What is the purpose and basic method of optimizing the problem in mathematical modeling?

It's a big topic, let's talk about my own experience:

The optimization problem in mathematical modeling is a typical type of problem, the main feature is that the method to achieve a certain process or achieve a certain result is not unique, but the cost of different methods is different, and the optimization problem is to find the method with the least cost. So simply put, the purpose of an optimization problem is to find the best way to implement it.

To express an optimization problem as a mathematical relation, there must be an objective function that wants to be the largest or smallest, and the independent variables of the objective function may be subject to some constraints, such as some independent variables must be integers, some independent variables must be within a certain range, and so on, and so ......on

For optimization problems, it covers many aspects and methods. However, sometimes we don't need to know what the principle of calculating the extreme value of the objective function is, we only need to apply some software

LINGO is very suitable for planning problems, its language is specially designed for optimization problems, very user-friendly, very intuitive, for example, a certain independent variable can only take 0, 1, there is a special function @bin (x) to achieve this requirement. But after the lingo that we were able to get to was cracked, the effect was greatly reduced.

MATLAB is absolutely indispensable software for mathematical modeling, it's so powerful that I don't know how to describe it, and it's never an exaggeration to say that it's "omnipotent", but only if you're familiar with it.

There are also some methods that should be learned, sometimes there are no problems that cannot be solved, such as genetic algorithms, simulated annealing, dynamic programming, search algorithms, etc., don't think it's very complicated, one is because there are ready-made MATLAB source programs available on the Internet, and the other is that there are many related textbooks.

The importance of mathematical modeling to engineering personnel will continue to be highlighted in the future study, and you will be glad that you have chosen mathematical modeling before, hehe, come on!

Summary. The third method of mathematical modeling is the system analysis method, which is a method of studying complexity problems or subjective problems, and expressing qualitative thinking and conclusions in quantitative means.

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Hello! The first method of mathematical modeling is mechanistic analysis, which uses classical mathematics as a tool to analyze its internal mechanistic laws.

Well, thanks, is that the way to do it?

Hello! The second method is statistical analysis, which is based on random mathematics and analyzes statistical data to obtain its internal laws.

The third method of mathematical modeling is the system analysis method, which is a research method for complex problems or subjective problems, and the qualitative thinking and conclusions are expressed in quantitative hand kernels. Thank you!

Summary. What are the characteristics of the solution model that is usually optimized for the problem.

Dear Hello Because this digital model is not easy to express in the text, I am in the form of a bend to make trouble, and I personally suggest that you can refer to the content of the collapse.

Solution: Lay the pipe as shown in the picture above.

Set: point p is located at x (km) downstream of the refinery, 0 x 10. The total cost of laying is Y million yuan.

According to the meaning of the topic and known, there are:

y=4x+6√[

y=4x+6√(x²-20x+

y'=4+3(2x-20)/√(x²-20x+y'=[4√(x²-20x+

1. Order: y'0, i.e.: [4 (x -20x+ has: 2 (x -20x+

30-3x＜2√(x²-20x+

9x²-180x+900＜4(x²-20x+x²-20x+95＜0

x-10)²＜5

10-√5＜x＜10+√5

Because: 0 x 10, so: when 10- 5 x 10, y is a monotonic increasing function;

2. Order: y'0, i.e.: [4 (x -20x+ has: 2 (x -20x+

30-3x＞2√(x²-20x+

9x²-180x+900＞4(x²-20x+x²-20x+95＞0

x-10)²＞5

x 10 + 5, or: x 10 - 5

Because: 0 x 10, therefore: when 0 x 10-5, y is a monotonic subtraction function;

To sum up, there are:

When x=10- 5(km), y has a minimum.

y min = 4 (10-5) + 6 [(10-5) -20 (10-5)+

10,000 yuan) A: When point P is located downstream, the cost is the lowest. The cost is about 10,000 yuan.

Suppose 3m is a, b is c, 1 is d, and e is e.

Now the question is that there are 200 B numbers, 300 C numbers, 400 D numbers, and 600 E numbers, and you ask how many A's you can compose, don't you know how to do it?

2 roots*100 pairs of du (3m root;

3 roots*100 pairs (3m roots*100 pairs (roots+roots)=150 roots*roots;

4pcs*100 pairs (3m 1m)=134pcs+1pcs*2m;

Six *100 pairs) - (150) (3m roots, so total.)

DAO3M has 100 angles + 150 + 134 + 90 = 474.