Particle swarm optimisation (PSO) has been enormously successful. Within little more than a decade hundreds of papers have reported successful applications of PSO. In fact, there are so many of them, that it is difficult for PSO practitioners and researchers to have a clear up-to-date vision of what has been done in the area of PSO applications. This brief paper attempts to fill this gap, by categorising a large number of publications dealing with PSO applications stored in the IEEE Xplore database at the time of writing.

1. Introduction

The class of complex systems sometimes referred to as swarm systems is a rich source of novel computational methods that can solve difficult problems efficiently and reliably. When swarms solve problems in nature, their abilities are usually attributed to swarm intelligence; perhaps the best-known examples are colonies of social insects such as termites, bees, and ants. In recent years, it has proved possible to identify, abstract, and exploit the computational principles underlying some forms of swarm intelligence, and to deploy them for scientific and industrial purposes. One of the best-developed techniques of this type is particle swarm optimisation (PSO) [1].

In PSOs, which are inspired by flocks of birds and shoals of fish, a number of simple entities, the particles, are placed in the parameter space of some problem or function, and each evaluates the fitness at its current location. Each particle then determines its movement through the parameter space by combining some aspect of the history of its own fitness values with those of one or more members of the swarm, and then moving through the parameter space with a velocity determined by the locations and processed fitness values of those other members, along with some random perturbations. The members of the swarm that a particle can interact with are called its social neighbourhood. Together the social neighbourhoods of all particles form a PSOs social network.

More precisely, in the canonical version of PSO, each particle is moved by two elastic forces, one attracting it with random magnitude to the fittest location so far encountered by the particle, and one attracting it with random magnitude to the best location encountered by any of the particle′s social neighbours in the swarm. If the problem is N dimensional, each particle′s position and velocity can be represented as a vector with N components (one for each dimension). Starting with the velocity vector, ν = (ν₁, … ,ν_N), each component, ν_i, is given by

()

where

is the ith component of the best point visited by the neighbours of the particle, x_i(t) is the ith component of the particle′s current location,

is the ith component of its personal best, R₁ and R₂ are two independent random variables uniformly distributed in [0, 1], ω is a constant known as the inertia weight [2], and ψ₁ and ψ₂ are two constants, known as the acceleration coefficients, which control the relative proportion of cognition and social interaction in the swarm. The same formula is used independently for each dimension of the problem, and synchronously for all particles. The position of a particle is updated every time step using the equation

()

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, is likely to move close to the best location.

The following alternative velocity-update equation was developed in [3] and is also widely used:

()

where κ is a constant called the constriction coefficient. If ψ₁, ψ₂, and κ (or ω) are correctly chosen, the PSO is guaranteed to be stable without the need for special constraints (e.g., bounding of velocities and positions).

The topology of the social network used by a PSO is at least as important in determining its behaviour and performance as are the details of the velocity update equation. Many variants of the canonical PSO and many topologies have been developed and tested in the last decade. We cannot review them here. The interested reader, however, will be able to find a comprehensive review of PSO techniques in [4].

PSO can be and has been used across a wide range of applications. In general, we can say that areas where PSO has shown particular promise include multimodal problems and problems for which there is no specialised method available or all specialised methods give unsatisfactory results. However, it is hard to be much more specific that PSO applications are so numerous and diverse that a whole book would be necessary just to review the most paradigmatic ones, assuming someone could identify them among the many hundreds of applications reported in the literature, a really enormous task.

Here we have a much more modest objective: to identify the main classes of applications where PSO has been successfully deployed. We have based our categorisation on an analysis of titles and abstracts of the over 1100 publications on particle swarm optimisation stored, at the time of writing, in the IEEE Xplore database. Of these publications, around 350 are proposals for improvements and specialisations of PSO. Around 700 papers (55 of which are journal papers) can be classified as applications of PSO, although many of them involve also the customisation or extension of the method to best suit the specific application of interest. (The remaining entries in the database are conference proceedings books and other miscellaneous entries.)

Although the analysis has been largely manual, because of the large size of this database, to speed up the work we have made use of several small computer programs which helped us in the identification of the main categories of applications and gave us a first rough classification of papers. Categories and class assignments were then checked and adjusted manually one-by-one. We describe the process in more detail in Section 2.

