A Particle Swarm Optimization Algorithm with Global Convergence and Significantly Improved Convergence Rate

The traditional Particle Swarm Optimization (PSO) algorithm may face premature convergence or local optimum trapping when solving complex optimization problems. In recent years, researchers have proposed various improvement strategies to enhance algorithm performance through parameter adjustments, introduction of new mechanisms, or integration with other optimization techniques.

The core approaches for improving global convergence typically focus on three aspects: dynamic adjustment of inertia weight, introduction of diversity preservation mechanisms, and enhancement of information exchange methods between particles. Common strategies include implementing non-linearly decreasing inertia weights, enabling the algorithm to maintain strong global exploration capability in early stages while transitioning to refined local exploitation later; or introducing random disturbance factors to help particles escape local optima when stagnation occurs. In code implementation, inertia weight adjustment can be achieved through functions like: w = w_max - (w_max - w_min) * (current_iteration / max_iteration)^k, where k controls the nonlinearity degree.

Convergence rate improvements often rely on more intelligent particle guidance mechanisms. For instance, establishing elite particle archives to guide population movement directions, or adopting group collaboration strategies where different subgroups handle specific search tasks at different stages. Some enhanced algorithms incorporate gradient information or local search operators to accelerate convergence. Code implementation typically involves maintaining an elite archive through data structures like priority queues, and implementing subgroup coordination through modular function calls.

These improved algorithms demonstrate more stable global convergence characteristics and faster convergence rates across various benchmark test functions and engineering optimization problems, making them particularly suitable for handling complex optimization scenarios involving multi-modal, high-dimensional search spaces. The algorithms can be validated through standardized testing frameworks that measure performance metrics like success rate and convergence curves.