Logistic Chaotic Search Method for Enhanced Particle Swarm Optimization

This text introduces the application of logistic chaotic search methodology to enhance traditional Particle Swarm Optimization (PSO) for multi-objective decision-making problems. We specifically employ logistic chaotic search to improve the search efficiency and convergence performance of PSO algorithms, enabling better solutions for complex multi-objective optimization scenarios.

The enhancement integrates chaotic dynamics from nonlinear systems through mathematical implementations such as: xₙ₊₁ = μxₙ(1-xₙ), where μ represents the growth parameter typically set between 3.57-4.0 to maintain chaotic behavior. This chaotic mapping generates pseudo-random sequences that replace conventional random number generation in PSO initialization and velocity updates.

Key algorithmic modifications include: 1) Chaotic population initialization using logistic maps to ensure uniform distribution across search space; 2) Dynamic parameter adaptation where chaotic variables modulate inertia weights and acceleration coefficients; 3) Chaotic local search operations that replace Gaussian mutations in personal best position updates.

Through MATLAB/Python implementation, the chaotic PSO demonstrates superior exploration-exploitation balance by leveraging ergodicity and randomness characteristics of chaotic systems. The改进 approach enables particles to escape local optima more effectively while maintaining population diversity, ultimately yielding improved Pareto fronts in multi-objective decision problems with enhanced accuracy and computational efficiency.