As a result of this effort we divide PSO applications into 26 different categories. Categories and related applications are listed in alphabetical order in the subsections of Section 3. For each class of applications we indicate what fraction of all the application papers in the IEEE Xplore is devoted to that class. However, one should bear in mind that many (if not most) papers span more than one category. For examples, many classifiers are hybrids of PSO and neural networks, many applications involve some form of design, and so on.

We provide some conclusions in Section 4.

2. Category Selection and Classification

Dividing PSO applications into areas is difficult. So, as we mentioned in the previous section, we partially mechanised the process. This was done through a number of programs in the Octave/Matlab language, Xemacs macros, and Unix utilities.

We started our analysis by searching the IEEE Xplore database for any papers matching the search phrase “particle swarm optimization.” This produced around 1,100 hits. We did not try to directly identify application papers. Instead, we mechanically extracted all terms used in titles and abstracts. After manually excluding determiners, adjectives, and so on, this produced well over 4,000 unique terms. These were then manually checked for relevance from the point of view of applications. 928 key terms remained after this filtering process.

We then used the key terms to define a similarity relationship between papers and used papers to define a similarity relationship between key terms, as follows. Each paper was assigned a vector with 928 components (as many as our key terms). Each component represented how many times the corresponding key term appeared in title and abstract of the paper. Given any two papers, we took the scalar product between the corresponding vectors as the similarity between the two papers. Similarly, each key term was assigned a vector with 1100 components (as many as the PSO papers in IEEE Xplore). Each component represented how many times the key term appeared in title and abstract of the corresponding paper. We then defined the similarity between key terms as the scalar product between the corresponding vectors.

These two similarities relationships induce corresponding graph structures on the paper and key term “spaces,” where each paper/term corresponds to a node and nodes are connected by edges wherever similarity between corresponding papers/terms is above some prefixed threshold (e.g., zero). The edges are weighted by similarity. We can then make use of graph drawing packages to obtain pictorial representations of PSO application papers, PSO application areas, and their relationships.

For this purpose we used the open-source graph drawing program neato (http://www.graphviz.org). In this program, the weights of the edges in a graph are interpreted as attractive forces between nodes. Starting from a random placement, the program iteratively adjusts the position of the nodes in an attempt to minimise the energy in the system. Attractive forces are balanced by a basic repulsive force between nodes to prevent the graph from collapsing to a single point. Figures 1 and 2 show two examples of the types of graphs one obtains.

Details are in the caption following the image — **Figure 1**
Open in figure viewer PowerPoint

Example of graph representation of the key terms relevant to PSO applications and their relationships. The rest-length for repulsive forces between nodes was set to 9. Only links (similarities) with strength greater than 5 were passed to neato.

By zooming on areas where a high density of links are present, one can obtain semiquantitative evidence of which are the important application areas in PSO. See, for example, Figure 3 where we show a zoomed version of Figure 1. One can clearly see there that some terms, such as design, control, power, and antenna, act as “hubs” in PSO applications.

After performing this information gathering exercise, we proceeded to do a more formal analysis. The key terms were scored on the basis of how many papers in the database used such terms in title and abstract. This further helped identify important application categories. Indeed, the most frequent terms were “network,” “control,” “model,” “design,” “power,” “neural,” “plan,” “fuzzy,” “class,” “cluster,” “antenna,” “image,” “planning,” and “scheduling,” but many others were identified as important. Based on this analysis, we created provisional categories (the headings of the subsections in Section 3).

All PSO papers in the IEEE Xplore database were then mechanically provisionally assigned to one of the most frequent keywords. Then we manually analysed each publication and either confirmed the mechanical classification, moved the paper to a different category, deleted the paper if it was not an application paper, or, occasionally, created a new category for that paper.

The result of this process is reported in the next section.

3. PSO Applications

In our search for PSO application papers, we eventually identified around 650 which deserved citation. However, it is very difficult for any journal to publish a paper including so many references. To circumvent the problem, in this paper we only cite journal papers, but provide an online technical report [5] (available from http://www.essex.ac.uk/dces/research/publications/technicalreports/2007/tr-csm469.pdf) with all citations and references. The BibTeX bibliography used for these papers is available at http://www.essex.ac.uk/staff/rpoli/ieeepso.bib.

