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 proper genetic operator is applied to capture the CNOP of a nonlinear model with discontinuous “on-off” switches.In order to verify the effectiveness of GA1,numerical experiments capturing CNOPs are conducted by using ADJ,GA1 and GA configured operators(GA2).More specifically,in the selection operation,both GA1 and GA2 use a tournament selection operator,and the comparison criteria are as follows:(1) When both comparative individuals are feasible solutions,the one with the larger fit value is preferred;and(2) When there is any infeasible solution among the two comparative individuals,first pull the infeasible solution to the edge of the spherical constraints to let it become feasible,then apply the comparison criteria(1).For the crossover operation,GA1 blends the simulation binary crossover(SBX) with the BLX-α,while GA2 only uses the BLX-α.In mutation operation,GA1 uses the multiply mutation and GA2 uses the non-uniform mutation.The numerical experiment results show that the ability of global optimization based on GA1and GA2 is much stronger than the one based on ADJ in non-smooth cases.Furthermore,similarity degree is used to test the sensitivity of the spatial structure of the CNOP respectively obtained by ADJ,GA1 and GA2 to the first guess value(initial population),and the results of 200 numerical experiments show that the CNOP capturing by GA1 can retain a steady spatial structure.