# Particle swarm stability: a theoretical extension using the non-stagnate distribution assumption

@article{Cleghorn2017ParticleSS, title={Particle swarm stability: a theoretical extension using the non-stagnate distribution assumption}, author={Christopher Wesley Cleghorn and Andries Petrus Engelbrecht}, journal={Swarm Intelligence}, year={2017}, volume={12}, pages={1-22} }

This paper presents an extension of the state of the art theoretical model utilized for understanding the stability criteria of the particles in particle swarm optimization algorithms. Conditions for order-1 and order-2 stability are derived by modeling, in the simplest case, the expected value and variance of a particle’s personal and neighborhood best positions as convergent sequences of random variables. Furthermore, the condition that the expected value and variance of a particle’s personal…

## 63 Citations

Variance of particle location in the stochastic model of PSO with inertia weight

- Mathematics2020 IEEE Congress on Evolutionary Computation (CEC)
- 2020

Stability areas in the particle configuration space are shown, which guarantee order-2* stability of particles also for probability distributions of movement parameters other than uniform.

Variance of particle location in the stochastic model of PSO with inertia weight

- Mathematics
- 2020

In the Particle Swarm Optimization (PSO) method, the behavior of particles depends on movement parameters. Effective application of the PSO method in real-world problems requires stable behavior of…

Weak convergence of particle swarm optimization

- Computer Science
- 2018

Assuming the convergence of PSO, two CLT for the particles corresponding to two kinds of convergence behavior are proposed, which can lead to build confidence intervals around the local minimum found by the swarm or to the evaluation of the risk.

Stability Analysis of the Multi-objective Multi-guided Particle Swarm Optimizer

- Computer ScienceANTS Conference
- 2018

It was found that the derived criteria for order-1 and order-2 stability are an accurate predictor of the unsimplified MGPSO’s particle behavior.

An Analysis of Parameter Control Mechanisms for the Particle Swarm Optimization Algorithm

- Computer Science
- 2018

This investigation provides strong empirical evidence that the best values to employ for the PSO control parameters change over time, and proposes novel PSO variants inspired by results of the aforementioned studies.

Particle Swarm Optimization - An Adaptation for the Control of Robotic Swarms

- Computer ScienceRobotics
- 2021

Simulation results from both MATLAB and Gazebo show close agreement and demonstrate that the proposed algorithm is capable of effective control of a robotic swarm and obstacle avoidance.

Particle Swarm Optimization: Understanding Order-2 Stability Guarantees

- Computer ScienceEvoApplications
- 2019

It is shown that the definition of order-2 stability which accurately reflects PSO behavior is that of convergence in second order moment to a constant, and not to zero.

A Theoretical Guideline for Designing an Effective Adaptive Particle Swarm

- Computer ScienceIEEE Transactions on Evolutionary Computation
- 2020

The underlying assumptions that have been used for designing adaptive particle swarm optimization (PSO) algorithms in the past years are theoretically investigated and provide a beneficial guideline for the successful adaptation of the coefficients in the PSO algorithm.

Particle Swarm Optimization: Stability Analysis using N-Informers under Arbitrary Coefficient Distributions

- MathematicsSwarm and Evolutionary Computation
- 2022

## References

SHOWING 1-10 OF 47 REFERENCES

Stability Analysis of the Particle Swarm Optimization Without Stagnation Assumption

- MathematicsIEEE Transactions on Evolutionary Computation
- 2016

It is proved that the convergence of expectation and variance of the positions generated by the stochastic recurrence relation is independent of the mean and varianceof the distribution of the personal and global best vectors.

The particle swarm - explosion, stability, and convergence in a multidimensional complex space

- Computer ScienceIEEE Trans. Evol. Comput.
- 2002

This paper analyzes a particle's trajectory as it moves in discrete time, then progresses to the view of it in continuous time, leading to a generalized model of the algorithm, containing a set of coefficients to control the system's convergence tendencies.

Stability analysis of the particle dynamics in particle swarm optimizer

- MathematicsIEEE Transactions on Evolutionary Computation
- 2006

Simulation results confirm the prediction from theory that stability of the particle dynamics requires increasing the maximum value of the random parameter when the inertia factor is reduced.

Particle swarm optimizer: The impact of unstable particles on performance

- Computer Science2016 IEEE Symposium Series on Computational Intelligence (SSCI)
- 2016

It is shown empirically that a majority of PSO parameters that are theoretically unstable perform worse than a trivial random search across 28 objective functions, and across various dimensionalities.

Exact analysis of the sampling distribution for the canonical particle swarm optimiser and its convergence during stagnation

- MathematicsGECCO '07
- 2007

A novel method is introduced, which allows one to exactly determine all the characteristics of a PSO's sampling distribution and explain how they change over any number of generations, in the presence stochasticity.

Dynamics and stability of the sampling distribution of particle swarm optimisers via moment analysis

- Business
- 2008

In this paper, a method is presented that allows one to exactly determine all the characteristics of a PSO's sampling distribution and explain how it changes over time during stagnation (i.e., while particles are in search for a better personal best) for a large class ofPSO's.

A generalized theoretical deterministic particle swarm model

- Computer ScienceSwarm Intelligence
- 2013

The model used in this paper greatly weakens the stagnation assumption, by instead assuming that each particle’s personal best and neighborhood best can occupy an arbitrarily large number of unique positions.

Mean and Variance of the Sampling Distribution of Particle Swarm Optimizers During Stagnation

- Computer Science, MathematicsIEEE Transactions on Evolutionary Computation
- 2009

A novel method is introduced that allows us to exactly determine all the characteristics of a PSO sampling distribution and explain how it changes over any number of generations, in the presence stochasticity.

Order-2 Stability Analysis of Particle Swarm Optimization

- MathematicsEvolutionary Computation
- 2015

The order-2 stability of PSO is analyzed based on a weak stagnation assumption, a new definition of stability is proposed and an order- 2 stable region is obtained.