization for probabilistic constrained programming[J].Evolving Systems,2019.1-16.
[16] 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(09):1785-1794. ZHANG Zhu-hong,ZHANG Ren-chong.Micro immune optimization algorithm for solving probabilistic optimization problems[J].Journal of Beijing University of Aeronautics and Astronautics,2016,42(09):1785-1794.(in Chinese)
[17] 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(05):900-914. ZHANG Ren-chong,ZHANG Zhu-hong.Immune optimization algorithm for nonlinear multi-objective probabilistic constrained programming[J].Journal of Beijing University of Aeronautics and Astronautics,2020,46(05):900-914.(in Chinese)
[18] 张铭鑫,张玺,彭建刚,等.不确定环境下再制造加工车间多目标调度优化方法[J].合肥工业大学学报(自然科学版),2016,39(4):433-439. ZHANG Ming-xin,ZHANG Xi,PENG Jian-gang,et al.Multi-objective optimization method of remanufacturing processing workshop scheduling under uncertain conditions[J].Journal of Hefei University of Technology (Natural Science),2016,39(4):433-439.(in Chinese)
[19] XU J P,DING C.A class of chance constrained multiobjective linear programming with birandom coefficients and its application to vendors selection[J].International Journal of production Economics,2011,131(2):709-720.
[20] 白牧可,唐巍,张璐,等.基于机会约束规划的DG与配电网架多目标协调规划[J].电工技术学报,2013,28(10):346-354. BAI Mu-ke,TANG Wei,ZHANG Lu,et al.Multi-objective coordinated planning of distribution network incorporating distributed generation based on chance constrained programming[J].Transactions of China Electrotechnical Society,2013,28(10):346-354.(in Chinese)
[21] 刘文学,梁军,负志皓,等.基于可信理论的多目标模糊机会约束无功优化[J].电工技术学报,2015,30(21):82-89. LIU Wen-xue,LIANG Jun,FU Zhi-hao,et al.Multi-objective chance constrained optimal reactive power flow based on credibility theory[J].Transactions of China Electrotechnical Society,2015,30(21):82-89.(in Chinese)
[22] VIRIVINTI N,MITRA K.Intuitionistic fuzzy chance constrained programming for handling parametric uncertainty:an industrial grinding case study[J].Industrial & Engineering Chemistry Research,2015,54(24):6291-6304.
[23] 谢仕炜,胡志坚,宁月.考虑最优负荷削减方向的电网多目标分层随机机会约束规划[J].电力自动化设备,2017,37(8):35-42. XIE S W,HU Z J,NING Y.Multi-objective hierarchical stochastic chance-constrained programming considering optimal load-shedding direction[J].Electric Power Automation Equipment,2017,37(8):35-42.(in Chinese)
[24] 徐斌,俞静.基于期权视角的海外市场拓展的双目标多项目多期优化随机机会约束模型[J].中国管理科学,2010,18(04):14-20. XU Bin,YU Jing.The bi-objective stochastic chance-constrained combination optimization model of multi-project and multi-item market development based on the perspective of real options[J].Chinese Journal of Management Science,2010,18(04):14-20.(in Chinese)
[25] WU J K,TANG L.Multi-objective stochastic scheduling models for hydrothermal plants based on fuzzy chance constrained programming[J].Proceedings of the CSEE,2011,31(25):26-34.
[26] MEHLAWAT M K,GUPTA P.COTS products selection using fuzzy chance-constrained multiobjective programming[J].Applied Intelligence,2015,43(4):732-751.
[27] TIMMIS J,HONE,STIBOR T,et al.Theoretical advances in artificial immune systems[J].Theoretical Computer Science,2008,403(1):11-32.
[28] 马元锋,李昂儒,余慧敏,等.基于动态拥挤距离的混合多目标免疫优化算法[J].计算机科学,2018,45(S1):63-68. MA Yuan-feng,LI Ang-ru,YU Hui-min,et al.Dynamic crowding distance-based hybrid immune algorithm for multi-objective optimization problem[J].Computer Science,2018,45(S1):63-68.(in Chinese)
[29] GONG M G,JIAO L C,DU H F,et al.Multiobjective immune algorithm with nondominated neighbor-based selection[J].Evolutionary Computation,2008,16(2):225-255.
[30] MARTINEZ-PENALOZA M,MEZURA-MONTES E.Immune generalized differential evolution for dynamic multi-objective environments:an empirical study[J].Knowledge-Based Systems,2018,142:192-219.
[31] XIA X,ZHOU Y.On the effectiveness of immune inspired mutation operators in some discrete optimization problems[J].Information Sciences,2018,426:87-100.
