(Below are some drafts and source codes. See also
(useful links about people, papers etc.)
Last item added or modified (2014-06-13): Simple Generators for List-based Optimisers
|DEMO/Fun||A simplified adaptive version (C source).No parameters to "guess", and you can add your own objective function.NEW: you can now solve Graph Coloring Problems. Also, you can generate a data file for post-mortem animation. If you want, you can try some options like local queens or Guided Random Generation.||2001-11-12||Some
Note: see Tribes for a more recent (and quite different) PSO version
|D E M O/Animation||A small animation showing how a swarm generates subswarms around suboptima for Alpine function.||2000/10/24||Animated GIF (zipped)|
|Some math about Particle Swarm Optimization (PSO)||Analytical
Explicit and Implicit Representations. Particle in Complexland.
Convergence and Spaceof States, constriction.
(quite big. you should better download the PDF file)
|Algebraic View||Basic case. Eigenvalues. Cycles.||1998/04/30||PDF file(zipped)|
|The Alpine Function||Many local optima, just one maximum.||1998/11/24||PDFfile (zipped)|
|The Most Stupid Algorithm (MSA)||Random search. Cost of the algorithm.||1998/11/24||PDF file(zipped)|
|Performance Maps||Deterministic PSO. Convergence time vs two parameters.||1998/11/24||PDFfile (zipped)|
|Mechanical Analogy||Two parameters. Virtual springs.||1998/11/24|| PDFfile
|The Simplest PSO||Deterministic, one equation,one parameter. No-hope/Re-hope method. Alpine and Banana functions.||1998/12/11||PDF file(zipped)|
|The Swarm & The Queen||A great improvement of the "Simplest PSO", particularly thanks to a gravity center (the "queen") and a better adaptive No-hope/Re-hope method. The paper has been presented atCEC99.||1999/09/22|| Play
with an worksheet(2D
French Excel version, 440Ko).
Slides (1999/07/26): Powerpoint file (Macintosh, may work on some PC)(zipped)
Online (Web pages)
Draft PDF version of the paper (slightly updated in 2001) (zipped)
|A little fuzzy toolbox||Fuzzy set computation tools to prepare a fuzzy PSO. Arithmetic functions and some classical ones (exp, log, sin).||1999/03/28||ANSI C sourcecode|
|The Particle Swarm: Explosion, Stability, and Convergencein a Multi-Dimensional Complex Space||by Maurice Clerc
Big paper about Algebraic and Analytical
views, with examples.
Published by IEEE in 2002, so I can give you here just the
IEEE Transactions on Evolutionary Computation award
Jim and me ;-) )
|Slides (1999/07/26): Powerpoint file (Macintosh, may work on some PC) online (Web pages).Presentations_5D/index.htm|
|DiscretePSO: Traveling Salesman Problem (v. 4.2).||PSO can work on finite state spaces and with non continuous functions. Here is an example: looking for shortest cycles in a valuated graph. The last version is more clean, and strictly written in ANSI C.||2000/02/29
C sources (4.4, zipped)
ANSI C sources (zipped)
|DiscretePSO: Fuzzy Combinatorial Black Box||When running a combinatorial black box with PSO,the problem is that, depending on parameters, results can be quitegood ... or worse than random or exhaustive search. If you have noway to guess what could be the best parameters, use fuzzy representations:you will never have very bad results (and almost never very good ones).||2000/04/28||PDF file(zipped)|
|Optimisation par essaim particulaire||Présentation faite à Paris lors de la JET5||2000/05/05||Fichiers PowerPoint zippés OEP1erOPE2|
|When Ant Colony Optimization does not need Swarm Intelligence||A very short paper formally proving that ACO, as defined by Marco Dorigo in 1999, does not really use swarm intelligence. The underlying idea is to analyze ACO in order to see if some principles could be useful to improve PSO.||2000/08/08||PDF file (zipped)|
|OEP et coloriage de graphe pour l'affectation defréquences (PSO and Graph Coloring for Frequency Assignement)||(in French, expurgated version). A hybrid system using an adaptive PSO and some more classical algorithmes gives interesting results||2001-07||PDF file (zipped)|
|PSO and Information||What kind of information PSO uses to find a solution and how it uses it? First part (draft) of this study||2001-11-16||MSWord file and PDF file(zipped)|
|A few words about constriction||A conjecture and a rule of thumb to find "good" parameters||2001-12-11||MSWord file and PDF file(zipped)|
|The old bias and its solution||All PSO works using randomness also use biased formulas. It does not prevent to converge, but in increases the variance of a set of runs. This short paper explain the bias and how to avoid it||2001-12-12
file and PDF file(zipped)
Warning. This version is also biased! See below Uniform hyperspherical distribution
|F(?)AQ||Not so F, but you quite often ask me some questions. Here are some answers. Don't hesitate to write me, however.||2006-03-11|
Locally, Act Locally: A Framework for Adaptive Particle Swarm
||In Particle Swarm Optimization, each particle moves in the search space and updates its velocity according to best previous positions already found by its neighbors (and itself), trying to find an even better position. This approach has been proved to be powerful but needs parameters predefined by the user, like swarm size, neighborhood size, and some coefficients, and tuning these parameters for a given problem may be, in fact, quite difficult. This paper presents a framework for designing adaptive particle swarm optimizers without any "supervisor", in order to obtain autonomous methods in which the user has almost nothing to do but describe the problem. To illustrate the adaptation process, a possible implementation for a simple PSO version is given, so that we can examine how different, and globally better, is the behavior of the swarm on some classical test functions.||2002-07-01
Zipped .doc file.
