Lagrange Interpolation Learning Particle Swarm Optimization.

Area of Science:

• Computational intelligence
• Optimization algorithms
• Swarm intelligence

Background:

• Comprehensive Learning Particle Swarm Optimization (CLPSO) is effective for multimodal problems due to its diversity preservation, preventing premature convergence.
• However, CLPSO suffers from low solution accuracy, limiting its practical application.
• Addressing this limitation is crucial for advancing optimization techniques.

Purpose of the Study:

• To propose a novel algorithm, LILPSO, to improve the solution accuracy of CLPSO.
• To enhance the convergence speed and maintain diversity in multimodal optimization.
• To overcome the limitations of existing CLPSO methods.

Main Methods:

• Introduced a Lagrange interpolation method for local search on the global best point (gbest).
• Developed a new exemplar selection strategy using Lagrange interpolation of gbest and two particle historical best points (pbest).
• Replaced the standard CLPSO comparison method with the new Lagrange interpolation-based exemplar approach.

Main Results:

• Numerical experiments on various functions demonstrated the superiority of the proposed LILPSO algorithm.
• The introduced Lagrange interpolation methods were proven effective in accelerating convergence.
• The algorithm successfully prevented premature convergence while improving solution accuracy.

Conclusions:

• LILPSO significantly outperforms CLPSO in solving multimodal problems, particularly in solution accuracy.
• The novel Lagrange interpolation techniques are key to LILPSO's enhanced performance.
• This research offers an effective approach to accelerate convergence without sacrificing diversity in particle swarm optimization.