TLE orbit determination using simplex method

Two-Line Element(TLE)datasets are the only orbital data source of Earth-orbiting space objects for many civil users for their research and applications.The datasets have uneven qualities that may affect the reliability of the propagated positions of space objects using a single TLE.The least squares approach to use multiple TLEs also suffers from the poor quality of some TLEs,and reliable error information cannot be available.This paper proposes a simplex algorithm to estimate an optimal TLE from multiple TLEs and obtain the uncertainty of each element.It is a derivative-free technique that can deal with various orbit types.Experiments have demonstrated that using the TLE estimated from the simplex method is more reliable,stable,and effective than those from the batch least squares method.As an application example,the optimal TLE and its uncertainty are used for predicting the fallen area,keeping the actual fallen site in the prediction areas.

Global convergent algorithm for the bilevel linear fractional-linear programming based on modified convex simplex method

A global convergent algorithm is proposed to solve bilevel linear fractional-linear programming, which is a special class of bilevel programming. In our algorithm, replacing the lower level problem by its dual gap equaling to zero, the bilevel linear fractional-linear programming is transformed into a traditional sin- gle level programming problem, which can be transformed into a series of linear fractional programming problem. Thus, the modi- fied convex simplex method is used to solve the infinite linear fractional programming to obtain the global convergent solution of the original bilevel linear fractional-linear programming. Finally, an example demonstrates the feasibility of the proposed algorithm.

Application of Simplex Method in the Radiotherapy Treatment

This work presents an application of the Simplex Method for solving an optimal planning problem for cancer treatment by radiotherapy. Linear Programming can aid the optimal planning for radiation therapy, where the concern is to apply a high enough radiation in the tumor while saving significantly healthy regions or critical organs.

Hybrid Improved Self-adaptive Differential Evolution and Nelder-Mead Simplex Method for Solving Constrained Real-Parameters

In this paper, a new hybrid algorithm based on exploration power of a new improvement self-adaptive strategy for controlling parameters in DE （differential evolution） algorithm and exploitation capability of Nelder-Mead simplex method is presented （HISADE-NMS）. The DE has been used in many practical cases and has demonstrated good convergence properties. It has only a few control parameters as number of particles （NP）, scaling factor （F） and crossover control （CR）, which are kept fixed throughout the entire evolutionary process. However, these control parameters are very sensitive to the setting of the control parameters based on their experiments. The value of control parameters depends on the characteristics of each objective function, therefore, we have to tune their value in each problem that mean it will take too long time to perform. In the new manner, we present a new version of the DE algorithm for obtaining self-adaptive control parameter settings. Some modifications are imposed on DE to improve its capability and efficiency while being hybridized with Nelder-Mead simplex method. To valid the robustness of new hybrid algorithm, we apply it to solve some examples of structural optimization constraints.

Partial Pricing Rule Simplex Method with Deficient Basis

A new partial pricing column rule is proposed to the basis-deficiency-allowing simplex method developed by Pan.Computational results obtained with a set of small problems and a set of standard NETLIB problems show its promise of success.

Numerical Optimization of Sand Casting Parameters Using the Dantzig’s Simplex Method

This study adopts the Dantzig’s Simplex method to investigate optimization of sand casting parameters for optimum service performance. Some process variables and mechanical properties were adapted into the Simplex method. Aluminium alloy samples were cast, machined and subjected to a series of mechanical tests. From the body of data collected, linear functions and constraint equations were formulated and employed in the Dantzig’s Simplex method for optimization of process parameters. The results showed that the Simplex method can be adapted for studying performance opti- mization of castings.

Using the Simplex Method for a Type of Allocation Problems

In this study we discuss the use of the simplex method to solve allocation problems whose flow matrices are doubly stochastic. Although these problems can be solved via a 0 - 1 integer programming method, H. W. Kuhn [1] suggested the use of linear programming in addition to the Hungarian method. Specifically, we use the existence theorem of the solution along with partially total unimodularity and nonnegativeness of the incidence matrix to prove that the simplex method facilitates solving these problems. We also provide insights as to how a partition including a particular unit may be obtained.

