Mathematical modeling algorithm commonly used outline
normal method
Scope
① Data processing (pre-clear data, numerical data fit)
② draw graphics
③ The Forecast
Algorithm theory
① reading the read data
method: Copy Paste
Method two: by MATLAB Link tool in Excel, Excel to interact with MATLAB.
Method three: by reading the MATLAB function data Load Notepad; Save function to write data to Notepad, notepad achieve interaction with MATLAB.
② Method data fitting
method a: a polynomial fit
determining polynomial coefficients methods: least-squares method
in the form of a: a polynomial fit instruction
polyfit (X, Y, N) : polynomial fitting, polynomial coefficients in descending return arrangement.
polyval (P.xi): Calcd polynomial.
Wherein, X, Y is the value of data point; N highest power is fitted; P polynomial coefficients is returned; XI abscissa is required points.
Two forms: the graphic window polynomial
fit the data in the graphics mode menu window
Method two: designated function fitting
the data format known to the user selected function to fit
three: Curve Fitting Toolbox
in MATLAB from with a toolbox to fit
Planning issues
Scope
① multi-constrained planning, integer programming;
② less complex and more constrained nonlinear programming, integer programming
Algorithm theory
Planning three elements: decision variables, objective function and constraints.
The real problem is the solution solution planning constraints into the objective function, the process of obtaining the optimal solution.
Gray forecast
Scope
Any amount of data (greater than three) of the prediction problem
Algorithm theory
GM (1,1) basic steps:
① raw data accumulated to weaken volatility and random random sequence to obtain new data sequence;
② establishing a first order linear differential equation;
③ to make the accumulated data to generate mean and constant term vector producing B yn;
④ solved by least squares parameter ash;
⑤ ash parameters into the solution of differential equations;
⑥ of the discrete function expression, and calculating the difference between both prosequence reduction, approximate data sequence;
⑦ gray established model test;
⑧ using the model to predict.
Genetic Algorithms
Scope
① solving multi-constrained programming model;
① trained artificial neural network.
Algorithm theory
Ways and means of forming a new species, there are two: gradual change and explosive. Tapered subspecies mainly formed by gradually accumulated variation, then the sub-species form one or more new species, new species divided into two types, i.e. Inheritance of new species formation and differentiation of the new species of the formula is formed; not explosive rapid formation of new species and subspecies by this stage, divided into three types, i.e., a new hybrid species, change in chromosome structure and a new species of the new forms polyploid. Hybrid genetic algorithm, two thought tapered and explosive.
Should assessment: generally, find the maximum objective function objective function directly as a function of the size of the detected individual fitness.
Particle Swarm Optimization
Scope
① multivariate unconstrained nonlinear programming model;
② trained artificial neural network.
Algorithm theory
During feeding the birds per bird in a random position in the initial state, and the flying direction is random. Do not know each bird food there, but over time, these birds initially in a random position within the group by learning from each other, share information and continue to accumulate experience in the breeding of individuals looking for food, accumulate into a self-organized community, and gradually super food only goal forward. Each bird can be estimated by some experience and current location information has little value to be able to find food that is much fitness; every bird can remember the best place to find their own, called local optimization, in addition, birds can remember the best position of all individuals could find, called the global optimum, the entire flock of feeding centers tend to move the global optimum, which is called "synchronization effect" in biology . By birds foraging position constantly moving, that is constantly iteration, super food can make birds looms.
Simulated annealing algorithm
Scope
① classic TSP, knapsack problem;
② responsible for solving multi-constrained nonlinear programming model.
Algorithm theory
The solid was heated to a sufficiently high temperature, then cooled slowly; during the heating, the solid particles with the internal temperature rises becomes disordered state, internal energy is increased, while slow cooling particles gradually become ordered, in theory , if the cooling process is slow enough, then any kind of a cooling temperature of the solid to achieve thermal equilibrium, and when cooled to cryogenic temperatures will reach a minimum energy state in the case that status.
Artificial neural networks
Scope
All clustering problem in mathematical modeling, evaluation and prediction mode
Algorithm theory
Artificial neural network is a large number of simple basic elements - neurons which are connected, by way of simulation of the human brain to process information, the parallel information processing systems and complex network of non-linear conversion. Advantage is that the neural network MIMO verses parallel processing and self-learning ability.
BP is a neural network having three or more than three neural network neurons, comprising an input layer, an intermediate layer and output layer. Achieve full connection between the upper and lower layers, and between neurons with no connection layer, the network is the weight between the input neurons and the hidden neurons in the sense that the strength of the connection between the two neurons. Hidden layer and output layer neurons either to the previous layer of information coming from all neurons integrate, usually adding a threshold value will then integrate the information process, which is mainly imitate biology of neurons must reach a certain principle threshold will start, and then integrate over information as the input layer neurons. When a pair of the learning samples are provided to the input neurons, neuron activation values (values of the input layer neurons) propagated from the input layer to the output layer through the hidden layer and each of the various output layer neurons and then obtaining input network appropriate, and then in the direction to reduce the error between the actual network output and the output samples, a direction from the output layer through the hidden layer back to the input of each layer, so as to gradually correcting the weight of each connection, which is called an error back propagation algorithm algorithm, BP algorithm.
Biologically feeling means visual field of central neurons can affect the visual field of a retina of neurons. Photoreceptors on the retina nerve output signal to activate a number of different levels of neural cells, cells and outer geniculate body neurons in the visual cortex by receiving light and converting it. QBF neural network function is to simulate the experience of the retina produced.
Wavelet Analysis
Scope
① massive data mining trend;
② assembly wavelet neural network.
Algorithm theory
And the difference between the logarithmic values averaged to obtain a final conversion error of the mean average, the evaluation is the average, the average error as error algorithm analysis.
Virtual Computer
Scope
① model is difficult to obtain analytical solution;
② dynamic (animated) show the mathematical model;
③ rough solving complex nonlinear programming problem.
Algorithm theory
The main use of mathematical modeling in virtual simulation technology there are still three numerical simulation, animation, simulation and image. The process is to set up a virtual mathematical models, computer experiments and in accordance with the mathematical model. Numerical Simulation for general mathematical model and recursive equations set differential equations; static simulation is based on the most image has been formed a good model, and then the MATLAB generated pseudo-random number as an initial value of the simulated model, and finally in the form of Figure output from the computer, eventually the result was a static graphic.
