摘要
本文以信息论极大熵原理为基础，着眼于一类新型的结构优化算法，在改进原有类似算法不足的基础之上，提出了控制参数自适应的观点，同时拓宽了原来代理概念的适用范围，系统研究了完全基于极大熵的结构优化理论和方法。
主要研究内容如下：
对极大熵方法在结构优化中的应用进行了全面详细的描述。在极大熵基础理论方面，重点介绍了以李兴斯教授为代表的学者们在结构优化极大熵方法中的研究现状和最新成果；在离散变量处理方面，重点介绍了霍达教授提出的附加约束方法的研究成果。这些开创性的研究成果构成了本文研究工作的背景和基础。
对于松弛参数的选取进行了深入研究，在传统的极大熵方法的基础上提出了基于参数自适应的MEMP方法。该方法不同于人工调试和仅凭经验的传统参数选取方法，由于在计算代理系数的时候不需要过分的依赖于频繁的调试，同时对于是否可以求解的问题给出一定的判断，避免了有些问题本身的条件不好而导致人工调试失效的问题。它可以根据迭代的结果判断计算状态的优劣而自动适应调整，迫使迭代返回到正常的轨迹上来。正是由于这个特点，MEMP算法具备一定的智能性。
在一阶近似的水平上推导了传统的尺寸优化模型，该方法不再基于常见的泛静定化假设而是从泰勒近似的角度研究问题，在数学上严格地证明了传统的泛静定化模型具备一阶精度。
在K-S函数的迭代简化形式的基础上，进一步的拓宽“代理”的概念，在迭代点上用“代理目标评价函数”代替K-S函数，提出了一种新的评价函数方法MOP。
在本文MEMP算法和MOP算法的基础上，研究了桁架结构的形状优化的二步算法，该算法两步均建立在极大熵的方法之上，不需要其他的优化方法作为辅助，这种运用极大熵原理统一处理目标函数和约束函数的方法是极大熵方法的一种综合应用。
深入的研究了霍达教授在八十年代提出的附加约束方法。拓宽了离散化的约束条件，提出了离散变量的MEMP算法，并且自然的将其推广到形状优化和混合离散变量的优化。
文中最后对于本文完成的研究成果进行了总结，并且对于本课题的进一步研究方向和有待解决的问题给出了作者的看法。
Focused on the Max Entropy principle of information theory, a new kind of structural optimization method based on parameter self adjustment is systemically studied in this dissertation.
In this thesis, the main achievements of research are as follows:
The application of max entropy in structural optimization is fully described. In the aspect of max entropy theory, the most up-to-date research and achievements in structure optimization of those scholars with the representative of Professor Li Xing Si is introduced; with optimization of discrete variable, the method of attached constrain bring forward by HuoDa is described. Those innovative achievements form the base and back ground of this dissertation.
By studying the selection of slack parameter from the viewpoint of iteration condition, a method, named MEMP, with main character of self adjustment based on traditional entropy principle is given. Instead of debugging with experience frequently in the calculation of parameters, this method , different from the traditional parameter selection meihod by manual adjustment, lirstly distinguish the good from the bad condition of iteration, and then take a few self adjustment steps with the corresponding iteration status.
In the level of first order, the inference of traditional truss size optimization model from the standpoint of Taylor approximation is given. Without the traditional assumption of static determinacy, this thesis prove first order precision of the model with reciprocal substitution in truss optimization.
With the simplified formality of K-S coherence function, the conception of proxy is broadened by substituting K-S function with proxy objective assessment function given in this thesis. In addition, a new kind of proxy method named MOP based on proxy objective function is also given.
With the combination of algorithm MEMP and MOP given by this dissertation, the shape optimization model of truss structure is researched and a kind of two-steps optimization algorithm based on max entropy is presented .The shape optimization problem of truss structure is been divided by this method into two stages: area stage and coordinate stage, with its corresponding algorithm named MEMP and MOP. In the view of max entropy principle, this method can be viewed as the model of comprehensive application.
The method of attached constrain is studied. By extending the discrete variable condition with continuous real smooth constrain function, further study is been carried out in truss size optimization model. In addition, the method is popularized in other optimization such as those optimization models with mixture variable of continuous type and discrete type.
In the last part, the summarization of this dissertation is given with the suggestion of further research on some remaining problem.
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