Optimal pivot path of the simplex method for linear programming based on reinforcement learning

Based on the existing pivot rules,the simplex method for linear programming is not polynomial in the worst case.Therefore,the optimal pivot of the simplex method is crucial.In this paper,we propose the optimal rule to find all the shortest pivot paths of the simplex method for linear programming problems based on Monte Carlo tree search.Specifically,we first propose the SimplexPseudoTree to transfer the simplex method into tree search mode while avoiding repeated basis variables.Secondly,we propose four reinforcement learning models with two actions and two rewards to make the Monte Carlo tree search suitable for the simplex method.Thirdly,we set a new action selection criterion to ameliorate the inaccurate evaluation in the initial exploration.It is proved that when the number of vertices in the feasible region is C_(n)^(m),our method can generate all the shortest pivot paths,which is the polynomial of the number of variables.In addition,we experimentally validate that the proposed schedule can avoid unnecessary search and provide the optimal pivot path.Furthermore,this method can provide the best pivot labels for all kinds of supervised learning methods to solve linear programming problems.

On the use of simplex methods in constructing quadratic models

In this paper, we investigate the quadratic approximation methods. After studying the basic idea of simplex methods, we construct several new search directions by combining the local information progressively obtained during the iterates of the algorithm to form new subspaces. And the quadratic model is solved in the new subspaces. The motivation is to use the information disclosed by the former steps to construct more promising directions. For most tested problems, the number of functions evaluations have been reduced obviously through our algorithms.

A simplex method for the orbit determination of maneuvering satellites

A simplex method of orbit determination （SMOD） is presented to solve the problem of orbit determination for maneuvering satellites subject to small and continuous thrust. The objective function is established as the sum of the nth powers of the observation errors based on global positioning satellite （GPS） data. The convergence behavior of the proposed method is analyzed using a range of initial orbital parameter errors and n values to ensure the rapid and accurate convergence of the SMOD. For an uncontrolled satellite, the orbit obtained by the SMOD provides a position error compared with GPS data that is commensurate with that obtained by the least squares technique. For low Earth orbit satellite control, the precision of the acceleration produced by a small pulse thrust is less than 0.1% compared with the calibrated value. The orbit obtained by the SMOD is also compared with weak GPS data for a geostationary Earth orbit satellite over several days. The results show that the position accuracy is within 12.0 m. The working efficiency of the electric propulsion is about 67% compared with the designed value. The analyses provide the guidance for subsequent satellite control. The method is suitable for orbit determination of maneuvering satellites subject to small and continuous thrust.

CALCULATION OF PENALTIES IN ALGORITHM OF MIXEDINTEGER PROGRAMMING SOLVING WITH REVISED DUALSIMPLEX METHOD FOR BOUNDED VARIABLES

The branch-and-bound method with the revised dual simplex for bounded variables is very effective in solving relatively large-size integer linear programming problems. This paper, based on the general forms of the penalties by Beale and Small and the stronger penalties by Tomlin, describes the modifications of these penalties used for the method of bounded variables. The same examples from Petersen are taken and the satisfactory results are shown in comparison with those obtained by Tomlin.

Simplexmethod建模研讨

目的 Linear Programming的simplexmethod建模求最优解。方法应用simplexmethod.结果建立了LinearProgramming的数学模型并用simplexmethod求得了最优解.结论因为单纯形表反映了Linear Programming的所有信息,故用simplexmethod可简便地求得最优解.simplexmethod的基本思路是:先将Linear Programming用sim-plexmethod划为标准型,根据问题的标准型,进行初等行变换,将主元素列除主元素化为1外其余的元素均化为0,当基变量值全为非负时,问题就得到了最优解.

Extended Simplex Method

Since the simplex method[1]of linear programming was established in 1947. It has been im proving unceasingly. But a major breakthrough has not been been,only a little quantity of computation was decreased. In this paper,the computation of the first stage of artificial basis method[l] is omited. Therefore, computational quantity is decreased greatly.

