# Particle Swarms: The Second Decade

Authors: Riccardo Poli; Jim Kennedy; Tim Blackwell; Alex Freitas
Journal: Journal of Artificial Evolution and Applications
 (2008)

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## Body

## 1. Introduction

Particle swarm optimisation (PSO) was born
just over ten years ago. The initial ideas on particle swarms of Kennedy and
Eberhart were aimed at producing computational intelligence by exploiting
simple analogues of social interaction, rather than purely individual cognitive
abilities. The first simulations [1] were influenced by Heppner's and Grenander's work [2] and involved analogues of
bird flocks searching for corn. These soon
developed [1, 3, 4] into a powerful optimisation method—the particle
swarm optimiser.In PSO, a number of simple entities—the particles—are placed in the search space of some problem or function, and each
evaluates the objective function at its current location. Each particle then
determines its movement through the search space by combining some aspect of
the history of its own current and best (best-fitness) locations with those of
one or more members of the swarm, with some random perturbations. The next
iteration takes place after all particles have been moved. Eventually, the
swarm as a whole, like a flock of birds collectively foraging for food, moves
close to an optimum of the fitness function.The particle swarm is more than just a collection of
particles. A particle by itself has almost no power to solve any problem;
progress occurs only when the particles interact. Problem solving is a
population-wide phenomenon, emerging from the individual behaviours of the
particles through their interactions. In any case, populations are organised
according to some sort of communication structure or topology, often thought of
as a social network. Each particle communicates with some other particles and
is affected by the best point found by any member of its topological
neighbourhood. The potential kinds of topologies of social networks are hugely
varied, but in practice certain types, such as rings and fully connected
networks, have been used more frequently.


## 2. Particle Swarm Optimisation is Coming of Age

The particle swarm paradigm, that was only a few years
ago a curiosity, has now attracted the interest of researchers around the
globe. In fact, simple queries in publication databases, such as IEEE Xplore
and Google Scholar, reveal that the number of publications in particle swarm
optimisation has been exponentially growing for the last few years.The aim of this special issue is to attract papers on
particularly innovative algorithms, speculative ideas, new theoretical
approaches, and novel applications that could act as seeds for PSO research in
its second decade. Topics we solicited included the
following: novel empirical and theoretical analyses of PSO
population dynamics; innovative studies and algorithms for setting PSO
parameters; new adaptive and parameterless PSO; analyses and new proposals of
social network topologies; PSOs for combinatorial and hierarchical search
spaces; novel PSOs for dynamic problems, noisy functions, and multimodal
functions; advanced barebones/distribution-based PSOs; unconventional hybrids
of PSO with other techniques; as well as novel applications in engineering, biomedicine,
clustering, classification, entertainment, finance, image and signal
processing, graphics, computational intelligence, and robotics. Amazingly, as
we will show in Section3, we managed to attract high-quality submissions in
almost all these areas.As a first step in the direction of identifying new
ideas for the second decade, we proposed and organised a workshop entitled
“Particle Swarms: The Second Decade” at the
Genetic and Evolutionary Computation Conference (GECCO) held in London in July
2007. Seven papers were selected by a peer-review process and presented at the
workshop. The level of attendance was very good, the ideas presented were
exciting, and the discussion that followed them was very lively.Encouraged by this first success, we felt that we had
to follow this on with a second, higher-impact initiative: this special issue
of the Journal of Artificial Evolution and Applications. All of the presenters
at the GECCO workshop were invited to extend their work and submit to this
special issue, although the special issue was also open to new contributions.
The special issue was a resounding success, attracting a total of 50
high-quality submissions. After a rigorous multistage review process, just
under 20 papers were eventually accepted, and are now presented in
this special issue. (Following the usual principles
of blind review, papers coauthored by one of the guest editors were handled by
another editor, so the former did not know which reviewers were assigned to his
paper and had no influence on the editorial decision about the
paper.)


## 3. The Papers in This Special Issue

We have chosen to divide the articles in this special
issue into three main categories (although some spanned more than one):
innovative theoretical/empirical analyses and theoretically sound design
(Section3.1), new exciting types of particle
swarms (Section 3.2), and novel applications (Section 3.3). We will briefly
introduce them in the next subsections.