|Tribes, a parameter free PSO||Particle Swarm Optimizers usually need some predefined parameters, i.e. numerical coefficients, swarm size, neighbourhood size and topology. It is not the case with the present version thanks to two techniques: hyperspheres instead of hyperparallelepipeds for proximity areas, and adaptation of the swarm size as well as the relationships between the particles.||2004-05-05
Warning: older than the C source code
|Tribes and Strategies||Here is the last
"public" source code. Different
strategies depending on the "past" of the particle, non uniform
distributions for proximity areas (Gaussian, for example),
fuzzification, noise, recursivity, etc.),
"no clamping and no evaluation" option, etc.
C version contains a QAP (Quadratic Assignment Problem) option and a Traveling Salesman Problem (TSP) option,. Not that good, but may be useful for small graphs (say 30 nodes). The multiobjective option can also be used to cope with indicative (soft) constraints.
|Fixed some bugs in the simplified
Results are now far
better (in particular for Schwefel+noise, and Elliptic)
Fixed a bug in the simplified Java version (about info-network)
Slightly simplified Java version
Java version. It includes the "sunnyspell" method. I have added the 24 constrained problems of CEC 2006. Also you can now safely launch several problems on the same time.
Zipped C sources of last public version
Added 14 of the 25 functions of the CEC05 benchmark set. If you want to use them, you must also download this BM repertory
Added a pseudo-gradient method to choose the best
Valid only if the search space is a metric one, so it is an
This version now contains a correct hyperspherical distribution. The independent Gaussian distributions are quite good for small problems partly combinatorial.
A new distribution has been added (positive ellipsoïdal sectors).
You can now use any kind of discrete
variable, by giving the
list of acceptable values.
"classical" examples have been added (gear train,
pressure vessel, coil spring). At this date, result are
better than the best published ones, without any parameter to
|Tribes and MO||A small "paper" about Multiobjective problems with Tribes, compared to MOPSO. Three examples are given, but the above source code contains far more (see myfunction.c).||2003-05-02||Obsolete, see TRIBES-D
|Distorted Gaussian Distribution||In order to escape "the old bias", Tribes can use different kind of distributions, for example spherical ones or Gaussian ones, but they are all symmetrical. This one is not, "distorted" along an axis, typically p_i <->p_g (best previous position <-> best previous position in informer group). For it can easily be adapted to any PSO version, I put here just a "generic" C code, using two points A and B. Of course, in real use, you take only one point of the distribution.||2003-06-25||Zipped C source|
|Uniform Hyperspherical Distribution||Last
week, Rui Mendes pointed
out my "unbiased distribution" was in fact biased. So I have
new version that should be perfect (and faster, anyway). It is now
included in Tribes.
||2003-07-10||C source (zipped)|
|Semi-continuous challenge||In order to improve Tribes, I need help to solve these six problems. What are the best PSO versions and the best parameters? Is it possible to define some rules to find these good parameters? For amatheurs, I have added a few words about "theoretical difficulty" and "handling constraints by homeomorphism".||2004-02-20||.pdf version|
it, here it is. The
parametric PSO I used for the Semi-continuous challenge. Note that
comments are in French ...
OEP and the no_parameters_at_all Tribes, this simple version may
enough for some people
peer reviewed electronic paper (in French)
M. Clerc et P. Siarry, Une nouvelle métaheuristique pour l'optimisation : la
PSO: toolbox, derivations, and mathematical insights
||Still a draft,
and quite long (40 p.) but you may be interested
|Open Archive HAL
C source (zipped)
Un livre en français, chez Hermès-Lavoisier. 260 pages, 70 €
par essaims particulaires. Versions paramétriques et
Contient pas mal de choses jamais publiées, ni ici, ni dans des revues, par exemple sur les distributions de possibilités ou les critères de convergence. Quelques annexes techniques pour les "amatheurs".
remplacer "K est un fait un maximum" par "K est en fait une valeur moyenne"
126.96.36.199 Remplacer 'Informatrices N" par "Exploratrices N"
Remplacer la dernière formule par
||or "What happens when nothing happens". Thanks
mathematical analysis, better confidence coefficients for
PSO are defined
|version edited by
Riccardo Poli (better English but not complete)
PDF here or on the XPS technical reports page (ref. CSM-460)
Complete PDF file on Open Archive HAL (see in particular Figure 4)
First version (not online anymore)
||Just a way to add a new particle not anymore
purely at random
Particle Swarm Optimization, ISTE
|This book contains some things never published in English even here, for exemple about non uniform distributions of possibilities, convergence criteria, rumor spreading, etc. This a translation of the 2005 book in French, with a few updates.||2006-02|
|Confinements and Biases||Because of the confinement, PSO performance is depending on where the solution point is (near the center of the search space, near the bound, etc.). Nine confinement methods (including no confinement at all) are studied. An hybrid more robust one is suggested.||2006-03-12||Open
When a particle leaves the search space the "no clamping and no evaluation" method is the simplest one. However it may happen that all particles are then moving outside the search space, and the algorithm never stops. Also, even if they induce a bias, some confinement methods may be more effective.