Estimation of mass transfer coefficient in ozone absorption by linear least square fitting and Simplex search methods

For physical ozone absorption without reaction,two parametric estimation methods,i.e.the common linear least square fitting and non-linear Simplex search methods,were applied,respectively,to determine the ozone mass transfer coefficient during absorption and both methods give almost the same mass transfer coefficient.While for chemical absorption with ozone decomposition reaction,the common linear least square fitting method is not applicable for the evaluation of ozone mass transfer coefficient due to the difficulty of model linearization for describing ozone concentration dissolved in water.The nonlinear Simplex method obtains the mass transfer coefficient by minimizing the sum of the differences between the simulated and experimental ozone concentration during the whole absorption process,without the limitation of linear relationship between the dissolved ozone concentration and absorption time during the initial stage of absorption.Comparison of the ozone concentration profiles between the simulation and experimental data demonstrates that Simplex method may determine ozone mass transfer coefficient during absorption in an accurate and high efficiency way with wide applicability.

PID Parameters for Tuning and Optimization of a Turbine EngineBased on the Simplex Search Method

A PID parameters tuning and optimization method for a turbine engine based on the simplex search method was proposed. Taking time delay of combustion and actuator into account, a simulation model of a PID control system for a turbine engine was developed. A performance index based on the integral of absolute error （IAE） was given as an objective function of optimization. In order to avoid the sensitivity that resulted from the initial values of the simplex search method, the traditional Ziegler-Nichols method was used to tune PID parameters to obtain the initial values at first, then the simplex search method was applied to optimize PID parameters for the turbine engine. Simulation results indicate that the simplex search method is a reasonable and effective method for PID controller parameters tuning and optimization.

Minimizing Complementary Pivots in a Simplex-Based Solution Method for a Quadratic Programming Problem

The paper presents an approach for avoiding and minimizing the complementary pivots in a simplex based solution method for a quadratic programming problem. The linearization of the problem is slightly changed so that the simplex or interior point methods can solve with full speed. This is a big advantage as a complementary pivot algorithm will take roughly eight times as longer time to solve a quadratic program than the full speed simplex-method solving a linear problem of the same size. The strategy of the approach is in the assumption that the solution of the quadratic programming problem is near the feasible point closest to the stationary point assuming no constraints.

融合历史记忆的单纯形引导鲸鱼优化算法

针对鲸鱼优化算法存在易陷入局部最优、收敛速度慢等缺点,提出一种融合历史记忆的单纯形引导鲸鱼优化算法。首先,为了避免初始化种群过于集中而陷入局部最优,提出了使用混沌映射对初始化种群进行改进,增加了种群多样性;其次,为了解决算法收敛精度低和收敛速度慢的问题,提出了融合历史记忆的单纯形引导策略,利用单纯形法和构建的历史记忆表求解出一个虚拟最优解作为下次随机搜索阶段的引导者,帮助种群在前期的勘探过程中进行细致地搜索;最后提出一种新的非线性参数策略,平衡算法的开发和勘探能力。将算法应用于12个典型的复杂函数优化问题,并与其他5种智能算法比较,实验结果表明,改进后的算法在收敛精度与速度方面均为第一,具有良好的全局搜索能力和局部开发能力。

改进麻雀搜索算法的入侵检测特征选择

针对网络入侵检测所处理数据存在特征维数高、检测效率低、准确率不高的问题,提出一种改进麻雀搜索算法的特征选择方法,旨在减少特征冗余的同时提高分类准确率。利用改进Circle映射初始化种群;结合秃鹰搜索算法中的螺旋搜索方式更新发现者位置;采用单纯形法和小孔成像法优化适应度较差和最优麻雀的位置,提升算法的寻优能力。将该算法与其它算法在6个经典基准函数上进行对比测试,其在收敛速度、精度等方面均有提升。使用数据集CIC-IDS2017进行特征选择实验,平均保留了7.6个特征,准确率达到了99.5%,结果表明,该算法可以在保证准确率的同时有效降低特征维度。

单纯形法的复杂性与计算效率

给出了三个线性规划例子,及用单纯形法求解的过程,解释了求解线性规划的单纯形法为什么属于指数算法.

基于谱方法和单纯形算法的一类偏微分方程参数反演研究

根据观测数据反演偏微分方程参数具有重要的应用价值。通过基于快速傅立叶变换的谱方法实现对偏微分方程快速高精度求解,与观测数据结合建立待优化的目标函数,再用带边界约束的Nelder-Mead单纯形优化方法进行参数反演。通过算例证实了算法的有效性。