最大熵DFP算法及其在水环境优化问题中的应用  

Maximum entropy DFP algorithm and its application in water environmental optimization

作　　者：杨晓华[1] 陆桂华[2] 陈晓燕[2] 郦建强[3] 

机构地区：[1]北京师范大学环境学院,水环境模拟国家重点实验室,北京100875 [2]河海大学科学研究院,南京210098 [3]水利部水利水电规划设计总院,北京100011

出　　处：《系统工程理论与实践》2008年第9期138-144,共7页Systems Engineering-Theory & Practice

基　　金：国家科技支撑计划项目(2006BAB04A09);水文水资源与水利工程科学国家重点实验室开放基金(2006411411);国家重点基础研究发展规划项目(2003CB415204)

摘　　要：为了提高求解约束优化问题的精度,将最大熵原理与DFP无约束优化方法相结合,将复杂的带约束的优化问题转化成无约束优化问题,建立了求解约束水环境优化问题的最大熵DFP算法(MEDFP).MEDFP算法不仅可以得到最优解,而且由收敛极小点处的Lagrange乘子可判断约束对该点的松紧程度.数值分析和在水环境优化问题中的应用结果表明,该算法精度高、收敛快、实用性强,好于模糊非线性规划方法,随机优化方法、模式搜索方法和LINGO方法,是处理带约束水环境优化问题的一种有效方法.In order to reduce the computational amount and improve computational precision for water environment constrained optimization, a maximum entropy DFP algorithm （MEDFP）is established by combining the maximum entropy principle with unconstrained DFP optimization method. Complicated constrained optimization can be changed into a simple unconstrained optimization by MEDFP. The optimal solution can be gotten, and constrained degree with Lagrange equation can also be calculated with MEDFP. The results of numerical analysis and applications in practical water environmental optimization indicate that MEDFP is inexpensive, rapid and convenient. Compared with the fuzzy nonlinear optimization method, random algorithm, pattern search algorithm and LINGO algorithm, MEDFP has higher precision and rapider convergent speed. It can be widely applied in the constrained water environmental optimization.

关 键 词：水环境优化 最大熵原理 DFP算法 约束优化 

分 类 号：P333[天文地球—水文科学]