Using Chaotic Perturbation Algorithm to Solve Premature Convergence in PSO Algorithm

This study proposes a method based on chaotic perturbation algorithm to solve the premature convergence problem in Particle Swarm Optimization (PSO) algorithm, and combines both techniques to train parameters for grey prediction models. The chaotic perturbation algorithm is an optimization technique grounded in chaos theory, which enhances global search capability by introducing chaotic disturbance factors to increase algorithmic randomness. In code implementation, this typically involves generating chaotic sequences using logistic maps or tent maps, then applying these sequences as dynamic perturbation coefficients. PSO algorithm is a swarm intelligence-based optimization method that simulates bird flock foraging behavior to search for optimal solutions. The standard PSO update equations for velocity and position are: v_i(t+1) = w*v_i(t) + c1*r1*(pbest_i - x_i(t)) + c2*r2*(gbest - x_i(t)) x_i(t+1) = x_i(t) + v_i(t+1) However, PSO suffers from premature convergence issues, where particles easily get trapped in local optima and fail to reach global optimal solutions. To address this limitation, we integrate chaotic perturbation factors into PSO's velocity update formula. The enhanced velocity equation becomes: v_i(t+1) = w*v_i(t) + c1*r1*(pbest_i - x_i(t)) + c2*r2*(gbest - x_i(t)) + λ*chaotic(t) where λ represents the perturbation intensity coefficient and chaotic(t) denotes the chaotic sequence value at iteration t. This modification increases algorithmic randomness and helps escape local optima. Furthermore, we combine chaotic perturbation algorithm with PSO through iterative optimization to train parameters for grey prediction models. Grey prediction models are differential equation-based forecasting systems that analyze time series data characteristics to predict future trends. The core GM(1,1) model involves whitening equation: dx^(1)/dt + ax^(1) = b, where parameters a and b require precise estimation. The hybrid optimization process typically follows this workflow: 1. Initialize PSO parameters and chaotic sequences 2. For each iteration, calculate chaotic perturbation values 3. Update particle velocities with chaotic components 4. Evaluate fitness using grey model prediction errors 5. Update personal and global best positions 6. Repeat until convergence criteria met By integrating chaotic perturbation with PSO, we significantly improve the prediction accuracy and stability of grey forecasting models. Our method effectively resolves PSO's premature convergence problem while enhancing the predictive capability of grey systems through optimized parameter training.