Summary of dynamic Planning thought

First, the idea of DP and implementation method:

Dynamic programming is a mathematical method to solve the optimal decision-making process, and its core idea is to transform the multi-stage process into a series of single-stage problems, and solve them by using the relationship between the stages.

Second, the dynamic planning of large categories:

(1) Linear motion Regulation, (2) Regional dynamic Regulation, (3) tree-shaped motion regulation, (4) Backpack motion regulation.

Three, the concept of dynamic planning, meaning

Dynamic programming programming is a way to solve the optimization problem, a method, not a special algorithm. Unlike search or numerical calculations, there is a standard mathematical expression and a clear and unambiguous method of solving the problem. Dynamic programming design is often aimed at an optimization problem, because of the different nature of various problems, the conditions for determining the optimal solution are not the same, so the dynamic programming method has its own characteristic problem solving method for different problems, and there is not a universal dynamic programming algorithm, which can solve all kinds of optimization problems. Therefore, in the study of the reader, in addition to the basic concepts and methods to understand correctly, must be specific problems specific analysis and treatment, with a wealth of imagination to build models, with creative skills to solve. We can also learn and master the design method by analyzing and discussing the dynamic programming algorithms of some representative problems.

It contains the idea of recursion and the principle of addition in mathematics, and the theory of multiplication.

Four, the basic idea of dynamic programming

Dynamic programming algorithms are often used to solve problems with some of the most significant properties. There may be many possible solutions to such problems, and each section corresponds to a value, and our purpose is to find the optimal solution by this thought. The method is to solve the sub-problem, and then get the solution of the original problem from the solution of these sub-problems. So we can save the answers to the sub-problems we've solved, and then find the answers we've already got when we need them, so we can avoid a lot of budget and save time. We can use a table to record the answers to all the sub-problems that have been resolved. Regardless of whether it will be used later, as long as he has been calculated, the results are filled in the table. This is the basic idea of dynamic programming, although the dynamic programming algorithms are various, but they have the same form of filling forms.

V. Basic Concepts

1. Multi-stage

Usually a class of activities can be divided into a number of interconnected phases, each of which requires decision-making (taking measures), a decision of a stage, which often affects the decision of the next stage, thus fully determining the route of an activity, is called a multi-stage decision-making issue.

2. Terminology in dynamic programming problems

Stage: The process of solving all the problems is properly divided into the bold and interrelated phase, and the solution, the process is different, the stage number is different.

Status: Represents the natural or objective conditions at which each stage begins and becomes an uncontrollable factor.

No effect: Given the state of a stage, the development of the process after this phase is not affected by the previous, there are many stages to determine, the whole process will be determined. The history of the process can only affect its future development through the current state.

Decision: A selection of a state that evolves from that state to the next stage, given a state, becomes a decision. Decisions can be expressed as a number or a group of numbers, and different decisions correspond to different values. Because they satisfy no-no-effect, each stage chooses a decision only to consider the current state without regard to the historical state.

State transition equation: Given the K-phase state variable X (k), if the k+1 phase state variable X (k+1) is also determined, this is the law of State transfer, called the state transition equation. Optimal principle: As the optimal decision of the whole process, he satisfies: relative to the previous state, the remaining sub-strategy must be the most sub-strategy.

VI. Basic Models

(1) Determine the decision-making object of the problem. (2) The decision-making process is divided into stages. (3) Determine the state variables for each stage. (4) The cost function and the objective function are determined according to the state variables. (5) Establish the transfer process of state variables in each stage and determine the state transfer equation.

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