[32] ZHANG Z H,WANG L,LONG F.Immune optimization approach solving multi-objective chance-constrained programming[J].Evolving Systems,2013,6(1):41-53.
[33] ZHANG Z H,TU X.Probabilistic dominance-based multi-objective immune optimization algorithm in noisy environments[J].Journal of Computational and Theoretical Nanoscience,2007,4(7):1380-1387.
[34] LIU B D.Theory and Practice of Uncertain Programming(2^nd ed)[M].Berlin:Springer-Varlag,2009.50-53.
[35] 黄席樾,张著洪,何传江,等.现代智能优化算法理论与应用[M].北京:科学出版社,2005.18-21. HUANG Xi-yue,ZHANG Zhu-hong,HE Chuan-jiang,et al.Modern Intelligence Algorithms:Theory and Application[M].Beijing,China:Science Press,2005.18-21.(in Chinese)
[36] LIN Q,CHEN J,ZHAN Z H,et al.A hybrid evolutionary immune algorithm for multiobjective optimization problems[J].IEEE Transactions on Evolutionary Computation,2016,20(5):711-729.
[37] DEB K,PRATAP A,AGARWAL S,et al.A fast and elitist multiobjective genetic algorithm:NSGA-Ⅱ[J].IEEE Transactions on Evolutionary Computation,2002,6(2):182-197.
[38] ZHU Q L,LIN Q Z,CHEN W N,et al.An external archive-guided multiobjective particle swarm optimization algorithm[J].IEEE Transactions on Cybernetics,2017,47(9):2794-2808.
[39] COELLO C A C,PULIDO G T,LECHUGA M S.Handling multiple objectives with particle swarm optimization[J].IEEE Transactions on Evolutionary Computation,2004,8(3):256-279.
[40] LI K,DEB K,ZHANG Q F,et al.An evolutionary many-objective optimization algorithm based on dominance and decomposition[J].IEEE Transactions on Evolutionary Computation,2015,19(5):694-716.
[41] ZHANG Q F,LI H.MOEA/D:a multiobjective evolutionary algorithm based on decomposition[J].IEEE Transactions on Evolutionary Computation,2008,11(6):712-731.
[42] QIAN S Q,YE Y Q,JIANG B,et al.Constrained multiobjective optimization algorithm based on immune system model[J].IEEE Transactions on Cybernetics,2015,46(9):2056-2069.
[43] ZITZLER E,LAUMANNS M,THIELE L.SPEA2:Improving the strength Pareto evolutionary algorithm[A].Evolutionary Methods for Design,Optimization and Control with Applications To Industrial Problems[C].Berlin:Springer-Verlag,2002.95-100.
[44] 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.
[45] 张著洪,黄席樾.一种新的免疫算法及其在多模态函数优化中的应用[J].控制理论与应用,2004,(01):17-21. ZHANG Zhu-hong,HUANG Xi-yue.Novel immune algorithm and its application to multi-modal function optimization[J].Control Theory & Applications,2004,(01):17-21.(in Chinese)
[46] DE CASTRO L N,VON ZUBEN F J.The clonal selection algorithm with engineering applications[A].Proceedings of Genetic and Evolutionary Computation Conference[C].CA,USA:Morgan Kaufman Publisher,2000.36-37.
[47] VELDHUIZEN D A V.Multiobjective evolutionary algorithms:classifications,analyses,and new innovations[J].Evolutionary Computation,1999,8(2):125-147.
[48] DEB K.Advances in evolutionary multi-objective optimization[A].Symposium on Search Based Software Engineering[C].Berlin:Springer,2012.1-26.
[49] LIM W J,JAMBEK A B,NEOH S C,et al.Kursawe and ZDT functions optimization using hybrid micro genetic algorithm (HMGA)[J].Soft Computing,2015,19(12):3571-3580.
[50] DEB K.Multi-objective genetic algorithms:Problem difficulties and construction of test problems[J].Evolutionary Computation,1999,7(3):205-230.
[51] 毕超超,范勤勤,王维莉.基于策略自适应的多目标差分进化算法及其应用[J].计算机应用研究,2019,37(7):1-7. BI Chao-chao,FAN Qin-qin,WANG Wei-li.Multi-objective differential evolution algorithm based on self-adaptive strategy and its application[J].Application Research of Computers,2019,37(7):1-7.(in Chinese)

非线性多目标概率优化问题的自适应采样免疫优化算法

Adaptive Sampling Immune Optimization Algorithm for Nonlinear Multi-Objective Probabilistic Optimization Problems

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 3

编辑推荐

Metrics

[1]	王蓉芳, 焦李成, 刘芳, 杨淑媛. 利用纹理信息的图像分块自适应压缩感知[J]. 电子学报, 2013, 41(8): 1506-1514.
[2]	练秋生, 周婷. 结合字典稀疏表示和非局部相似性的自适应压缩成像算法[J]. 电子学报, 2012, 40(7): 1416-1422.
[3]	侯文广, 吴梓翠, 丁明跃. 测地空间中泊松碟采样的地形模型约简方法[J]. 电子学报, 2012, 40(6): 1274-1278.