空间网格结构优化设计的模糊判决方法研究  

Study on fuzzy decision making method of optimum design of space frame structures

作　　者：郦亮[1] 孙仁范 葛心[1] 牟在根[1] 

机构地区：[1]北京科技大学土木系,北京100083 [2]中国建筑技术集团有限公司,北京100013

出　　处：《空间结构》2005年第1期40-44,共5页Spatial Structures

基　　金：国家自然科学基金资助项目(50078004).

摘　　要：在空间网格结构的优化设计过程中,必然会遇到大量的不确定性信息和因素,而且往往要考虑多个目标函数,而各个目标之间存在矛盾及各目标的解具有冲突性,多目标优化问题要求各个目标函数都达到最优一般很难.本文在经典模糊判决法的基础上,提出了四种改进的模糊判决法,并利用隶属函数建立模糊优化数学模型转化为非模糊的单目标优化模型,从而可以使用普通优化程序得到模糊优化解.最后,通过二十五杆塔架的数值例题来说明本方法的求解过程并验证了其模糊判决方法的有效性和可行性.In design process of structure, a lot of uncertain information and factor will be encountered and it is needed to consider multi objectives, while the objectives are contradictive and the solution of the objectives are conflictive. It is difficult to require every objective of the multi-objective optimization problem to reach the optimum. To solve the problem, the paper presents four kinds of improved fuzzy decision making methods on the basis of the classical fuzzy decision making methods. Membership function is used to build fuzzy optimum mathematic model that will be converted into non-fuzzy single-objective optimum model. So we can find the solution of multi-objective fuzzy optimization problem with general optimum programming. Finally, illustrative numerical example of 25 bar truss for minimum weight and minimum deflection is provided to illustrate the process of finding the solution and to demonstrate reliability and feasibility of the fuzzy decision making method.

关 键 词：判决方法 结构优化设计 多目标优化问题 空间网格结构 不确定性信息 目标函数 模糊判决 设计过程 优化模型 模型转化 模糊优化 隶属函数 优化程序 求解过程 优化解 

分 类 号：O224[理学—运筹学与控制论] V557.3[理学—数学]