动态规划

When problem scale is small, we can adopt many classical algorithms such as linear programming integer programming, branch and bound method to solve this problem.

当问题规模较小时，可用线性规划、整数规划、动态规划等经典算法求解。

This course offers an introduction to primary convex analysis, linear programming, non-linear programming, dynamic programming, multi-objective programming, multi-level programming, calculus of variations, and optimal control, which are the optimization methods commonly used in economics and finance.

课程内容简介：本课程介绍凸分析基础、线性规划、非线性规划、动态规划、多目标规划、多层规划、变分法、最优控制，这些都是西方经济学、金融学中常用的最优化方法。

Water deficiency sensitive index; water production function; optimal irrigation schedule; dynamic planning model; non-linear model

农业科技，农业基础科学，农业数学缺水敏感指数；水分生产函数；灌溉制度优化；动态规划模型；非线性规划

Consider the problem 1|s_, outtree |∑w_jC_j , we use the method of the maximal family tree to sol...

最后把NP-难的问题P_m|s_|∑w_jC_j转化为整数规划模型，并设计了LMP的列生成算法，结合Dantzig-Wolfe分解技术，利用动态规划对其进行求解。

All the sub-plans are described by a group of general mathematic formulae. The computation of the sub- plan can be decomposed into two sub-problems by relaxing the constraint that production level at production period of a sub-plan must be more than zero. Based on the properties of an optimal solution, two polynomial algorithms are devised to solve sub-problems and reintegrate the relaxed constraint. Finally, a dynamic programming algorithm with complexity O(T^4) is developed to solve the global problem, where T is number of periods in planning horizon.

给出了所有子计划的通用数学描述，并通过松弛正生产量约束将子计划的计算分成两个子问题；依据子问题和子计划最优解的性质，设计了求解子问题和重新集结松弛约束的多项式算法；在此基础上提出了一个复杂性为O(T^4)的求解整个规划问题的多项式动态规划算法，这里T是规划时段上的周期数。

Based on the principle of Markov process and multiobjective programming, a stochastic multiobjective dynamic programming model considering faced runoff prediction is developed for the optimization of generation and water supply at Danjiangkou reservoir. The reservoir will be used for water supply of the south-north water transfer project.

本文通过对丹江口水库综合利用任务的分析，运用随机规划与多目标规划的基本理论和方法，建立了考虑面临时径流预报下丹江口水库发电及向外流域供水的随机多目标动态规划模型，并分析了长期平稳运行特性。

This book discusses linear and nonlinear programming, dynamic programming, integer programming and stochastic programming.

本书讨论了线性和非线性规划，动态规划，整数规划和随机规划。

In order to meet the complex requirements in hydropower stations optimal operation, a hybrid optimal model consisted DPSA,DDDP and POA organically with the system constrain of up-down bound is presented.The model is seized of the advantages including decreasing the number of hydropower stations by DPSA,minifying the discrete states by DDDP and reducing the computational time by POA.

2针对规模库群的复杂调度要求，结合逐次逼近动态规划可以减少每次参与计算的电站数目，增量动态规划减少离散状态数目，而逐步优化算法减少计算时段数目等特点，以满足系统上下限带宽的发电量最大为目标，提出耦合DPSA，DDDP及POA的混合求解算法来建立梯级长期优化调度模型。

In chapter three, with the effective combination of the prior preference, posterior preference and interactive method, and based on the theory of satisficing decision making and goal programming, an interactive method for solving static or dynamic multicriteria programming is devised. In the method, by constructing the simplexes in the set of parameters and transforming them, the local preference information is interactively quested in th process of decision making. The prior and posterior preference are used to speed up the process of decision making and overcome the false convergency which may be occured in pure interactive algorithms. This method can be used to cope with linear, nonlinear and dynamic multicritcria programming.

在第3章多目标数学规划的参数单纯形方法中，通过多目标数学规划的验先偏好方法，交互式方式与验后偏好方法的有效组合，在满意决策和目标规划的理论基础上提出了一种求解多目标静态及动态规划的交互式方法，该方法通过在参数集中构造单纯形并进行其变换，在决策过程中交互地索取决策者的局部偏好信息，并利用决策者的验先偏好来提高决策过程进行的速度，及利用决策者的验后偏好来克服纯交互式算法中可能出现的假收敛现象。

This method's characteristics is that shape and gauge close\|circuit control is achieved by means of static load distribution, dynamic load distribution and dynamic setting Automatic Gauge Control,and Bellman dynamic programming is employed in calculation.

该方法的主要特点：系统中采用了静、动态负荷分配，动态设定厚度自动控制系统完成了板形板厚的闭环控制，在算法中采用了贝尔曼动态规划。

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。