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.

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.

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.

Optimal Design of Aperture Illuminations for Microwave Power Transmission with Annular Collection Areas

This work presents an optimal design method of antenna aperture illumination for microwave power transmission with an annular collection area.The objective is to maximize the ratio of the power radiated on the annular collection area to the total transmitted power.By formulating the aperture amplitude distribution through a summation of a special set of series,the optimal design problem can be reduced to finding the maximum ratio of two real quadratic forms.Based on the theory of matrices,the solution to the formulated optimization problem is to determine the largest characteristic value and its associated characteristic vector.To meet security requirements,the peak radiation levels outside the receiving area are considered to be extra constraints.A hybrid grey wolf optimizer and Nelder–Mead simplex method is developed to deal with this constrained optimization problem.In order to demonstrate the effectiveness of the proposed method,numerical experiments on continuous apertures are conducted;then,discrete arrays of isotropic elements are employed to validate the correctness of the optimized results.Finally,patch arrays are adopted to further verify the validity of the proposed method.

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.

镍精矿除铜的单纯形优化

本文简要叙述了单纯形优化的基本思想与寻优步骤。应用单纯形法对镍精矿—阳极泥—镍电解阳极液反应体系的深度除铜条件进行了寻优试验,其结果与前人的试验及工业实践基本相同,表明单纯形优化方法是确定多变量湿法冶金体系中某些重要因素的一种快速而简单的方法。

Supply-based optimal scheduling of oil product pipelines

Oil product pipelines have features such as transporting multiple materials, ever-changing operating conditions, and synchronism between the oil input plan and the oil offloading plan. In this paper, an optimal model was established for a single-source multi-distribution oil pro- duct pipeline, and scheduling plans were made based on supply. In the model, time node constraints, oil offloading plan constraints, and migration of batch constraints were taken into consideration. The minimum deviation between the demanded oil volumes and the actual offloading volumes was chosen as the objective function, and a linear programming model was established on the basis of known time nodes＇ sequence. The ant colony optimization algo- rithm and simplex method were used to solve the model. The model was applied to a real pipeline and it performed well.

ON ALTERNATIVE OPTIMAL SOLUTIONS TO QUASIMONOTONIC PROGRAMMING WITH LINEAR CONSTRAINTS

In this paper, the nonlinear programming problem with quasimonotonic （ both quasiconvex and quasiconcave ）objective function and linear constraints is considered. With the decomposition theorem of polyhedral sets, the structure of optimal solution set for the programming problem is depicted. Based on a simplified version of the convex simplex method, the uniqueness condition of optimal solution and the computational procedures to determine all optimal solutions are given, if the uniqueness condition is not satisfied. An illustrative example is also presented.

Multiple optimal solutions to a sort of nonlinear optimization problem

The optimization problem is considered in which the objective function is pseudolinear（both pseudoconvex and pseudoconcave） and the constraints are linear. The general expression for the optimal solutions to the problem is derived with the representation theorem of polyhedral sets, and the uniqueness condition of the optimal solution and the computational procedures to determine all optimal solutions （if the uniqueness condition is not satisfied ） are provided. Finally, an illustrative example is also given.

A review of the formulation and application of the spatial equilibrium models to analyze policy

This paper reviews alternative market equilibrium models for policy analysis. The origin of spatial equilibrium models and their application to wood and wood-processing industries are described. Three mathematical programming models commonly applied to solve spatial problems - namely linear programming, non-linear programming and mixed complementary programming - are reviewed in terms of forms of objective functions and constraint equalities and inequalities. These programming are illustrated with numerical examples. Linear programming is only applied in transportation problems to solve quantities trans, ported between regions when quantities supplied and demanded in each region are already known. It is argued that linear programming can be applied in broader context to transportation problems where supply and demand quantities are unknown and are linear. In this context, linear programming is seen as a more convenient method for modelers because it has a simpler objective function and does not require as strict conditions, for instance the equal numbers of variables and equations required in mixed complementary programming. Finally, some critical insights are provided on the interpretation of optimal solutions generated by solving spatial equilibrium models.

Modified Burzynski criterion with non-associated flow rule for anisotropic asymmetric metals in plane stress problems

The Burzynski criterion is developed for anisotropic asymmetric metals with the non-associated flow rule （NAFR） for plane stress problems. The presented pressure depending on the yield criterion can be calibrated with ten experimental data, i.e., the tensile yield stresses at 0°, 45°, and 90°, the compressive yield stresses at 0°, 15°, 30°, 45°, 75°, and 90° from the rolling direction, and the biaxial tensile yield stress. The corresponding pressure independent plastic potential function can be calibrated with six experimental data, i.e., the tensile R-values at 0°, 15°, 45°, 75°, and 90° from the rolling direction and the tensile biaxial R-value. The downhill simplex method is used to solve these ten and six high nonlinear equations for the yield and plastic potential functions, respectively. The results show that the presented new criterion is appropriate for anisotropic asymmetric metals.

