Particle Swarm Optimization Algorithm with Differential Evolution

The Differential Evolution Particle Swarm Optimization (DEPSO) algorithm integrates the advantages of Differential Evolution (DE) and Particle Swarm Optimization (PSO) to form a more robust global optimization methodology.

PSO algorithm simulates the social behavior of bird flocks or fish schools, utilizing individual experience and collective cooperation to search for optimal solutions. However, it tends to fall into local optima, particularly when handling complex multimodal problems. Differential Evolution enhances global search capability through mutation, crossover, and selection operations to prevent premature convergence.

The hybrid algorithm typically employs DE's mutation strategy to update PSO particles' velocity and position. For instance, during iteration, some particles generate new solutions through differential mutation, combined with PSO's velocity update formula. This approach maintains population diversity while improving convergence accuracy. Key implementation involves calculating mutation vectors using donor vectors from randomly selected particles, followed by binomial crossover operations.

This improved strategy is particularly suitable for high-dimensional, nonlinear optimization problems such as engineering design and machine learning parameter tuning scenarios. The core challenge lies in balancing exploration (global search) and exploitation (local refinement) to reliably approach the global optimum. Algorithm parameters like mutation factor F, crossover rate CR, and inertia weight w require careful tuning for optimal performance.