可靠性多目标优化设计的自适应行为博弈算法
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摘要
为解决可靠性多目标优化设计问题,并考虑各博弈方行为方式的动态性特点,提出一种自适应行为博弈算法。每个设计目标被视为一个博弈方,在计算随机设计变量对目标函数影响因子的基础上,结合模糊聚类将随机设计变量集分解为博弈方的策略集;建立了自适应行为规则,在新一轮博弈开始之前调整各博弈方的博弈行为,以及目标函数与各博弈方自身收益函数之间的映射关系;在经历多轮博弈后,根据收敛准则得到博弈均衡解。汽车制动器的案例设计结果表明,在计算效率方面,自适应行为博弈算法比竞争博弈与合作博弈算法具有更明显的优势。
To solve the problem of reliability multi-objective design optimization,an adaptive behavior-based game algorithm was proposed by considering the dynamic characteristics of players'behaviors in the game process.Each design objective was regarded as a player,and the random design variable set was decomposed into the strategy sets of players through the fuzzy clustering analysis for the influence factors of random design variables about the objective functions.The adaptive behavior rule was established.Then,the behavior and the mapping relationship between the objective function and the payoff function of each player were adjusted before the new round of game based on the rule.After multi-round of games,the equilibrium solution was obtained based on the convergence criterion.The design results of the automobile brake indicated that the proposed algorithm had the higher calculation efficiency by comparing with the competitive game and cooperative game.
To solve the problem of reliability multi-objective design optimization,an adaptive behavior-based game algorithm was proposed by considering the dynamic characteristics of players'behaviors in the game process.Each design objective was regarded as a player,and the random design variable set was decomposed into the strategy sets of players through the fuzzy clustering analysis for the influence factors of random design variables about the objective functions.The adaptive behavior rule was established.Then,the behavior and the mapping relationship between the objective function and the payoff function of each player were adjusted before the new round of game based on the rule.After multi-round of games,the equilibrium solution was obtained based on the convergence criterion.The design results of the automobile brake indicated that the proposed algorithm had the higher calculation efficiency by comparing with the competitive game and cooperative game.
引文
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[19]ZHANG Tao,JI Deyun.Fuzzy clustering analytical methods[J].Journal of Shenyang University,2000,12(2):73-79(in Chinese).[张弢,纪德云.模糊聚类分析法[J].沈阳大学学报,2000,12(2):73-79.]
[20]QU Fuheng,CUI Guangcai,LI Yanfang,et al.Fuzzy clustering algorithm and its application[M].Beijing:National Defense Industry Press,2011:57-66(in Chinese).[曲福恒,崔广才,李岩芳,等.模糊聚类算法及应用[M].北京:国防工业出版社,2011:57-66.]
[21]SUN Linsong,ZHANG Weihua,XIE Nenggang.Multi-objective optimization for shape design of arch dams based on game theory[J].Journal of Hohai University,2006,34(4):392-396(in Chinese).[孙林松,张伟华,谢能刚.基于博弈理论的拱坝体形多目标优化设计[J].河海大学学报,2006,34(4):392-396.]
[22]HU Wenjie,CHEN Liang.Multidisciplinary design optimization for automobile disk brake based on iSIGHT[J].Transactions of the Chinese Society for Agricultural Machinery,2010,41(5):17-20(in Chinese).[胡文婕,陈亮.基于iSIGHT的汽车盘式制动器多学科设计优化[J].农业机械学报,2010,41(5):17-20.]
[23]LI Liaoping,CHEN Liang,XIAO Pinhui.The simple method to deal with the coupling factors in complex product design[J].Journal of Fuzhou University,2015,43(4):506-511(in Chinese).[李廖平,陈亮,肖品辉.复杂产品设计决策中耦合因素处理的简便方法[J].福州大学学报,2015,43(4):506-511.]
[2]FU Chao,HU Xujie,YU Hongyan,et al.Unified multidisciplinary reliability analysis by chi-squared distributions[J].Computer Integrated Manufacturing Systems,2017,23(7):1439-1446(in Chinese).[付超,胡旭洁,于红艳,等.基于卡方分布的统一多学科可靠性分析[J].计算机集成制造系统,2017,23(7):1439-1446.]
[3]GARG H,RANI M,SHARMA S P,et al.Intuitionistic fuzzy optimization technique for solving multi-objective reliability optimization problems in interval environment[J].Expert Systems with Applications,2014,41(7):3157-3167.
[4]YU Miao,SHI Boqiang,JIANG Yong.Application of physical programming in uncertainty optimization design of multidisc wet brake[J].Transactions of the Chinese Society of Agricultural Machinery,2011,42(4):22-26(in Chinese).[于淼,石博强,姜勇.基于物理规划的湿式多盘制动器可靠性优化设计[J].农业机械学报,2011,42(4):22-26.]
[5]KOGISO N,KODAMA R,TOYODA M.Reliability-based multi-objective optimization using the satisficing trade-off method[J].Mechanical Engineering Journal,2014,1(6):1-12.
[6]WANG Ruobing,GU Liangxian,GONG Chunlin.A stratified sequencing multi-disciplinary reliability analysis method under random and interval uncertainty[J].Journal of Northwestern Polytechnical University,2016,34(1):139-146(in Chinese).[王若冰,谷良贤,龚春林.随机-区间混合可靠性分层序列化多学科可靠性分析方法[J].西北工业大学学报:2016,34(1):139-146.]
