Optimizing RBF Network Weights Using Particle Swarm Algorithm

The Radial Basis Function (RBF) network is a widely used feedforward neural network for function approximation and pattern recognition applications, whose performance critically depends on the configuration of hidden layer weights. Traditional RBF weight optimization methods often face challenges like slow convergence rates and susceptibility to local optima. Particle Swarm Optimization (PSO), as an efficient swarm intelligence algorithm, significantly enhances RBF network weight optimization through global search capabilities.

PSO mimics collective behaviors of bird flocks or fish schools to locate optimal solutions. In RBF weight optimization, each particle represents a candidate weight combination, with its position vector encoding specific weight values. The algorithm's core mechanism involves dynamically adjusting particle velocities and positions based on fitness evaluations (e.g., reciprocal of network output error), driving the swarm toward improved solutions through iterative updates.

The implementation follows a structured workflow: First, initialize the particle swarm by randomly generating multiple RBF weight sets as initial solutions. During each iteration, compute fitness values (performance metrics of RBF networks under current weights). Update both personal best (historical optimal weights per particle) and global best (swarm-wide optimal weights). Particles then adjust velocities by integrating individual experience (personal best) and social experience (global best), subsequently updating weight positions. This process iterates until meeting termination criteria (e.g., maximum iterations or fitness convergence).

Key code components include:
- Fitness function: Calculates mean squared error between RBF outputs and targets
- Velocity update: v_i(t+1) = w*v_i(t) + c1*rand()*(pbest_i - x_i(t)) + c2*rand()*(gbest - x_i(t))
- Position update: x_i(t+1) = x_i(t) + v_i(t+1)
PSO-optimized RBF weights demonstrate superior approximation accuracy and generalization performance, particularly for nonlinear complex problems. The method's strengths include robust global exploration and compatibility with hybrid optimization strategies for extended applications.