First of all, we need to separate "basic" PSO from "standard" PSO. Here's a good set of papers:

http://www.mendeley.com/groups/2579251/standard-particle-swarm-optimisation/

Second, the list of variants is nearly endless, and my summary of variants has several classifications:

- topology variations (e.g. star, ring, torus, etc)

- multi-swarm variations:

http://www.mendeley.com/groups/2389861/multi-swarm-systems/

-- note: this is my group and I've focused more on a fixed number of swarms in sequence as opposed to other obvious variations such as parallel swarms with or without an adaptive number of subswarms

- single swarm variations:

http://www.mendeley.com/groups/2536901/variations-of-particle-swarm-optimization/

-- note: this is also my group. In general, any change to standard PSO that improves motion/prevents convergence improves results. Since convergence occurs when all current locations are at the personal best locations, all personal best locations are the same, and all particles have zero velocities, my categorizations are methods that 1) prevent zero velocities, 2) prevent current locations from being personal best locations (by moving one or the other or both -- e.g. crossover), and 3) prevent pbest locations from all becoming the same (e.g. niching and thresheld convergence).

Hope that helps!

First of all, we need to separate "basic" PSO from "standard" PSO. Here's a good set of papers:

http://www.mendeley.com/groups/2579251/standard-particle-swarm-optimisation/

Second, the list of variants is nearly endless, and my summary of variants has several classifications:

- topology variations (e.g. star, ring, torus, etc)

- multi-swarm variations:

http://www.mendeley.com/groups/2389861/multi-swarm-systems/

-- note: this is my group and I've focused more on a fixed number of swarms in sequence as opposed to other obvious variations such as parallel swarms with or without an adaptive number of subswarms

- single swarm variations:

http://www.mendeley.com/groups/2536901/variations-of-particle-swarm-optimization/

-- note: this is also my group. In general, any change to standard PSO that improves motion/prevents convergence improves results. Since convergence occurs when all current locations are at the personal best locations, all personal best locations are the same, and all particles have zero velocities, my categorizations are methods that 1) prevent zero velocities, 2) prevent current locations from being personal best locations (by moving one or the other or both -- e.g. crossover), and 3) prevent pbest locations from all becoming the same (e.g. niching and thresheld convergence).

Hope that helps!

Thanks so much Stephen. Great answer! I will definitely be going through your papers.

Just curious, have you had any experience with decentralized PSO, where the global best is not known to any particle?

It would be awkward and even weird for no particle (including itself?) to not know the global best position. Offhand, I would think of a ring topology if someone mentioned "decentralized" PSO to me. If it's a specific term/variation, I would be happy to have a link.

I've personally used the predator-prey particle swarm optimization approach, which worked well in terms of not getting stuck in local optima.

@Stephen: Sure, check out this link: http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=4668304&url=http%3A%2F%2Fieeexplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D4668304 .

Basically, rather than broadcasting the global best and assuming it is common knowledge for all particles, particles exchange and update their local best via local interactions.

Hi Dariusz,

Sorry for the delay, but I finally got a chance to look at the paper. My understanding is the decentralization is based on a parallel implementation, and through the coordination of the parallel processes, a dynamic neighbourhood structure arises. However, within these neighbourhoods, lbest (gbest for a given neighbourhood) information is communicated and known.

To me, the dynamic neighbourhoods creates a multi-swarm behaviour similar to DMS-PSO -- by changing the attractors, more motion is injected into the swarm:

http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=01501611

The asynchronous updates also tend to increase exploration since the speed at which exploitation can occur is reduced.

Hope that helps.

Cheers,

Stephen

Hi

First of all, i do not think there is a best variant. some variants are good on some problems while others are better on another (no free launch theorem). nevertheless,I will definitely compare with the two standard PSO (SPSO 2006 and SPSO 2011.)

Regards

Mahamed

You should also have a look at Quantum-like Particle Optimization methods [1], which are considered as improvement of standard PSO method, since the standard SPO has a low convergence rate and premature convergence to local minimum.

[1] . Fang, W., et al. A review of Quantum-behavied Particle Swarm Optimization. IETE Technical Review. 2010, Vol. 27, 4, pp. 337-348.

I do not think that QPSO is better than SPSO 2007 and 2011. I tried a new variant of PSO developed by Jun Sun (developer of QPSO). The variant is called a random drift pso. It is easy to implement but not much better than SPSO.

There exist several variants of the QPSO as well; by carefully choosing the probability distribution of quantum particles and the width you may be able to increase the convergence rate.

Recently, I have also been interested on these kind of the algorithms, and I came to the conclusion that using non-Gaussian distribution for the particles avoids the premature convergence to local minimum by increasing the diversity of particles, and so exploring better the searching space.

I also compared with the so called standard and classical PSO, but still the convergence rate is better with some improved versions of QPSO. You have to tune a little bit some of the dependence parameters. I will have a look at the random drift pso.

Dear all

I think our new paper may help you to find an appropriate answer to these question:

"Chaotic Swarming of Particles: A New Method for Size Optimization of Truss Structures";

Advances in Engineering Software; 67:136-147; DOI:http://dx.doi.org/10.1016/j.advengsoft.2013.09.006

I think Quantum Particle Swarm Optimization gives better result for different variant of PSO. Most of the researcher used PSO-CO, QPSO, Weighted QPSO and Gaussian QPSO

I think chaotic sequence based PSO is the best PSO variate.

MATLAB programming codes for PSO

https://www.researchgate.net/publication/296636431_Codes_in_MATLAB_for_Particle_Swarm_Optimization?ev=prf_pub

https://www.researchgate.net/publication/280244004_A_comparative_study_of_metaheuristic_optimization_approaches_for_directional_overcurrent_relays_coordination?ev=prf_pub

Code Codes in MATLAB for Particle Swarm Optimization

Article A comparative study of metaheuristic optimization approaches...

Kindly, go through the following publication.

Y. del Valle, G. Venayagamoorthy, S. Mohagheghi, J.-C. Hernandez, R. Harley, Particle swarm optimization: Basic concepts, variants and applications in power systems, IEEE Transactions on Evolutionary Computation, 12 (2) (2008) 171-195.

I hope it will be very helpful to you.

Kindly, go through the following publication.

Y. del Valle, G. Venayagamoorthy, S. Mohagheghi, J.-C. Hernandez, R. Harley, Particle swarm optimization: Basic concepts, variants and applications in power systems, IEEE Transactions on Evolutionary Computation, 12 (2) (2008) 171-195.

I hope it will be very helpful to you.

Regards,

M.N.Alam

https://www.researchgate.net/publication/297245624_Particle_Swarm_Optimization_Algorithm_and_its_Codes_in_MATLAB

Research Particle Swarm Optimization: Algorithm and its Codes in MATLAB