Iterative integral versus dynamic programming

This paper discusses the similarities and differences between the processes of integration and optimization.     

Modelling Jackson's programming method

The aim of this paper is to present a modelling scheme for programming methods and to illustrate it on Jackson's programming method. We first give a formal semantics to the objects of this method and we model the basic strategy of matching trees in order to build a program structure. In the next section we study how to support a formal development, its automatization, and the building of a formal specification within the scope of our model. Then an example is developed. The last section addresses alternative strategies suggested by the method in order to solve clash problems, where the basic strategy fails. Boundary and ordering clash situations are presented and their strategies are modelled.     

穷举法在程序设计中的应用

穷举法是程序设计中经常用到的一种算法,用来解决一些用常规的数学方法无法解决的问题.文章通过两个典型的例子对穷举法的思路和有关注意事项进行了分析,供编程学习者参考.     

Differential dynamic programming and Newton's method

A modified version of the original differential dynamic programming (DDP) algorithm for unconstrained discrete optimal control problems is described. This version, which differs from the original by a second-order term which vanishes if the dynamics are linear, is proven to be a stagewise implementation of the classical Newton's method.     

An approximate programming method based on the simplex method for bilevel programming problem

Many real problems can be modeled to the problems with a hierarchical structure, and bilevel programming is a useful tool to solve the hierarchical optimization problems. So the bilevel programming is widely applied, and numerous methods have been proposed to solve this programming. In this paper, we propose an approximate programming algorithm to solve bilevel nonlinear programming problem. Finally, the example illustrates the feasibility of the proposed algorithm.     

Interactive tools for conceptual programming using APL-graphics: The integral and derivative operators

The notion of conceptual programming is defined by way of illustrations in the context of interactive problem solving. The numerical implementations of a DERIVATIVE and an INTEGRAL operators are discussed. These operators have been integrated, together with some basic graphical operators, into the APL system in a manner consistent with the syntax of the host language, providing extremely powerful tools for interactive problem solving. The performance of the system as well as some error analysis are demonstrated.     

Discretization method for semi-definite programming

Semi-definite programs are convex optimization problems arising in a wide variety of applications and the extension of linear programming. Most methods for linear programming have been generalized to semi-definite programs. This paper discusses the discretization method in semi-definite programming. The convergence and the convergent rate of error between the optimal value of the semi-definite programming problems and the optimal value of the discretized problems are obtained. An approximately optimal division is given under certain assumptions. With the significance of the convergence property, the duality result in semi-definite programs is proved in a simple way which is different from the other common proofs.     

动态规划方法的应用研究

动态规划是运筹学的一个分支,是求解决策过程最优化的数学方法,其最终目的是确定各决策变量的取值,以使目标函数达到极大或极小。动态规划在工程技术、经济管理等社会各个领域有着广泛的应用,并且获得了显著的效果,是经济管理中一种重要的决策技术。文章例举了动态规划在最短路线、资源分配、设备更新、排序、装载等方面的应用。通过求解不同的实例,总结出用动态规划方法比用其他方法求解更容易、效率更高,并且所得到的解信息更丰富。     

Combination of the boundary integral equation method and the extrapolation method

Many numerical methods including the boundary integral equation method start with division of the domain of calculation into intervals. The accuracy of their results can be improved considerably by extrapolation. To be able to apply the extrapolation method it is necessary to know the asymptotic expansion of the error.In this paper the principle of the extrapolation method and subjects important for its application are described. Above all it is shown how to determine the asymptotic expansions numerically by trial and error. In the first sections the matter is explained in a general manner to encourage users of various numerical methods—among them users of the finite element method—to try to extrapolate their results. Then the investigations are exemplified in detail by the boundary integral equation method. The accuracy of approximate solutions of integral equations for plane elastostatic problems with prescribed boundary tractions and displacements is improved by extrapolation. Particular attention is paid to boundary tractions and displacements with discontinuous derivatives.To induce also practically orientated readers without specialized mathematical knowledge to think about applying the extrapolation method the basic topics are represented in an extensive manner and illustrated by simple examples. (For a survey of this paper see end of Section 1.)     

自适应扰动估计的相关积分优化方法及应用

针对传统相关积分优化方法,当系统扰动与调优变量相关时,在迭代优化的过程中,目标函数难以收敛到最优值的问题,提出了一种改进的相关积分优化方法用于稳态操作调优.基于数据驱动稳态模型,构造了自适应扰动估计器用来估计扰动均值,对最小二乘方法计算得到的调优变量梯度均值进行补偿,并修正调优变量,确保目标函数在调优的过程中收敛于最优值.仿真对比及工业应用结果证实了所提方法的可行性和有效性.     

约束规划方法在原油混输调度中的应用

应用约束规划方法建立炼厂原油混输模型,并通过搜索求解获得可操作的调度方案。约束规划允许以逻辑约束表达混输过程中的操作规则,使模型简洁直观,而对整型变量及非线性约束不敏感,则降低了模型的求解难度。选取了一个时间跨度为300小时实际调度问题作为案例,模型中包含约8000个变量和14000条约束,在普通PC机上计算求解,能够在30秒内获得调度方案,方案具有可操作性且优于人工方案,表明以约束规划方法解决原油混输调度问题是可行的。     

Dynamic programming method in the generalized courier problem

A problem of successive traversal of sets under constraints in the form of precedence conditions is investigated. In what follows, this problem is called the generalized courier problem. To solve it, the method of dynamic programming is used, which is implemented in a shortened version, taking into account the specific features of the generalized courier problem. The Bellman function is not determined for all positions, which saves PC memory and, in principle, increases the efficiency of the procedure based on the dynamic programming method. Applications can be connected with the transportation problem (sea and air transportation with visiting many destinations and multiple choices of travels from one destination to another).     

任务驱动教学法在程序设计课程中的实践与分析

先后在双一流大学、职业技术学院和普通本科院校主讲过编程类课程,教过各个层次的学生,通过运用多种教学方法,并比较分析教学效果,发现将任务驱动教学法应用于程序设计课程,对于提高教学效果有明显作用,值得尝试和推广应用。但是,对于不同层次的学生也需要采用不同的实施方案,并配套相应的实践环境和考核机制才能取得理想的效果。     

Initialization method for grammar-guided genetic programming

This paper proposes a new tree-generation algorithm for grammar-guided genetic programming that includes a parameter to control the maximum size of the trees to be generated. An important feature of this algorithm is that the initial populations generated are adequately distributed in terms of tree size and distribution within the search space. Consequently, genetic programming systems starting from the initial populations generated by the proposed method have a higher convergence speed. Two different problems have been chosen to carry out the experiments: a laboratory test involving searching for arithmetical equalities and the real-world task of breast cancer prognosis. In both problems, comparisons have been made to another five important initialization methods.