A New Geochemical Reaction Model for Groundwater Systems

Through a survey of the literature on geology, hydrogeology and hydrogeochemistry, this paper presents a hydrogeochemical model for the groundwater system in a dross-dumping area of the Shandong Aluminium Plant. It is considered that the groundwater-bearing medium is a mineral aggregate and that the interactions between groundwater and the groundwater-bearing medium can be described as a series of geochemical reactions. On that basis, the principle of minimum energy and the equations of mass balance, electron balance and electric neutrality are applied to construct a linear programming mathematical model for the calculation of mass transfer between water and rock with the simplex method.

A Way to Find All the Optimal Solutions in Linear Programming

With the expression theorem of convex polyhedron, this paper gives the general expression for the solutions in standard linear programming problems. And the calculation procedures in determining the optimal solutions are also given.

New Approach to Solve Cubic Objective Function Programming Problem

In this paper, a cubic objective programming problem (COPP) is defined. Introduced a new modification to solve a cubic objective programming problem. Suggested an algorithm for its solution. Also reported the algorithm of the usual simplex method. Application talks about how the developed algorithm can be used to unravel non-linear. The proposed technique, modification simplex technique, can be used with the constructed numerical examples an illustrative numerical problems are given to demonstrate the algorithms.

Bald Eagle Search Optimization Algorithm Combined with Spherical Random Shrinkage Mechanism and Its Application

Over the last two decades,stochastic optimization algorithms have proved to be a very promising approach to solving a variety of complex optimization problems.Bald eagle search optimization(BES)as a new stochastic optimization algorithm with fast convergence speed has the ability of prominent optimization and the defect of collapsing in the local best.To avoid BES collapse at local optima,inspired by the fact that the volume of the sphere is the largest when the surface area is certain,an improved bald eagle search optimization algorithm(INMBES)integrating the random shrinkage mechanism of the sphere is proposed.Firstly,the INMBES embeds spherical coordinates to design a more accurate parameter update method to modify the coverage and dispersion of the population.Secondly,the population splits into elite and non-elite groups and the Bernoulli chaos is applied to elite group to tap around potential solutions of the INMBES.The non-elite group is redistributed again and the Nelder-Mead simplex strategy is applied to each group to accelerate the evolution of the worst individual and the convergence process of the INMBES.The results of Friedman and Wilcoxon rank sum tests of CEC2017 in 10,30,50,and 100 dimensions numerical optimization confirm that the INMBES has superior performance in convergence accuracy and avoiding falling into local optimization compared with other potential improved algorithms but inferior to the champion algorithm and ranking third.The three engineering constraint optimization problems and 26 real world problems and the problem of extracting the best feature subset by encapsulated feature selection method verify that the INMBES’s performance ranks first and has achieved satisfactory accuracy in solving practical problems.

A NEW PERTURBATION SIMPLEX ALGORITHM FOR LINEARPROGRAMMING

In this paper, we first propose a perturbation procedure for achieving dual feasibility, which starts with any basis without introducing artificial variables. This procedure and the dual simplex method are then incorporated into a general purpose algorithm; then, a modification of it using a perturbation technique is made in order to handle highly degenerate problems efficiently. Some interesting theoretical results are presented. Nmerical results obtained are reported, which are very encouraging though still preliminary.

A simplex method for the orbit determination of maneuvering satellites

simplex method;;orbit determination;;electric propulsion;;orbit

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.

A GENERATOR AND A SIMPLEX SOLVER FOR NETWORK PIECEWISE LINEAR PROGRAMS

This is a brief report on our recent work in network piecewise linear programming (NPLP),and it consists of two parts. In the first park, we describe a generator for NPLP problems which is derived from the classical network linear program generator NETGEN. The generator creates networks of the same topological structures as NETGEN, but each arc is associated with a convex piecewise linear cost. The purpose of this program is to provide a set of standard test problems which can be used to compare the performance of various algorithms for NPLP. In the second part,we introduce a network simplex method that directly solves a network piecewise linear program without reformulating it as a network linear program of higher dimension. Forty benchmark NPLP problems are solved by this method and a reformulation method. The computational results are in favor of the direct method and show that solving an NPLP problem is not much harder than solving a network linear program of the same dimension.