中文摘要：

求解条件非线性最优扰动（Conditional Nonlinear Optimal Perturbation,CNOP）属约束最优化问题,一般采用基于伴随模式提供梯度信息的约束优化算法（简称ADJ）进行求解。当优化问题涉及不连续的“开关”过程时,传统优化算法的寻优能力会受到较大的影响。近年来遗传算法（Genetic Algorithm,GA）因其在非光滑优化问题中的鲁棒性备受关注,但GA的性能不仅与优化问题有关,还取决于遗传算子的配置。本文将一种新的约束GA（GA1）用于求解CNOP,并对GA1,ADJ及具有不同遗传算子配置的约束GA（GA2）求解含“开关”过程的CNOP时的性能进行了比较。数值试验结果显示,GA1和GA2的全局寻优能力明显优于ADJ,后者易于陷入局部最优;对于不同的初猜值（不同的初始种群）,GA1求解的CNOP能够保持一个较为一致的空间结构,ADJ求解的CNOP呈现了明显的两种结构,一种代表的是全局CNOP,一种是局部CNOP。通过验证不同遗传策略对优化结果的影响发现,对不同的优化问题,采用合适的遗传策略以及合适的参数设置是获取更好优化结果的一种有效途径。

英文摘要：

A conditional nonlinear optimal perturbation（CNOP） represents a kind of initial perturbation which has the largest nonlinear evolution at the end of the concerned time window.Physically, a CNOP describes the initial error which satisfies a certain constraint and yields the largest prediction error at the prediction time.Therefore, solving the CNOP is categorized as a constrained optimization problem.In most cases,CNOPs are obtained by using gradient descend algorithms, such as the spectral projected gradient method （SPG） and sequential quadratic programming （SQP）, and the required gradient is obtained by backward integrating the associated adjoint model.This optimization method is hereafter referred to as ADJ. However , the adjoint technology can ＂work＂ well only when the nonlinearity of the governing equation is not excessively strong, and when the objective function is differentiable with respect to the optimization variables.When the nonlinear model contains discontinuous ＂on-off＂ switches, the ability of the ADJ to capture CNOPs will be weakened much more greatly.In addition, not all models have corresponding adjoint models, and writing the adjoint model of a complex model is very tedious and time-consuming.A genetic algorithm is a population-based heuristic search method, and possesses the characteristic of information sharing among its population members. A member in the population of the GA represents a potential solution which is a point in the search space,and each member has a fit value from which one can judge how strong the current potential solution is.Recently, genetic algorithms （GAs） have received much attention for their effectiveness and robustness in solving constrained non-smooth optimal problems.There are three basic genetic operators in a GA,i.e.selection,crossover and mutation operators.The performance of a GA rests with not only optimization problems,but also with the configuration of the genetic operators.In this study,a new constraint GA（GA1 ） configured pr