[Matlab bp regression prediction] GA Optimized BP regression prediction (including comparison before optimization) [including source code 1901]

One 、 Code run video （ Bili, Bili ）

【Matlab BP Regression prediction 】GA Optimize BP Regression prediction （ Including the comparison before optimization ）【 Including source code 1901 period 】

Two 、 Introduction to relevant technical principles

1 BP Principle of neural network
Back propagation （Back Propagation,BP） Neural network is applied to 1986 Year by year Rumelhart and McCelland The team of scientists led by Mr , It is a multilayer feedforward neural network trained by error back propagation algorithm .BP Neural network can learn and store a large number of input and output mode mapping relations , There is no need to reveal the mathematical equation describing this mapping relationship in advance . The learning rule is to use the steepest descent method , The weights and thresholds of the network are continuously adjusted through back propagation , Thus, the sum of square errors of the network is minimized .BP The topological structure of neural network can be divided into 3 layer , It's the input layer 、 Hidden layer and output layer . among , The formula for calculating the number of neurons in the hidden layer is ：

In style ：m Is the number of input layer nodes ,n Is the number of output layer nodes ,a Usually take 1～10 The whole number inside . The more hidden layers , The smaller the error range .

2 Genetic optimization algorithm
Genetic algorithm is a computational model that simulates the biological evolution process such as natural selection and genetic mechanism in Darwin's theory of biological evolution , It is a method to search the optimal solution by simulating the natural evolution process . basis BP Topology of neural networks , Determine optimization BP The number of parameters of neural network weight threshold , Thus, the coding length of the individual in the genetic algorithm is determined , Then calculate the fitness value of the individual according to the fitness function , By choice 、 cross 、 The mutation operation obtains the optimal weight threshold .

2.1 Roulette algorithm
Roulette algorithm is proposed to prevent individuals in a group with small fitness values from being eliminated directly , The probability of each individual being selected is proportional to the value of its fitness function . The higher the fitness value , The more likely it is to be selected . Let an individual xi The fitness value of is f(xi), Then the probability of partial selection is ：

The cumulative probability is ：

In style ：xi and xj Both represent an individual .

First , Calculate the probability of each part being selected p(xi) And cumulative probability q(xi). secondly , Randomly generate an array m, Array m The value range of the element in is [0,1]. If cumulative probability q(xi) Larger than the elements in the array m[i], Then the individual xi To be selected ; If less than m[i], Then compare the next individual xi+1, Until an individual is selected . Last , If you need to select N Individuals , Repeat the above steps N Next time .

2.2 Two point crossover algorithm
Two point crossing refers to the random setting of two crossing points in an individual chromosome , And then part of the gene exchange . First, select two intersections from the coding string , Then the two crossing points were partially crossed , After crossing, new individuals are produced , Pictured 1 Shown . among , On the left is the individual before crossing , On the right is the new individual after two points cross .

chart 1 Two point intersection example

2.3 Gauss mutation
Gaussian mutation refers to the mutation operation , Use the consistent mean as μ、 The variance of S2 The normal distribution of a random number to replace the original gene value . According to the properties of normal distribution , Gaussian mutation focuses on searching a local area near the original individual . The Gaussian probability density formula is ：

among , Standard Gaussian probability density μ and S Set as 0 and 1. Gaussian mutation not only improves the optimization accuracy of the optimization algorithm , And it is helpful to jump out of the local optimal region .

3、 ... and 、matlab Edition and references

1 matlab edition
2014a

2 reference
[1] Zhangsanniu . Optimization based on genetic algorithm BP Research on prediction of Telecom Customer Churn Based on neural network [J]. Television technology . 2022,46(05)