### 3.1. Theory, Analysis, and Principled Design of Particle Swarms

After a decade of relatively slow progress, the theory
of PSO is now making significant and rapid progress, and this trend is likely
to continue in the second decade. Indeed, four papers in this special issue
deal with either theoretical explanations or theoretically driven design of
PSOs.The success or failure of stochastic optimisation
algorithms depends on their ability to explore the search space associated with
a problem effectively. The search is controlled by what is known as thesampling
distribution of the optimiser. The article “Dynamics and stability of the
sampling distribution of particle swarm optimisers via moment analysis” by R.
Poli looks at the precise identification of the sampling distribution and its
changes over time for standard forms of PSO. The article “Examination of particle
tails” by T. Blackwell and D. Bratton focuses also on the characterisation of
the way PSOs sample the search space, but, in this case, the analysis coarse-grains over the time variations of the
distribution; the resulting distribution is shown to follow a power law.One important source of innovation in PSO is the
extension of the paradigm to the exploration of discrete search spaces. This is
difficult because certain notions, such as the notion of velocity, are not
easily extended to such spaces. So, until now, designing discrete PSOs has been
essentially a black art. In this special issue, however, we are fortunate to
have two articles—“Geometric particle swarm optimisation” by A. Moraglio
et al. and “Forma analysis of particle swarm optimisation for permutation
problems” by T. Gong and A. L. Tuson—which provide two different general
approaches to derive theoretically sound PSOs for generic discrete search spaces.


### 3.2. Novel Particle Swarms

Broadly speaking, a particle swarm has two elements:
particle dynamics and a mechanism for the sharing of information. The dynamics
tells a particle how to move given the information that it has available; the
result of this movement is subsequently communicated to other particles. These
components, which mutually interact to deliver a swarm's searching capability,
can be modified in various ways to derive new particle swarms.Novel particle dynamics are represented here by a number
of papers. S. Kok and J. A. Snyman in “A strongly interacting dynamic particle
swarm optimization method” consider how particle dynamics can be affected by
both position (as in standard PSO) and function value at that position, thereby
introducing gradient information explicitly into the update rules. In a novel
approach, J. L. Fernández-Martínez and E. García-Gonzalo consider how PSOs can
be derived from discretisations of continuous particle trajectories. Their
paper “The generalized PSO: a new door to PSO evolution” presents theoretical
stability analysis and experimental testing. A general trend in the work
represented by these two papers is a growing interest in considering a swarm as
an interacting system of  “physical” particles, that is, as physical entities
with continuous trajectories, momentum, energy dissipation, and force laws.Two more papers consider alternative dynamics. In
“Novel orthogonal momentum-type particle swarm optimization applied to
solve large parameter optimization problems,” J.-L. Liu and C.-C. Chang
introduce an alternative velocity update rules with a “delta momentum” rule.
They combine this rule with fractional factorial design for efficient
optimisation. In “A simplified recombinant PSO,” D. Bratton and T. Blackwell
consider a series of simplifications to a biologically motivated dynamics based
on genetic recombination. They demonstrate that velocity can be eliminated from
the algorithm altogether, thereby making contact with distribution-based PSOs
(“barebones” formulations).The final two papers in this section consider how
biological metaphors can induce changes to swarm algorithms at the population
level. In “What else the evolution of PSO is telling us,” L. Diosan and M.
Oltean suggest changes to the order and frequency by which particles are
updated. They use a genetic algorithm to explore various strategies. In “Particle swarm optimization for multimodal functions: a clustering
approach,” A. Passaro and A. Starita use k-means clustering to establish
subswarm “niches.” This approach involves dynamic information topologies that
are linked to local spatial behaviour, features that are surely likely to be
the subject of much second decade work.


