Genetic Algorithm Optimized RBF Network Approximation

Genetic Algorithm optimized RBF network approximation represents an intelligent computational method that integrates biological evolution principles with neural network technology. The RBF (Radial Basis Function) network, as a feedforward neural network, is renowned for its simple architecture and excellent local approximation capabilities, while genetic algorithms emulate natural selection mechanisms to discover optimal solutions.

In conventional RBF networks, critical parameters such as center positions, width parameters, and connection weights are typically determined using clustering methods or least squares algorithms. However, with the introduction of genetic algorithms, the optimization process for these parameters becomes significantly more intelligent and efficient. The genetic algorithm encodes each potential parameter combination as a chromosome, then progressively evolves optimal network configurations through selection, crossover, and mutation operations.

The implementation process begins with determining the RBF network structure, including the number of hidden layer nodes. Subsequently, network parameters are encoded into chromosome representations, and an initial population is generated. During each evolutionary generation, individual fitness is calculated (typically represented as the reciprocal of approximation error), elite individuals are preserved, and new generations are produced through genetic operations. After multiple generations of evolution, the optimal chromosome is decoded to obtain the optimized RBF network parameters. In code implementation, this involves creating chromosome encoding functions, fitness evaluation routines, and genetic operation modules.

This approach is particularly suitable for complex nonlinear function approximation problems, demonstrating superior global search capabilities and robustness compared to traditional methods. In practical applications, careful attention must be paid to genetic algorithm parameter settings, such as population size and mutation probability, as these directly impact optimization effectiveness and convergence speed. Code implementation typically includes parameter tuning functions and convergence monitoring mechanisms.