Simplified Iterative Tikhonov Regularization and Posteriori Parameter Choice Rules

In this paper, a simplified iterative regnlarization method was used to solve the operator equations of the first kind involving semi-positive definite operators, the convergence rates of regularized solutions were obtained and a posteriori parametr choice strategy was given.

Parameter value selection strategy for complete coverage path planning based on the Lüsystem to perform specific types of missions

We propose a novel parameter value selection strategy for the Lüsystem to construct a chaotic robot to accomplish the complete coverage path planning(CCPP)task.The algorithm can meet the requirements of high randomness and coverage rate to perform specific types of missions.First,we roughly determine the value range of the parameter of the Lüsystem to meet the requirement of being a dissipative system.Second,we calculate the Lyapunov exponents to narrow the value range further.Next,we draw the phase planes of the system to approximately judge the topological distribution characteristics of its trajectories.Furthermore,we calculate the Pearson correlation coefficient of the variable for those good ones to judge its random characteristics.Finally,we construct a chaotic robot using variables with the determined parameter values and simulate and test the coverage rate to study the relationship between the coverage rate and the random characteristics of the variables.The above selection strategy gradually narrows the value range of the system parameter according to the randomness requirement of the coverage trajectory.Using the proposed strategy,proper variables can be chosen with a larger Lyapunov exponent to construct a chaotic robot with a higher coverage rate.Another chaotic system,the Lorenz system,is used to verify the feasibility and effectiveness of the designed strategy.The proposed strategy for enhancing the coverage rate of the mobile robot can improve the efficiency of accomplishing CCPP tasks under specific types of missions.

LAVRENTIEV'S REGULARIZATION METHOD FOR NONLINEAR ILL-POSED EQUATIONS IN BANACH SPACES

In this paper, we deal with nonlinear ill-posed problems involving m-accretive mappings in Banach spaces. We consider a derivative and inverse free method for the imple- mentation of Lavrentiev regularization method. Using general HSlder type source condition we obtain an optimal order error estimate. Also we consider the adaptive parameter choice strategy proposed by Pereverzev and Schock （2005） for choosing the regularization parameter.

MSSSA:a multi-strategy enhanced sparrow search algorithm for global optimization

The sparrow search algorithm(SSA) is a recent meta-heuristic optimization approach with the advantages of simplicity and flexibility. However, SSA still faces challenges of premature convergence and imbalance between exploration and exploitation, especially when tackling multimodal optimization problems. Aiming to deal with the above problems, we propose an enhanced variant of SSA called the multi-strategy enhanced sparrow search algorithm(MSSSA) in this paper. First, a chaotic map is introduced to obtain a high-quality initial population for SSA, and the opposition-based learning strategy is employed to increase the population diversity. Then, an adaptive parameter control strategy is designed to accommodate an adequate balance between exploration and exploitation. Finally, a hybrid disturbance mechanism is embedded in the individual update stage to avoid falling into local optima. To validate the effectiveness of the proposed MSSSA, a large number of experiments are implemented, including 40 complex functions from the IEEE CEC2014 and IEEE CEC2019 test suites and 10 classical functions with different dimensions. Experimental results show that the MSSSA achieves competitive performance compared with several state-of-the-art optimization algorithms. The proposed MSSSA is also successfully applied to solve two engineering optimization problems. The results demonstrate the superiority of the MSSSA in addressing practical problems.

Performance-Driven Multi-Objective Optimization Method for DLR Transonic Tandem Cascade Shape Design

Transonic tandem cascades can effectively increase the working load,and this feature conforms with the requirement of the large loads and pressure ratios of modern axial compressors.This paper presents an optimization strategy for a German Aerospace Center(DLR)transonic tandem cascade,with one front blade and two rear blades,at the inlet Mach number of 1.051.The tandem cascade profile was parameterized using 19 control parameters.Non-dominated sorting Genetic algorithm(NSGA-II)was used to drive the optimization evolution,with the computational fluid dynamics(CFD)-based cascade performances correction added for each generation.Inside the automatic optimization system,a pressure boundary condition iterative algorithm was developed for simulating the cascade performance with a constant supersonic inlet Mach number.The optimization results of the cascade showed that the deflection of the subsonic blade changed evidently.The shock wave intensity of the first blade row was weakened because of the reduced curvatures of the optimized pressure and suction sides of the front blade part and the downstream moved maximum thickness position.The total pressure losses decreased by 15.6%,20.9%and 19.9%with a corresponding increase in cascade static pressure ratio by 1.3%,1.8%and 1.7%,for the three cascade shapes in the Pareto solution sets under the near choke,the design and near stall conditions,respectively.

A MULTISCALE PROJECTION METHOD FOR SOLVING NONLINEAR INTEGRAL EQUATIONS UNDER THE LIPSCHITZ CONDITION

We propose a multiscale projection method for the numerical solution of the irtatively regularized Gauss-Newton method of nonlinear integral equations.An a posteriori rule is suggested to choose the stopping index of iteration and the rates of convergence are also derived under the Lipschitz condition.Numerical results are presented to demonstrate the efficiency and accuracy of the proposed method.