3.1. Antennas

The area of antenna design is extremely popular with approximately 5.8% of all application papers in the IEEE Xplore database covering this area. Applications include (see [6]) the optimal control [7] and design [8, 9] of phased arrays, broadband antenna design [10, 11] and modelling, design of Yagi-Uda arrays [12], array failure correction, optimisation of profiled corrugated horn antennas, optimisation of a reflectarray antenna, far-field radiation pattern reconstruction [13], antenna modelling, design of planar antennas, conformal antenna array design [14], design of patch antennas, antenna miniaturisation, design of multiband antennas [15], design of aperiodic antenna arrays, near-field antenna measurements [16], synthesis of antenna arrays, reflector antennas, adaptive array antennas, design of implantable antennas.

3.2. Biomedical

Biological, medical, and pharmaceutical applications are also very popular with approximately 4.3% of all application papers in the IEEE Xplore database covering these areas. Applications include human tremor analysis for the diagnosis of Parkinson′s disease, inference of gene regulatory networks, human movement biomechanics optimisation, phylogenetic tree reconstruction, cancer classification [17], and survival prediction, DNA motif detection, gene clustering, identification of transcription factor binding sites in DNA, biomarker selection, protein structure prediction and docking, drug design, radiotherapy planning, analysis of brain magnetoencephalography data, RNA secondary structure determination, electroencephalogram analysis, biometrics [18].

3.3. Communication Networks

The design and optimisation of communication networks is the subject of around 30 papers (4.4%) in the applications database. Applications include bluetooth networks, autotuning for universal mobile telecommunication system networks, optimal equipment placement in mobile communication, routing, radar networks, wavelength-division-multiplexed network, peer-to-peer networks, TCP network control, bandwidth and channel allocation, WDM telecommunication networks, wireless networks, grouped-and-delayed broadcasting, bandwidth reservation.

3.4. Clustering and Classification

Clustering, classification, and data mining are the topics of approximately 29 papers (4.3%) in the bibliography. Applications include clustering, clustering in large spatial databases, dynamic clustering, dimensionality reduction, genetic-programming-based classification, fuzzy clustering, cascading classifiers, classification threshold optimisation, classification of hierarchical biological data, electrical wafer sort classification, document and information clustering, data mining, feature selection.

3.5. Combinatorial Optimisation

Around 24 papers (3.5%) in the database deal with combinatorial optimisation problems. These include applications on floorplanning, travelling-sales man problems, packing and knapsack, minimum spanning trees, satisfiability, path optimisation, knights cover problem, n-queens problem, layout optimisation, vehicle routing, urban planning, FPGA placement and routing.

3.6. Control

Control applications have one of the largest shares (7.0%) of application papers in the IEEE Xplore database. Application areas include automatic generation control tuning, design of controllers, traffic flow control, adaptive inverse control, predictive control, PI and PID controllers [19], strip flatness control, ultrasonic motor control, power plants and systems control [20, 21], control of chaotic systems, process control, adaptive PMD compensation in WDM networks, fractional order controllers, combustion control, inertia system control, automatic landing control.

3.7. Design

Around 4.4% of the bibliography is devoted to design applications. These include conceptual design, induction heating cooker design, VLSI design, RF circuit synthesis [22], worst case electronic design, filter design [23], antenna design [24], CMOS wideband amplifier design, motor design, logic circuits design, power systems [25], transmission lines, mechanical design, electromagnetics, case library search.

3.8. Distribution Networks

Design and restructuring of electricity networks and load dispatching are among the problems most frequently attacked with PSO, occupying around 7.1% of the applications bibliography. Applications include transmission network planning, network reconfiguration and expansion [26], distributed generation [27], microgrids, economic dispatch problem [28–32], voltage regulation, congestion management.

3.9. Electronics and Electromagnetics

A substantial proportion of the papers in the IEEE database describe applications in the areas of electronics and electromagnetics. Here we list further applications representing approximately 5.8% of the database. These include on-chip inductors, fuel cells, FPGA-based temperature control [33], AC transmission system control, electromagnetic shape design [34], microwave filters, generic electromagnetics design and optimisation applications [35–38], linear array antenna synthesis, RF IC design and optimisation, semiconductor optimisation, high-speed CMOS [39], conductors [40], frequency selective surface and absorber design [41], CMOS RF wideband amplifier design, voltage flicker measurement, circuit synthesis, shielding, configuration of FPGAs and parallel processor arrays, digital circuit design.