### 3.3. Applications

Particle swarm optimisation has been enormously
successful at solving problems of practical interest. This is reflected in this
special issue by approximately half the articles reporting novel and exciting
applications for PSO. We briefly review them below. Before we start, however,
we would like to emphasise that several of the particle swarms proposed in the
articles mentioned in this section are discrete PSOs, a characteristic shared
by two theoretical approaches mentioned in Section3.1. This indicates how prolific and important the area of discrete PSOs is
becoming. We expect this area to grow significantly in the second decade.The article “Optimizing the operation sequence of a
multi-head surface mounting machine using a discrete particle swarm
optimization algorithm” by Y.-M. Chen and C.-T. Lin, for example, describes
how PSO can be used to optimise the process of picking and placing components
onto printed circuit boards. R. Armellin and M. Lavagna's article entitled
“Multidisciplinary optimization of aerocapture maneuvers” shows how PSO can
design maneuvers that ensure that a spacecraft is captured by the gravitational
attraction of a planet, with minimal expenditure of energy.In “A hybrid PSO/ACO algorithm for discovering
classification rules in data mining,” N. Holden and A. A. Freitas extend a PSO
algorithm with ideas borrowed from ant colony optimisation in order to cope
with nominal (nonnumerical) variables, and apply the proposed algorithm to a
data mining problem. In the article “An improved particle swarm optimizer for
placement constraints,” S.-T. Hsieh et al. show how PSO can solve
floor-planning problems very effectively. With their paper entitled “Inverse
parameter identification technique using PSO algorithm applied to geotechnical
modeling,” J. Meier et al. show how the PSO can provide valuable solutions in
the difficult area of inverse-problem solving.In “Particle swarm optimization for antenna designs
in engineering electromagnetics,” N. Jin and Y. Rahmat-Samii propose a PSO
tailored to antenna design in engineering. The proposed PSO can cope with both
real and binary variables, as well as multiobjective problems. In “Generating
complete bifurcation diagrams using a dynamic environment particle swarm
optimization algorithm,” J. Barrera et al. apply PSO to the analysis of
dynamical systems, which are represented as a set of equations specifying how
variables change over time. In “A discrete particle swarm optimization
algorithm for uncapacitated facility location problem,” A. R. Guner and M.
Sevkli propose a discrete PSO, as well as a hybrid version with local search,
for solving a combinatorial optimization problem. In “Particle swarm for
attribute selection in Bayesian classification: an application to protein
function prediction,” E. S. Correa et al. propose another type of discrete PSO
algorithm to the problem of selecting attributes in data mining, and apply the
algorithm to a bioinformatics problem.


## 3.1. Theory, Analysis, and Principled Design of Particle Swarms

After a decade of relatively slow progress, the theory
of PSO is now making significant and rapid progress, and this trend is likely
to continue in the second decade. Indeed, four papers in this special issue
deal with either theoretical explanations or theoretically driven design of
PSOs.The success or failure of stochastic optimisation
algorithms depends on their ability to explore the search space associated with
a problem effectively. The search is controlled by what is known as thesampling
distribution of the optimiser. The article “Dynamics and stability of the
sampling distribution of particle swarm optimisers via moment analysis” by R.
Poli looks at the precise identification of the sampling distribution and its
changes over time for standard forms of PSO. The article “Examination of particle
tails” by T. Blackwell and D. Bratton focuses also on the characterisation of
the way PSOs sample the search space, but, in this case, the analysis coarse-grains over the time variations of the
distribution; the resulting distribution is shown to follow a power law.One important source of innovation in PSO is the
extension of the paradigm to the exploration of discrete search spaces. This is
difficult because certain notions, such as the notion of velocity, are not
easily extended to such spaces. So, until now, designing discrete PSOs has been
essentially a black art. In this special issue, however, we are fortunate to
have two articles—“Geometric particle swarm optimisation” by A. Moraglio
et al. and “Forma analysis of particle swarm optimisation for permutation
problems” by T. Gong and A. L. Tuson—which provide two different general
approaches to derive theoretically sound PSOs for generic discrete search spaces.


