结构多目标优化设计的合作博弈解法  

COOPERATIVE GAME METHOD FOR STRUCTURAL OPTIMIZATION WITH MULTIPLE OBJECTIVES

作　　者：陈忠[1,2] 谢能刚[3] 张子明[1] 

机构地区：[1]河海大学土木工程学院,江苏南京210098 [2]中天建设集团,浙江杭州310008 [3]安徽工业大学机械工程学院,安徽马鞍山243002

出　　处：《工程力学》2009年第4期32-37,共6页Engineering Mechanics

基　　金：教育部新世纪优秀人才计划项目(070003);教育部科学技术研究重点项目(207050);安徽省自然科学基金项目(070414174);安徽高校省级自然科学研究重点项目(2006KJ001A)

摘　　要：提出结构多目标优化设计的合作博弈求解方法,给出多目标问题的博弈描述,将设计变量集合分解为各博弈方拥有的策略空间,采用共谋合作模型,遵守"你中有我,我中有你"协议,将绝对收益和相对收益组合起来作为博弈方的得益函数,各博弈方分别以自身得益为目标函数,在各自的策略空间中进行单目标优化,获得本博弈方对其余博弈方的最佳对策,所有博弈方的最佳对策形成一轮博弈的策略组合,并根据收敛判别,通过多轮博弈,获得最终的博弈均衡解。以4杆桁架和拱坝体型设计为例,设计结果表明了合作博弈求解方法的有效性和可靠性。This paper presents a cooperative game method for structural optimization design with multiple objectives. It also presents the game description about multi-objective problems i.e. decomposing design variable assembly into a stratagem set of all the game players. This method adopts conspiring cooperative model, which complies with the agreement of “I have you with me and you have me with you”. It combines absolute benefits with relative benefits to be the payoff function of game players. Single objective optimization is carried on in each game player＇s strategy set to obtain the player＇s optimal countermeasure to the other players, by taking his payoff as the objective function. The entire optimal countermeasures form a new game strategy set. The game equilibrium solution will be obtained finally by playing the game several times, according to the convergence criterion. The design of a four-bar truss and an arch dam demonstrates the efficiency and reliability of the cooperative game method.

关 键 词：结构优化 多目标 博弈 共谋合作模型 拱坝 

分 类 号：O302[理学—力学] TU318[建筑科学—结构工程]