摘要
本文采用加权中心来改善反射方向,利用单调性分析估算搜索步长,并应用梯度投影方向进行后期搜索迭代,示例表明应用上述措施将大大加快收敛速度,所需计算目标与约束函数次数仅为一般复形法的1/2～1/3。 文章还讨论了宽缝坝优化设计,按水工规范要求塑造数学模型,用上法优化,效果良好。
In engineering optimization, objective functions and constraints are always not differentiable or even not continuous. Some of them may be implicit functions. Their derivaties with respect to design variables can not be calculated analytically . Therefore, the direct search methods are still widely used because there are robustness, ease of problem preparation, without requirement of derivatives, etc. The chief drawback of direct search algorithms is that they converge very slowly, but the efficiency can be improved if we utilize reasonably the information which has been accumulated during the iteJative process.The main strategies presented here are:1 .The concept of weighted centroid of flexible polyhedron is adopted to form a better search direction. Differences in the objective function values between the worst point and other vertex of flexible polyhedron are taken as the weight coeffients. The effect on improvement has been demonstrated theoretically and also illustrated with the Rosenbrock's test functions.2.Clobal and regional monotonicity analyses are used to simplify mathematical model of a given problem and to estimate the step-length at each stage. This can save much more CPU times.3.The gradient projection directions are used to further improve convergence of the algorithms at final search stage.Illustrative examples clearly show that the number of functon evaluatiionand CPU times required by the algorithm decrease to 1/2-1/4 of those by con-ventional flexible polyhedron method.Applications to optimum design of gravity dams and dams with broad joints are presented at the end. Results are desirable and promising.
基金
中科院科学基金