## 3.2. Novel Particle Swarms

Broadly speaking, a particle swarm has two elements:
particle dynamics and a mechanism for the sharing of information. The dynamics
tells a particle how to move given the information that it has available; the
result of this movement is subsequently communicated to other particles. These
components, which mutually interact to deliver a swarm's searching capability,
can be modified in various ways to derive new particle swarms.Novel particle dynamics are represented here by a number
of papers. S. Kok and J. A. Snyman in “A strongly interacting dynamic particle
swarm optimization method” consider how particle dynamics can be affected by
both position (as in standard PSO) and function value at that position, thereby
introducing gradient information explicitly into the update rules. In a novel
approach, J. L. Fernández-Martínez and E. García-Gonzalo consider how PSOs can
be derived from discretisations of continuous particle trajectories. Their
paper “The generalized PSO: a new door to PSO evolution” presents theoretical
stability analysis and experimental testing. A general trend in the work
represented by these two papers is a growing interest in considering a swarm as
an interacting system of  “physical” particles, that is, as physical entities
with continuous trajectories, momentum, energy dissipation, and force laws.Two more papers consider alternative dynamics. In
“Novel orthogonal momentum-type particle swarm optimization applied to
solve large parameter optimization problems,” J.-L. Liu and C.-C. Chang
introduce an alternative velocity update rules with a “delta momentum” rule.
They combine this rule with fractional factorial design for efficient
optimisation. In “A simplified recombinant PSO,” D. Bratton and T. Blackwell
consider a series of simplifications to a biologically motivated dynamics based
on genetic recombination. They demonstrate that velocity can be eliminated from
the algorithm altogether, thereby making contact with distribution-based PSOs
(“barebones” formulations).The final two papers in this section consider how
biological metaphors can induce changes to swarm algorithms at the population
level. In “What else the evolution of PSO is telling us,” L. Diosan and M.
Oltean suggest changes to the order and frequency by which particles are
updated. They use a genetic algorithm to explore various strategies. In “Particle swarm optimization for multimodal functions: a clustering
approach,” A. Passaro and A. Starita use k-means clustering to establish
subswarm “niches.” This approach involves dynamic information topologies that
are linked to local spatial behaviour, features that are surely likely to be
the subject of much second decade work.


## 3.3. Applications

Particle swarm optimisation has been enormously
successful at solving problems of practical interest. This is reflected in this
special issue by approximately half the articles reporting novel and exciting
applications for PSO. We briefly review them below. Before we start, however,
we would like to emphasise that several of the particle swarms proposed in the
articles mentioned in this section are discrete PSOs, a characteristic shared
by two theoretical approaches mentioned in Section3.1. This indicates how prolific and important the area of discrete PSOs is
becoming. We expect this area to grow significantly in the second decade.The article “Optimizing the operation sequence of a
multi-head surface mounting machine using a discrete particle swarm
optimization algorithm” by Y.-M. Chen and C.-T. Lin, for example, describes
how PSO can be used to optimise the process of picking and placing components
onto printed circuit boards. R. Armellin and M. Lavagna's article entitled
“Multidisciplinary optimization of aerocapture maneuvers” shows how PSO can
design maneuvers that ensure that a spacecraft is captured by the gravitational
attraction of a planet, with minimal expenditure of energy.In “A hybrid PSO/ACO algorithm for discovering
classification rules in data mining,” N. Holden and A. A. Freitas extend a PSO
algorithm with ideas borrowed from ant colony optimisation in order to cope
with nominal (nonnumerical) variables, and apply the proposed algorithm to a
data mining problem. In the article “An improved particle swarm optimizer for
placement constraints,” S.-T. Hsieh et al. show how PSO can solve
floor-planning problems very effectively. With their paper entitled “Inverse
parameter identification technique using PSO algorithm applied to geotechnical
modeling,” J. Meier et al. show how the PSO can provide valuable solutions in
the difficult area of inverse-problem solving.In “Particle swarm optimization for antenna designs
in engineering electromagnetics,” N. Jin and Y. Rahmat-Samii propose a PSO
tailored to antenna design in engineering. The proposed PSO can cope with both
real and binary variables, as well as multiobjective problems. In “Generating
complete bifurcation diagrams using a dynamic environment particle swarm
optimization algorithm,” J. Barrera et al. apply PSO to the analysis of
dynamical systems, which are represented as a set of equations specifying how
variables change over time. In “A discrete particle swarm optimization
algorithm for uncapacitated facility location problem,” A. R. Guner and M.
Sevkli propose a discrete PSO, as well as a hybrid version with local search,
for solving a combinatorial optimization problem. In “Particle swarm for
attribute selection in Bayesian classification: an application to protein
function prediction,” E. S. Correa et al. propose another type of discrete PSO
algorithm to the problem of selecting attributes in data mining, and apply the
algorithm to a bioinformatics problem.



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*Source: 108972-2008-05-25.xml*