|Some ideas about PSO||Some of them are so crazy that they might work. Some others seems reasonable but may not work.||2006-11-06||PDF file|
|Comparing two algorithms||How to compare two stochastic algorithms from an user point of view||2006-07-04||Link to the corresponding item on the Math page|
|Non parametric optimisation for unimodal functions: DIchotomy||In order to improve Tribes as long as it seems the fitnesse function may be unimodal, we need a specific strategy. Here is one (by dichotomy).||2006-08-14
|New version, that includes a non unimodality test: SciLab/MatLab code|
||Contains a lot of options, in order to "simulate" most of interesting PSO variations.||2007-03-01||C source|
|Back to Random topology||A small paper re-explaining the method used in some of my "basic" PSOs, why it is equivalent to some "new" ones, and suggesting how it could be improved.||2007-02-26||PDF file|
|When Nearer is Better||Most of iterative optimisation algorithms, if not all, do assume that "nearer is better", more or less. A mathematical definition, and some fascinating derivations.||2007-03-22||Open archive HAL|
simplified version for real heterogeneous problems. It easily
best known solution for the classical "Pressure vessel"
For multiobjective problems, it is also far better than the
|Just for fun, added a Magic square problem. C code and some results (ZIP file)|
|Simple Binary PSO||Coming partly from the binary toolbox, a C program easy to use and nevertheless quite effective||2010-09-08
|Bimetric Binary PSO||Coming from the previous one. Even simpler, and slightly better.||2008-11-04||C source (zipped)|
|Balanced PSO||Variable swarm size
More options (orthogonal walk, bi-strategy, etc.)
More options (variable ring topology, orthogonal learning, etc.)
Contrarily to often claimed, Standard PSO does not ensure a good balance between exploration and exploitation. This small paper explains why, and suggests then an improved variant.
C source (zipped)
C source (zipped)
C source (zipped)
C source (zipped)
C source (zipped) Version for the Handbook of Swarm Intelligence
PDF paper (2008-10-3, obsolete, there were a few bugs)
||PSO can be significantly improved, just by using a good initialisation scheme for the positions and the velocities||2008-12-24
See Balanced PSO
|A method to improve standard PSO||Sometimes you know that your problem belongs to a given class. For example : quite low dimension (say smaller than 30) and weakly multimodal. In such a case, it is possible to design a specific PSO more efficient than the standard one. Here is a method.||2009-03-13||PDF paper|
|Universal Random Number Generator (in Maths Results, but useful for some PSO variants)||2009-12-22
carefully chosen problems, and some results with Standard
PSO 2007 and Variable PSO (see below).
Very useful to quickly estimate whether your own brand new
really promising or not.
||By playing with Balanced PSO, I
have found this simple and effective variant: like SPSO 2007, but
variable ring topology and variable swarm size. You may try
various rules to generate/delete particles
C source (zipped)
C source (zipped)
Cream Cone PSO
||Towards Standard PSO 201x? Almost
as simple as SPSO 2007, but not biased
||SPSO 2006, 2007, 2011, as
available on the Particle Swarm Central. Unformal and formal
descriptions, with a few comments
|Open archive HAL
||Open Office presentation (ICSI 2011
seminar in Cergy)
file+TrueType font (zipped)
build a PSO
||Open Office presentation (ICSI 2011 seminar in Cergy)||2011-07-26
file+TrueType font (zipped)
||L-DE is a "geometrical"
Differential Evolution variant, whose behaviour is not depending
on the coordinate system.
Computing doesn't need to hard
||SocPros 2011 presentation in
Roorkee. Include the presentation file (you need LibreOffice or
OpenOffice to open it), and the text of the talk.
||When you have to often solve
some variants of the same kind of problem, the random number
can be replaced by a short list of predefined numbers with far
results. Here, a short paper explains how to do, along with the C
Note that it includes a classical RNG, for tests and comparisons.
for the same price, i.e. nothing, you have also a pretty simple
bad classical PSO.
source + lists (zipped), Version 2
C source +lists (zipped)
Open archive HAL
Specific SPSO 2011 as LBO (C source + lists)
Generators for List-based Optimisers
Talk (presented at ICSIBO 2014)
LibreOffice Impress file (zipped)
||Depending on the kind of
"randomness" you use, performances can be very different.
||Open archive HAL
Mechanisms in PSO
||Five cooperations mechanisms,
viz. Vicinity, Reciprocity, Kin, Reputation and Anybody, are
The appendix gives some details about fair comparison of success
and the concepts of valued
topology and chains of
information, which may be worth further investigation.
C source (zipped)