3.10. Engines and Motors

Around 10 papers (1.4%) in the applications bibliography deal with the design or optimisation of engines and electrical motors. Topics include engine data classification, locomotive torque control, motor control in electric and hybrid vehicles, induction motor speed control, direct motor torque control, fault and parameter estimation in induction motors, optimisation of internal combustion engines, optimisation of nuclear electric propulsion systems.

3.11. Entertainment

Music generation and games have also a small niche in PSO applications, occupying approximately (1.3%) in the applications publication database. In the area of games, applications include analysis of leaf nodes in game trees [42], learning to play board games, iterated prisoner dilemma, learning to play solo Pong. In the area of music, swarms have been used for interactive music improvisation.

3.12. Faults

The detection or diagnosis of faults and the recovery from them occupy approximately (2.3%) of the application papers in the bibliography. Topics include fault diagnosis of steam-turbine generators, circuits that automatically recover from component failure, gearbox fault diagnosis, automatic defect classification in semiconductor wafers, service restoration in power distribution, fault-tolerant power systems, missing sensors restoration, fault diagnosis in digital circuits, test pattern generation for circuits, software fault detection, defensive islanding of power system, power transformers fault diagnosis, optimisation of repairable systems, diagnosis of faults in motors.

3.13. Financial

Around 1.0% of the papers in the bibliography have to do with finance and economics. Topics include financial risk early warning, investment decision-making, option pricing, investment portfolio selection, electricity market.

3.14. Fuzzy and Neurofuzzy

Around 26 papers (3.8% of the bibliography) attack problems in the area of fuzzy and neurofuzzy systems and control. These include design of neurofuzzy networks, fuzzy rule extraction, fuzzy control, membership functions optimisation, fuzzy modelling, fuzzy classification, design of hierarchical fuzzy systems, fuzzy queue management.

3.15. Graphics and Visualisation

Applications in the areas of computer graphics and visualisation also have a share of the applications bibliography (1.7%). Specific topics include graphic presentation of networks, dimensionality reduction, collision detection in graphic models, texture synthesis, interactive particle swarms, 3D graphics.

3.16. Image and Video

A large proportion of the applications bibliography (7.6%) of PSO applications is devoted to image and video analysis applications. Image analysis applications include iris recognition, fruit quality grading, face detection and recognition, image segmentation, synthetic aperture radar imaging, locating treatment planning landmarks in orthodontic x-ray images, image classification, inversion of ocean colour reflectance measurements [43], image fusion, traffic stop-sign detection, defect detection, image retrieval, human detection in infrared imagery, image registration [44], pixel classification, detection of objects, pedestrian detection and tracking, texture synthesis, microwave imaging [45, 46], scene matching, photo time-stamp recognition, contrast enhancement, 3D recovery with structured beam matrix, autocropping for digital photographs, character recognition, shape matching, image noise cancellation. Video applications include MPEG optimisation, motion estimation, object tracking, body posture tracking, traffic incident detection.

3.17. Metallurgy

About 9 papers (1.3% of the bibliography) deal with applications in metallurgy. These include optimisation of steelmaking process and modelling in sintering process.

3.18. Modelling

Many papers in the bibliography involve some form of modelling. Several that have not been described under other headings are listed here. These form about 2.8% of the bibliography. Topics include inversion of underwater acoustic models, modelling MIDI music, customer satisfaction models, thermal process system identification, friction models, ultrawideband channel modelling, chaotic time series modelling, identifying ARMAX models [47], nonlinear model identification, nonlinear system identification, model selection, power plants and systems, model order reduction.

3.19. Neural Networks

Neural networks are used in combination with PSO in many applications. Some have already been listed under a different heading elsewhere. Here we list further PSO applications to neural networks (3.8% of the bibliography). Topics include inversion of neural networks, neural network control for nonlinear processes [48], design of radial basis function networks [49], product unit networks, neural gas networks, feedforward neural network training, design of recurrent neural networks [50], cellular neural networks, wavelet neural networks, neuron controllers.

3.20. Prediction and Forecasting

About 2.9% of the papers on applications in the bibliography have to do with prediction and forecasting. Topics include water quality prediction and classification, prediction of chaotic systems, ecological models, meteorological predictions, electric load forecasting, battery pack state of charge estimation, time series prediction, predictions of elephant migrations, prediction of the flow stress in steel, prediction of surface roughness in end milling, streamflow forecast, urban traffic flow forecasting.

