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双语推荐:单纯形法

在介绍运输问题的数学模型基础上,论述了表上作业法与单纯形法的一致性,说明其实质是单纯形法.
On the basis of describing mathematical model of the transport problems , the article discussed the consistency between the tabular method and simplex method , and explained the essence of the tabular method is the simplex method .

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单纯形法是解决线性规划问题的重要方法之一,表格直接求解法则是单纯形法中最直接有效的方法。本文主要研究了线性规划中的单纯形算法的表格直接求解法,并且通过所给算例验证了表格求解法的可行性与有效性。
The simplex algorithm is one of the important methods to solve the problem of linear programming, and the table al-gorithm is the most direct and effective method of the simplex algorithm. In this paper, we mainly research the table algorithm of the linear programming. Moreover, some numerical exampls are given to illustrate the validity and the feasibility of our re-search.

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建立目标规划的数学模型时,对于偏差变量dk-,dk+,总是要求dk-×dk+=0.这个约束条件是非线性的,但是并没有对单纯形法的求解造成影响.在课程教学中,学生很容易对此产生疑惑,而大部分教材中并没有对这个问题进行阐述.从单纯形法的基本求解过程出发,对此进行了分析,得出在单纯形法迭代时dk-*dk+=0总是成立的结论.
There always be 0k kd??d ? ? for the deviation variable dk?, dk?when the goal programming model is built. The condition is nonlinear,but it do not affect the solution of the goal programming by the simplex algorithm.The students may be confused about this,but most books do not explain this clearly.Based on the process of the simplex algorithm,obtained a conclusion that 0k kd??d ? ? is always satisfied during the process of the simplex algorithm.

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在综合分析传统单纯形法及目前微地震定位算法选用的各类速度模型及其相关误差的基础上,提出一种无需测速和反演的速度模型,并基于此对传统单纯形法进行微地震定位改进研究,结合不同速度模型、不同迭代算法在差异化速度误差和速度各向异性变化条件下的定位精度进行算例分析和工程验证,研究结果表明:无需测速和反演的速度模型能有效避免传统速度反演模型在速度反演过程中的方法误差和现场测速造成的测速误差,将其应用于传统单纯形法,不仅能有效避免传统单纯形法易陷入局部最优的问题,充分发挥单纯形法迭代易收敛的优势,且对于检波器阵列外的震源进行定位时相比其他迭代方法求解时定位精度显著提高,可为微地震定位领域提供一种新的研究思路。
A new type of velocity model without the velocity inversion and velocity measuring was put forward for the improvement of the traditional simplex method based on the comprehensive analysis of the traditional simplex method,the velocity models and the related errors of the microseism locating method. Numerical analysis and engineering validation on the precision of locating under the conditions of different velocity models,different iteration algorithms with velocity errors and velocity anisotropy were carried out. The results show that the new velocity model can effectively avoid the errors happened in the process of velocity inversion and measuring and avoid the problem of local minimum in traditional simplex method. In comparison with the other iterative methods, significantly higher accuracy of locating the seismic sources outside the sensor arrays is achieved,taking advantage of the easy convergence of iterations of the simplex method.

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提出了一种基于聚类和单纯形法的中心引力优化算法,该算法引入了一种聚类单纯形算子,利用聚类方法选择合适的个体以构成单纯形的顶点,周期性地把单纯形算子搜索得到的最优个体迁移到中心引力算法的种群个体中。依靠聚类单纯形算子提高中心引力算法的局部搜索能力和收敛速度,聚类单纯形算子依靠中心引力算法跳出局部最优。实验结果表明,改进后的算法比其他常见优化算法有更好的收敛精度和收敛速度。
An improved central force optimization(CFO)is proposed based on the clustering and simplex method for global optimization.The clustering simplex (CS) operator is introduced to a new algorithm in the evolution process.Vertices of simplex are selected by clustering methods,and a periodical migrating of the best individual is introduced by the CS operator.CS can get away from local converged points by virtue of CFO,and CFO can improve its local exploiting capability and effectively speed up the convergence under the help of CS.Experimental results show that the proposed hybrid CSCFO algorithm is better than other algorithms in convergent speed and searching precision.

