Empirically characteristic analysis of chaotic PID controlling particle swarm optimization

Area of Science:

• Computational Intelligence
• Optimization Algorithms
• Chaos Theory

Background:

• Chaos systems possess properties like sensitivity to initial conditions, enabling effective global optimization.
• Particle Swarm Optimization (PSO) is a widely used metaheuristic, but can suffer from premature convergence.
• Existing chaotic PSO variants show promise but have limitations in search efficiency and adaptability.

Purpose of the Study:

• To propose a novel chaotic proportional integral derivative (PID) controlling PSO algorithm.
• To enhance PSO's performance by integrating chaotic logistic dynamics and a hierarchical inertia weight.
• To improve global search capabilities and avoid premature convergence in optimization problems.

Main Methods:

• Hybridization of chaotic logistic dynamics with PSO.
• Implementation of a hierarchical inertia weight adaptively adjusted by local best fitness values.
• Utilization of the chaotic logistic map to replace random parameters and enhance local search.
• Convergent analysis of the proposed chaotic PID-controlling PSO algorithm.

Main Results:

• The chaotic PID-controlling PSO algorithm demonstrated significantly better search efficiency and solution quality.
• Empirical simulations confirmed superiority over other chaotic PSO variants (logistic map, tent map, catfish PSO).
• The algorithm also outperformed standard PSO, Genetic Algorithm (GA), and chaotic catfish PSO in parameter estimation tasks.

Conclusions:

• The proposed chaotic PID-controlling PSO effectively leverages chaotic dynamics and adaptive weights for superior optimization.
• This hybrid approach mitigates premature convergence and enhances the exploration-exploitation balance.
• The algorithm shows strong potential for solving complex optimization problems and parameter estimation tasks.