Convergence analysis of particle swarm optimization using stochastic Lyapunov functions and quantifier elimination
This work addresses theoretical stability analysis for PSO, an incremental contribution to optimization algorithms.
The paper tackles the problem of analyzing particle swarm optimization (PSO) stability by using stochastic Lyapunov functions and quantifier elimination, resulting in a computational procedure that reevaluates and extends previously known stability regions under stagnation assumptions.
This paper adds to the discussion about theoretical aspects of particle swarm stability by proposing to employ stochastic Lyapunov functions and to determine the convergence set by quantifier elimination. We present a computational procedure and show that this approach leads to reevaluation and extension of previously know stability regions for PSO using a Lyapunov approach under stagnation assumptions.