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针对混沌优化算法收敛速度较慢的缺点,将单纯形算法和混沌优化算法结合,构造单纯形混沌优化算法,并将该方法应用于分析一维河流水团示踪试验数据,求解河流水质模型参数的函数优化问题。结果表明,该算法可以有效确定河流水质模型参数,较单纯形法具有更好的收敛性、较混沌优化算法具有更快的收敛速度。
To overcome the shortcomings of slow convergence of the chaos optimization algorithm, the simplex algorithm and the chaos optimization algorithm were combined to establish the simplex-chaos optimization algorithm. The established algorithm was used to analyze the tracer experiment data of the water quality of a one-dimensional river stream for estimation of the parameters of the water quality model. The results show that the established algorithm can effectively determine the parameters of the water quality model of the river, and it has better convergence compared with the simplex algorithm and faster convergence compared with the chaos optimization algorithm.
在对参数不确定性导弹控制系统进行多通道鲁棒稳定性评估时,传统方法在计算效率及结果可靠性方面存在不足。提出一种遗传-Nelder-Mead单纯形混合优化算法,利用遗传算法的全局搜索能力,寻找目标函数的近似最优解,并将其作为Nelder-Mead单纯形法搜索的初值,利用Nelder-Mead单纯形法局部寻优的优势,在近似解的邻域内搜索精确解。通过测试函数验证,算法在计算效率和计算精度方面都有很大提升。最后讨论了算法在导弹控制系统鲁棒稳定性评估中的应用价值。
When evaluating multi-channel robust stability of missile control system with parameters uncer-tainty,the traditional method has disadvantage in computational efficiency and reliability of results. There-fore,a Genetic-Nelder-Mead simplex hybrid optimization algorithm is presented in this paper. Using the global search ability of genetic algorithm to find the approximate optimal solution of the objective function, then we use it as the initial value of Nelder-Mead simplex method ,which has merit in local optimization, to search exact solution in the adjacent domain of approximate solution. It’s validated by test functions that the algorithm is improved in computational efficiency and precision of calculation. Finally application of the algorithm in missile control system robust stability evaluation is discussed.

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钢轨的疲劳重伤失效概率服从威布尔分布。但在估计其威布尔分布的三个参数时,传统的图解法效率低,且误差较大。而将威布尔函数转换成线性函数后进行最小二乘拟合的算法,则需要在一维上搜索相关系数的最大值。提出利用下山单纯形算法进行参数估计,并根据钢轨重伤威布尔模型的参数一般分布情况,构造合理的初始单纯形。结果表明,下山单纯形法在估计参数时,精度高,速度快,能有效地估计钢轨重伤威布尔分布的三个参数。
Rail fatigue and severe defects rates follow the Weibull distribution.When estimating three parameters of their Weibull distribution,traditional graphic method is of low efficiency and large error.It needs to search the maximum value of correlation coefficient in one dimension when using the least-squares fitting method after transforming the Weibull function into linear function.In the paper we propose to apply downhill simplex method to estimating the parameters,and construct reasonable initial simplex based on the general distribution of the Weibull model parameters of severe rail defects.The result indicates that the downhill simplex method is of high-precision and fast pace in parameters estimation,it can effectively estimate three parameters of Weibull distribution of severe rail defects.

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在建立几何误差评定规划模型的基础上,以轴类零件圆度的评定为例,应用改进单纯形法对几何误差规划模型进行优化求解,并给出了详细的求解进程。将评定结果与现有的优化算法结果进行了对比,结果表明基于改进单纯形法的几何误差评定,具有精度高和计算速度快的优点,在实际生产中有较好的实用性。
We proposed the modified simplex method on solving optimization programming model of geometric errors based on the establishment of geometric error evaluation planning model. We also present a detailed solving process. The assessment results are compared with the results of existing optimization algorithm. The results show that the geometric error evaluation based on the modified simplex method has the advantages of high accuracy and fast calculation speed, which has the good practicality in actual production.

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运用对偶单纯形法求解线性规划问题时,需要先给定一个初始对偶可行的基本解.然而在线性规划问题的约束条件Ax=b中,矩阵A一般不含m阶单位矩阵,此时初始对偶可行的基本解不易求得.文中通过对线性规划问题增加人工变量和一个约束条件,给出一步便能求出其初始对偶可行基本解的简便方法,进而通过对偶单纯形法进行迭代解决线性规划问题.
His necessary to give an initial dual feasible basic solution ,when solving linear programming problems by the dual simplex method .However ,the matrix A of the linear programming constraint Ax= b does not usually contain the identity matrix .So ,the initial dual feasible basic solution is difficult to obtain directly .In this paper ,by adding artificial variables and a constraint ,an initial dual feasible basic solution is obtained at one step ,and then the optimal solution of the original problem is obtained by iterations .

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