改进复合形法及其在边坡稳定分析中的应用

Modified complex method and its application to the slope stability analysis

基本复合形法寻优考虑了复形顶点目标函数的改进,但忽略了保持复形顶点的多样性,从而有可能使算法易陷入局部极优.为此,进行了以下改进:对每个顶点构造寻优直线,即该顶点与其余顶点几何中心的连线;在该直线上寻找该顶点的改善点并替换掉该顶点构造新的复形;在构造的多个新复形中,选择多样性最强的新复形作为本次迭代产生的复形;如此迭代直至没有新的复形产生.顶点多样性采用复形相似距度量.通过对1个复杂边坡最小安全系数的搜索证明,这些改进措施是有效的.

The search strategy of the basic complex method is based on the replacement of “bad” design point, whose objective function value is the maximum among all the design points, with better design point. And this better point was found on the line through the “bad” design point and the center of all design points except bad point. In this replacement process, the objective function value of the design points was improved, whereas the diversity of these points was ignored, and the basic complex method would be fall into the local optimum in half probability. In this paper, a new search strategy has been presented as follows： each design point is replaced with its corresponding new better design point located at the line through the current design point and the center of the rest design points, thereby the old complex can generate several new complexes. The new complex, whose diversity quantified by hamming distance is the strongest among all new complexes, is the desirable complex in the current iterative step. The method continues until no new complex is generated. The modified complex method is applied to the search for the minimum factor of safety of two complex soil slopes and the results show that the modified search strategy is valid.