3.21. Power Systems and Plants

A large proportion (5.8%) of the application papers in the bibliography deals with power generation and power systems. Specific applications include (see also [51]) automatic generation control, power transformer protection, load forecasting, STATCOM power system, fault-tolerant control of compensators, optimal power dispatch, power system performance optimisation [52], secondary voltage control, power control and optimisation, design of power system stabilisers, control of photovoltaic systems, large-scale power plant control, operational planning for cogeneration systems, analysis of power quality signals, generation planning and restructuring, hybrid power generation systems [53], optimal strategies for electricity production [54], power loss minimisation, production costing, and operations planning.

3.22. Robotics

Numerous papers describing PSO applications in robotics are present in the literature. These cover about 3.4% of the applications bibliography. Topics include control of robotic manipulators and arms, motion planning and control, robot running, collective robotic search, unsupervised robotic learning, path planning, obstacle avoidance, swarm robotics, unmanned vehicle navigation, soccer playing, robot vision, transport robots, odour source localisation, environment mapping, voice control of robots [55].

3.23. Scheduling

About 5.6% of the bibliography deals with scheduling applications. These include generator and transmission maintenance scheduling, flow shop scheduling [56], hydrothermal scheduling, optimal operational planning of energy plants, blending scheduling, power generation scheduling, tasks scheduling in distributed computer system, scheduling in battery energy storage systems [57], jobshop scheduling, radar time management, project scheduling, train scheduling, timetable scheduling, production scheduling, assembly scheduling, holonic manufacturing scheduling.

3.24. Security and Military

About 1.3% of the bibliography is devoted to security and military applications. These include network security, security-constrained power generation, intrusion detection, cryptography and cryptanalysis, security border identification in power systems [58], weapon-target assignment, missile effectiveness optimisation.

3.25. Sensor Networks

13 papers (1.9%) are devoted to sensors and, particularly, sensor networks. Applications include wireless sensor network sink node optimisation, ad hoc sensor networks node clustering, wireless sensor network design [59], estimation of target position in wireless sensor networks, cluster formation in wireless sensor networks, multicast routing in wireless sensor networks, odour source localisation, wireless video sensor networks optimisation, swarm-based mobile sensor networks, sensor scheduling for target tracking, distributed sensor placement, and topology planning.

3.26. Signal Processing

Approximately 3.8% of the bibliography is devoted to applications of PSO in signal processing. These include pattern recognition of flatness signal, design of IIR filters, particle filter optimisation, nonlinear adaptive filters, Costas arrays, wavelets, blind detection, blind source separation, analogue filter tuning, localisation of acoustic sources, distributed odour source localisation, speech coding [60], 2D IIR filters.

4. Conclusions

This paper presents a bird′s eye view of PSO applications. This has been obtained by identifying and analysing around 700 PSO application papers stored in IEEE Xplore database at the time of writing.

The picture we obtain is that of a technique with an immense scope of applications, ranging from biological and medical to electrical, electronic, and electromagnetic, to practical computational intelligence applications, to combinatorial problem solving, to image analysis, signal processing and graphics, to robotics. What is particularly amazing is the rate of growth of PSO publications (see Figure 4), most of which are in fact about applications of the technique. The number of publications reporting PSO applications has grown nearly exponential for the last few years, and seems to show no sign of slowing down at the present moment.

What makes PSO so attractive to practitioners? Clearly, the algorithm shines for its simplicity and for the ease with which it can be adapted to different application domains and hybridised with other techniques. This is perhaps what most people want from a practical problem solver: being able to learn the basics of a new technique quickly, and being able to use it as a building block to be mixed and matched with whatever tools they are already familiar with. Also, the PSO routinely delivers good optimisation results. Most people will not care as to whether their new tool is guaranteed to give the absolute best performance on a problem. What they want is something simple and reliable. Finally, probably the PSO has, at the moment, in the mind of many people the sort of magical black box flavour that attracted so many researchers to other areas of artificial/computational intelligence (such as neural network, genetic algorithms, or fuzzy systems) before.

What application areas should we expect PSO to do well in? It is very hard to make specific suggestions. The PSO seems to have worked very well in almost all areas where it has been applied, with perhaps the exception of combinatorial optimisation problems where further improvements to PSO techniques may still be needed before the PSO can compete on par with other techniques. Naturally, the best predictor of future performance is the past. All of the 26 areas identified in this paper appear to be still very fertile.

The reader interested in advanced PSO techniques and open questions in PSO algorithms and theory should refer to [4] for an extensive treatment.

