A PSO-Based Zero-Order Optimization for Large-Scale Optimization.

Particle swarm optimization (PSO) is widely utilized in various optimization problems. The traditional PSO optimization algorithm relies on inertial, cognitive, and social factors to update the positions and velocities of the particles. It is difficult to produce an effective downward direction due to the curse of dimensionality for large-scale optimization problems. The local and global optimal solutions are unchanging for a long time, and then the particle's velocity tends to vanishing or exploding. Meanwhile, zero-order optimization is a straightforward, effective, and robust optimization algorithm that demonstrates an apparent convergence bound even in high-dimensional optimization. However, this kind of pointto-point optimization search algorithm tends to exhibits premature convergence at suboptimal equilibria. Therefore, we propose a particle swarm optimization based on zero-order optimization, namely PSO-ZO, to solve large-scale optimization problems. It dynamically adjusts the search stride and updates the direction of particle evolution by integrating the zero-order optimization sampling method to enhance the search efficiency. Experiments conducted in 11 benchmark functions demonstrate the efficacy of our algorithm in solving large-scale optimization problems. Additionally, this paper calculates the cosine similarity between the gradient direction obtained by PSO-ZO and the gradient direction of the objective functions to prove the algorithm's feasibility.