Symbiotic Structure Learning Algorithm for Feedforward Neural-Network-Aided Grey Model and Prediction Applications

The learning ability of neural networks (NNs) enables them to solve time series prediction problems. Off-line training can be applied to design the structure and weights of NNs when sufficient training data are available. However, this may be inadequate for applications that operate in real time, possess limited memory size, or require online adaptation. Furthermore, the structural design of NNs (i.e., the number of hidden neurons and connected topology) is crucial. This paper presents a novel algorithm, called the symbiotic structure learning algorithm (SSLA), to enhance a feedforward neural-network-aided grey model (FNAGM) for real-time prediction problems. Through symbiotic evolution, the SSLA evolves neurons that cooperate well with each other, and constructs NNs from the neurons with hyperbolic tangent and linear activation functions. During construction, the hidden neurons with the linear activation function can be simplified to a few direct connections from the inputs to the output neuron, leading to a compact network topology. The NNs share the fitness value with participating neurons, which are further evolved through neuron crossover and mutation. The proposed SSLA was evaluated through three real-time prediction problems. Experimental results showed that the SSLA-derived FNAGM possesses a partially connected NN with few hidden neurons and a compact topology. The evolved FNAGM outperforms other methods in prediction accuracy and continuously adapts the NN to the dynamic changes of the time series for real-time applications.