A lyapunov-based extension to particle swarm dynamics for continuous function optimization.

Area of Science:

• Computational Intelligence
• Optimization Algorithms
• Swarm Intelligence

Background:

• Classical global-best particle swarm optimization (PSO) is a widely used metaheuristic.
• Existing PSO algorithms face limitations in convergence speed and accuracy for complex optimization problems.

Purpose of the Study:

• To propose and evaluate three novel extensions to the standard particle swarm optimization dynamics.
• To mathematically analyze the convergence properties of the proposed PSO variants.
• To compare the performance of the new extensions against the classical PSO algorithm.

Main Methods:

• Development of three distinct extensions to the global-best PSO velocity update equation.
• Mathematical formulation of the first extension based on Lyapunov's stability theorem.
• Empirical evaluation through computer simulations comparing convergence speed and solution accuracy.

Main Results:

• The first extension, incorporating local and global attractors, demonstrates improved convergence and accuracy.
• The second and third extensions, modifying velocity adaptation and inertial terms respectively, show superior performance.
• The latter two extensions consistently outperform both the classical PSO and the first proposed extension.

Conclusions:

• The proposed extensions offer significant improvements in PSO performance.
• Novel modifications to PSO dynamics can lead to faster convergence and higher accuracy.
• The second and third extensions represent promising advancements in swarm intelligence optimization techniques.