Chaotic Particle Swarm Optimization Algorithm

Chaotic Particle Swarm Optimization (CPSO) is an intelligent optimization algorithm that integrates chaos theory into the traditional Particle Swarm Optimization (PSO) framework to enhance global search performance. By simulating bird flock foraging behavior combined with the randomness characteristics of chaotic mapping, this algorithm can more effectively escape local optima. In code implementation, this typically involves modifying the standard PSO velocity update equation with chaotic perturbations.

The algorithm core contains three critical parameters: inertia weight, individual learning factor, and social learning factor. Proper adjustment of these parameters controls the exploration and exploitation capabilities of particles in the search space. The inertia weight determines the particle's tendency to maintain its previous velocity, while the learning factors influence the particle's movement toward individual best and global best positions respectively. In programming terms, these parameters are typically implemented as configurable constants in the particle velocity update function: v_i(t+1) = w*v_i(t) + c1*r1*(pbest_i - x_i(t)) + c2*r2*(gbest - x_i(t)).

The introduction of chaotic mapping brings richer diversity to the algorithm, with common chaotic models including Logistic map or Tent map. This nonlinear perturbation mechanism helps maintain active exploration capability during later search stages, preventing premature convergence to suboptimal solutions. From an implementation perspective, chaotic sequences are usually generated separately and incorporated into the position update process or parameter adaptation mechanism.

This algorithm is suitable for various continuous optimization problems, particularly multimodal function optimization. When applying CPSO, users need to adjust parameters such as population size and maximum iteration number according to specific problems. Appropriate parameter settings can balance convergence speed and solution quality, typically requiring experimental determination of optimal parameter combinations through systematic parameter tuning procedures.