Neural Network Algorithm in Intelligent Optimization (With Matlab Code)

When building a feedforward neural network using MATLAB, the following three functions are primarily used:

newff: Function to create a feedforward neural network;

train: Function to train a neural network;

sim: Function to simulate using the neural network.

Below is a brief introduction to the usage of these three functions.

Syntax: net=newff(P, T, [S1 S2…S(N-1)], {TF1 TF2…TFN}, BTF, BLF, PF, IPF, OPF, DDF)

P: Input matrix vector;

T: Target matrix vector;

[S1 S2…S(N-1)]: Number of neurons in each of the first N-1 layers of the neural network;

{TF1 TF2…TFN}: Activation functions of the neural network, default is ‘tansig’;

BTF: Training algorithm used for the learning rule, default is ‘trainlm’;

BLF: BP weight/bias learning function, default is ‘learngdm’;

PF: Performance function, default is ‘mse’;

IPF: Input processing function;

OPF: Output processing function;

DDF: Validation data partition function. Generally, the first seven parameters are set during use, while the last three parameters can use system default values.

Common Activation Functions

Only when you want to limit the output of the network (e.g., to restrict it between 0 and 1) should the S-shaped activation function be included in the output layer. Generally, the bipolar S-shaped activation function is used in the hidden layers, while the linear activation function is used in the output layer.

The train function is the neural network training function.

Syntax: [net, tr, Y1, E] = train(net, X, Y)

X: Network input matrix; Y: Network output matrix; tr: Training tracking information; Y1: Actual output of the network; E: Error matrix.

The sim function is the neural network simulation calculation function.

Syntax: Y = sim(net, X)

net: Trained neural network; X: Network input matrix; Y: Network output matrix.

Using Bayesian regularization algorithm to improve the generalization ability of the BP network. This is used to train the BP network to fit a sine sample data with added white noise.

Solution: The simulation process is as follows:

(1) Construct a 3-layer BP neural network: 1 input node, 3 hidden layer nodes, and the activation function of the hidden layer is ‘tansig’; 1 output node, and the activation function of the output layer is ‘logsig’.

(2) Train the BP network using the Bayesian regularization algorithm ‘trainbr’, with a target error goal=1×10-3, learning rate lr=0.05, maximum iteration epochs=500, fitting the sine sample data with added white noise, and the fitting data root mean square error is 0.0054. The fitted graph is shown below.

BP Network Fitting Sine Curve with Added White Noise

The MATLAB source code is as follows:

The table shows the monthly sales of a certain drug, using the BP neural network to predict the sales of the drug. The prediction method uses a rolling forecast, i.e., using the sales volume of the previous three months to predict the sales volume of the fourth month. For example, using the sales volumes of January, February, and March as input to predict the sales volume for April; using the sales volumes of February, March, and April as input to predict the sales volume for May. This process is repeated until the prediction accuracy requirement is met.

Solution: The simulation process is as follows:

(1) Construct a 3-layer BP neural network to predict the drug sales: 3 input nodes, 5 hidden layer nodes, and the activation function of the hidden layer is ‘tansig’; 1 output node, and the activation function of the output layer is ‘logsig’.

(2) Train the BP network using gradient descent momentum and adaptive lr algorithm ‘traingdx’, with a target error goal=1×10(-3), learning rate lr=0.05, maximum iteration epochs=1000. The comparison curve of actual and predicted sales values is shown below.

Comparison Curve of Actual and Predicted Drug Sales Values

The MATLAB source code is as follows:

The table shows the historical statistical data of highway transportation capacity in a certain area. Please establish the corresponding BP neural network prediction model and predict the corresponding highway passenger and freight volume based on the data from 2010 and 2011.

Solution: The simulation process is as follows:

(1) Construct a 3-layer BP neural network to predict the highway transportation capacity: 3 input nodes, 8 hidden layer nodes, and the activation function of the hidden layer is ‘tansig’; 2 output nodes, and the activation function of the output layer is ‘purelin’.

(2) Train the BP network using gradient descent momentum and adaptive lr algorithm ‘traingdx’, with a target error goal=1×10-3, learning rate lr=0.035, maximum iteration epochs=2000. The fitted curves for historical highway passenger volume and freight volume are shown in Figures 9.6 and 9.7, respectively. The predicted results are: 2010 highway passenger volume is 452.77 million people, highway freight volume is 222.90 million tons; 2011 highway passenger volume is 453.08 million people, highway freight volume is 222.96 million tons.

Historical Highway Passenger Volume Fitting Curve

Historical Highway Freight Volume Fitting Curve

The MATLAB source code is as follows:

Code Acquisition

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