# Self-adaptive Potential-based Stopping Criteria for Particle Swarm Optimization

## TL;DR

This paper introduces a self-adaptive stopping criterion for Particle Swarm Optimization based on counting forced moves, enabling the algorithm to terminate efficiently near local optima.

## Contribution

It proposes a novel potential-based stopping criterion for PSO that self-adapts by monitoring forced moves, improving convergence speed.

## Key findings

- Stopping criteria effectively detect convergence near optima.
- The method finds good solutions faster than traditional criteria.
- Theoretical analysis confirms behavior near local optima.

## Abstract

We study the variant of Particle Swarm Optimization (PSO) that applies random velocities in a dimension instead of the regular velocity update equations as soon as the so-called potential of the swarm falls below a certain bound in this dimension, arbitrarily set by the user. In this case, the swarm performs a forced move. In this paper, we are interested in how, by counting the forced moves, the swarm can decide for itself to stop its movement because it is improbable to find better solution candidates as it already has found. We formally prove that when the swarm is close to a (local) optimum, it behaves like a blind-searching cloud, and that the frequency of forced moves exceeds a certain, objective function-independent value. Based on this observation, we define stopping criteria and evaluate them experimentally showing that good solution candidates can be found much faster than applying other criteria.