A Hybrid PSO-BFGS Strategy for Global Optimization of Multimodal Functions.

Area of Science:

• Computational intelligence
• Optimization algorithms
• Swarm intelligence

Background:

• Particle Swarm Optimization (PSO) is widely used but faces challenges like premature convergence and slow convergence rates.
• Existing optimization methods require enhancement for multimodal function optimization in constrained spaces.

Purpose of the Study:

• To develop a hybrid global optimization strategy addressing PSO's limitations.
• To improve both local and global search abilities of optimization algorithms.

Main Methods:

• Integrating a modified Broyden-Fletcher-Goldfarb-Shanno (BFGS) method into PSO to enhance local search.
• Implementing a repositioning technique with territory concepts to maintain particle diversity and improve global search.
• Utilizing a reconstruction technique to refine solutions based on found local optima.

Main Results:

• The hybrid approach effectively finds multiple local or global solutions for multimodal functions within box-constrained spaces.
• Experimental results on 20 benchmark problems show superior performance compared to other recent optimization algorithms.
• The method achieves high-quality solutions for complex optimization tasks.

Conclusions:

• The proposed hybrid optimization strategy significantly enhances PSO's performance by overcoming premature convergence and slow convergence.
• This novel approach offers a robust solution for multimodal function optimization, demonstrating effectiveness and efficiency.