复合形法基本思想是什么？有什么特点

求解最优化问题的一种算法。该法较为适合解决有约束优化问题。使用该法仅需比较目标函数值即可决定搜索方向，算法较简单，对目标函数的要求不苛刻。

complex method

求解最优化问题的一种算法。该法较为适合解决有约束优化问题。使用该法仅需比较目标函数值即可决定搜索方向，算法较简单，对目标函数的要求不苛刻。

复合形是多个单纯形合并成的超多面体，顶点个数

（

维空间）。

复合形法与单纯形法极为相似，却也有不同：

1）复合形法不限制顶点个数为

，复合形法的顶点个数k取值范围为

；

2）复合形法需要检查顶点的可行性，即是否满足约束。

复合形法是由n+1个以上的顶点组合而成的多面体。他的基本思路是：在可行域内构造一初始复合型，然后通过比较各顶点目标函数值，在可行域中找一目标函数值有所改善的新点，并用其替换目标函数值较差的顶点，构成新的复合形。不断重复上述过程，复合形不断变形、转移、缩小，逐渐地逼近最优点。当复合形各顶点目标函数值相差不大或者各顶点相距很近时，则目标函数值最小的顶点即可作为最优点。复合形点点数目k一般取值(n+1)≤k≤2n，n是设计变量的个数。为了减小计算变量，复合形法在寻优过程中一般只以在可行域内的反射作为基本搜索策略。

复合形法寻优方法主要工作是生成初始复合形和更新复合形。

综合来说复合型法的算法思路清晰，容易掌握；不需求导数，不需作一维搜索，对函数性态没有特殊要求；程序结构简单，计算量不大；对初始点要求低，能较快地找到最优解，算法较为可靠。求解时需给出变量取值区间及初始复合形；随着变量维数增多计算效率明显降低；对约束条件较多的非凸问题，常出现多次想形心收缩，使收敛速度减慢。

复合形法适用于变量少，最好不超过15维，约束条件不多的优化问题。是机械优化设计中较为广泛的可靠算法之一。

The papers of the two helical gears reducer for multi-objective parameters, structural optimization and design. This paper on multi-objective optimization fuzzy conducted a preliminary design of a simple, and introduced a complex, multi-objective function of the optimization method, method of determining the membership function. According to achieve the greatest degree reducer smallest of the purpose of access to relevant information identified design variables, constraints, and the establishment of two helical gears reducer structural parameters of multi-objective fuzzy optimal design a mathematical model. In this paper, the integrated use of the design theory of fuzzy fuzzy comprehensive evaluation, selected through access to information collection and judgement factors set, and then using VB languages of the parameter optimization process, which optimize the process parameters used in the optimum design method of complex method, this Mathematical model parameters optimized, the results output.

The results showed that: Based on the fuzzy comprehensive evaluation of the multi-objective fuzzy optimal design is a more practical value of the integrated design, multi-objective design of the strong uncertainty, the results will certainly be the difference. Complex method in the optimization process of simply calculating function of the need for other processing functions, the objective function of the solution or bound function more complex engineering problems, is a direct optimization of the effective ways. Designers need to carefully consider all the factors can affect the results.

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