[7]HE Li,LIU Qinghuai.Multi-objective optimization theory and continuous method[M].Beijing:Science Press,2015:35-37(in Chinese).[贺莉,刘庆怀.多目标优化理论与连续化方法[M].北京:科学出版社,2015:35-37.]
[8]JUANG C H,WANG L.Reliability-based robust geotechnical design of spread foundations using multi-objective genetic algorithm[J].Computers and Geotechnics,2013,48(4):96-106.
[9]LIU Li,XING Chao,LONG Teng.Study of multi-objective trajectory optimization based on physical programming[J].Transactions of Beijing Institute of Technology,2013,33(4):357-362(in Chinese).[刘莉,邢超,龙腾.基于物理规划的弹道多目标优化[J].北京理工大学学报,2013,33(4):357-362.]
[10]XIAO M,SHAO X,GAO L,et al.A new methodology for multi-objective multidisciplinary design optimization problems based on game theory[J].Expert Systems with Applications an International Journal,2015,42(3):1602-1612.
[11]SHANKARAN S,VANDEPUTTE T.Game-theoretic models for cooperative equilibrium solutions of interacting engineering sub-systems[C]//Proceedings of ASME Turbo Expo2014:Turbine Technical Conference and Exposition.New York,N.Y.,USA:ASME,2014:1-12.
[12]ZHENG Cheng,JIN Sun,LAI Xinmin.Robust tolerance design method based on cooperative game[J].Journal of Shanghai Jiaotong University,2011,45(11):1587-1591(in Chinese).[郑丞,金隼,来新民.基于合作博弈的公差稳健设计方法[J].上海交通大学学报,2011,45(11):1587-1591.]
[13]CHEN Zhong,XIE Nenggang,ZHANG Ziming.Cooperative game method for structural optimization with multiple objectives[J].Engineering Mechanics,2009,26(4):32-37(in Chinese).[陈忠,谢能刚,张子明.结构多目标优化设计的合作博弈解法[J].工程力学,2009,26(4):32-37.]
[14]MENG R,XIE N,WANG L.Multi-objective game method based on self-adaptive space division of design variables and its application to vehicle suspension[J].Mathematical Problems in Engineering,2014(2):1-13.
[15]AHMADI B,NARIMANZADEH N,JAMALI A.Path synthesis of four-bar mechanisms using synergy of polynomial neural network and Stackelberg game theory[J].Engineering Optimization,2017,49(6):932-947.
[16]SHANG Yuchang.Animal behavior[M].2nd ed.Beijing:Peking University Press,2014:232-237(in Chinese).[尚玉昌.动物行为学[M].2版.北京:北京大学出版社,2014:232-237.]
[17]TONG Lingsheng,SHI Boqiang,SHEN Yanhua,et al.First-order reliability method based multidisciplinary design optimization on gear transmission[J].Journal of Mechanical Engineering,2010,46(3):42-46(in Chinese).[仝令胜,石博强,申焱华,等.基于FORM的齿轮传动多学科优化设计[J].机械工程学报,2010,46(3):42-46.]
[18]FENG Jiazhen,ZHANG Jianguo,QIU Jiwei.Multi-objective reliability design optimization approach based on competition game[J].Journal of Beijing University of Aeronautics and Astronautics,2018,44(4):887-894(in Chinese).[冯嘉珍,张建国,邱继伟.基于竞争博弈的多目标可靠性优化设计方法[J].北京航空航天大学学报,2018,44(4):887-894.]
[19]ZHANG Tao,JI Deyun.Fuzzy clustering analytical methods[J].Journal of Shenyang University,2000,12(2):73-79(in Chinese).[张弢,纪德云.模糊聚类分析法[J].沈阳大学学报,2000,12(2):73-79.]
[20]QU Fuheng,CUI Guangcai,LI Yanfang,et al.Fuzzy clustering algorithm and its application[M].Beijing:National Defense Industry Press,2011:57-66(in Chinese).[曲福恒,崔广才,李岩芳,等.模糊聚类算法及应用[M].北京:国防工业出版社,2011:57-66.]
[21]SUN Linsong,ZHANG Weihua,XIE Nenggang.Multi-objective optimization for shape design of arch dams based on game theory[J].Journal of Hohai University,2006,34(4):392-396(in Chinese).[孙林松,张伟华,谢能刚.基于博弈理论的拱坝体形多目标优化设计[J].河海大学学报,2006,34(4):392-396.]
[22]HU Wenjie,CHEN Liang.Multidisciplinary design optimization for automobile disk brake based on iSIGHT[J].Transactions of the Chinese Society for Agricultural Machinery,2010,41(5):17-20(in Chinese).[胡文婕,陈亮.基于iSIGHT的汽车盘式制动器多学科设计优化[J].农业机械学报,2010,41(5):17-20.]
[23]LI Liaoping,CHEN Liang,XIAO Pinhui.The simple method to deal with the coupling factors in complex product design[J].Journal of Fuzhou University,2015,43(4):506-511(in Chinese).[李廖平,陈亮,肖品辉.复杂产品设计决策中耦合因素处理的简便方法[J].福州大学学报,2015,43(4):506-511.]