References

1 Kennedy J. and Eberhart R. C., Swarm Intelligence, 2001, Morgan Kaufmann Publishers, San Francisco, Calif, USA.
Google Scholar
2 Shi Y. and Eberhart R. C., A modified particle swarm optimizer, Proceedings of the IEEE Congress on Evolutionary Computation (CEC ′99), 1999, Piscataway, NJ, USA, 69–73.
Google Scholar
3 Clerc M. and Kennedy J., The particle swarm-explosion, stability, and convergence in a multidimensional complex space, IEEE Transactions on Evolutionary Computation. (2002) 6, no. 1, 58–73, https://doi.org/10.1109/4235.985692.
10.1109/4235.985692
Web of Science® Google Scholar
4 Poli R., Kennedy J., and Blackwell T., Particle swarm optimisation: an overview, Swarm Intelligence Journal. (2007) 1, no. 1.
Google Scholar
5 Poli R., An analysis of publications on particle swarm optimization applications, Tech. Rep. CSM-469, 2007, May–NovemberDepartment of Computing and Electronic Systems, University of Essex, Colchester, Essex, UK.
Google Scholar
6 Jin N. and Rahmat-Samii Y., Advances in particle swarm optimization for antenna designs: real-number, binary, single-objective and multiobjective implementations, IEEE Transactions on Antennas and Propagation. (2007) 55, no. 3 I, 556–567, https://doi.org/10.1109/TAP.2007.891552.
10.1109/TAP.2007.891552
CAS PubMed Web of Science® Google Scholar
7 Donelli M., Azaro R., Natale F. D., and Massa A., An innovative computational approach based on a particle swarm strategy for adaptive phased-arrays control, IEEE Transactions on Antennas and Propagation. (2006) 54, no. 3, 888–898, https://doi.org/10.1109/TAP.2006.869912.
10.1109/TAP.2006.869912
Web of Science® Google Scholar
8 Boeringer D. and Werner D., Particle swarm optimization versus genetic algorithms for phased array synthesis, IEEE Transactions on Antennas and Propagation. (2004) 52, no. 3, 771–779.
10.1109/TAP.2004.825102
Web of Science® Google Scholar
9 Khodier M. and Christodoulou C., Linear array geometry synthesis with minimum sidelobe level and null control using particle swarm optimization, IEEE Transactions on Antennas and Propagation. (2005) 53, no. 8, 2674–2679, https://doi.org/10.1109/TAP.2005.851762.
10.1109/TAP.2005.851762
Web of Science® Google Scholar
10 Jin N. and Rahmat-Samii Y., Parallel particle swarm optimization and finite-difference time-domain (PSO/FDTD) algorithm for multiband and wide-band patch antenna designs, IEEE Transactions on Antennas and Propagation. (2005) 53, no. 11, 3459–3468, https://doi.org/10.1109/TAP.2005.858842.
10.1109/TAP.2005.858842
Web of Science® Google Scholar
11 Kim Y., Keely S., Ghosh J., and Ling H., Application of artificial neural networks to broadband antenna design based on a parametric frequency model, IEEE Transactions on Antennas and Propagation. (2007) 55, no. 3 I, 669–674, https://doi.org/10.1109/TAP.2007.891564.
10.1109/TAP.2007.891564
Web of Science® Google Scholar
12 Migliore M., Pinchera D., and Schettino F., A simple and robust adaptive parasitic antenna, IEEE Transactions on Antennas and Propagation. (2005) 53, no. 10, 3262–3272, https://doi.org/10.1109/TAP.2005.856361.
10.1109/TAP.2005.856361
Web of Science® Google Scholar
13 Wu X., Kishk A., and Glisson A., A transmission line method to compute the far-field radiation of arbitrarily directed Hertzian dipoles in a multilayer dielectric structure: theory and applications, IEEE Transactions on Antennas and Propagation. (2006) 54, no. 10, 2731–2741, https://doi.org/10.1109/TAP.2006.882164.
10.1109/TAP.2006.882164
Web of Science® Google Scholar
14 Boeringer D. and Werner D., Effciency-constrained particle swarm optimization of a modified bernstein polynomial for conformal array excitation amplitude synthesis, IEEE Transactions on Antennas and Propagation. (2005) 53.
10.1109/TAP.2005.851783
Web of Science® Google Scholar
15 Azaro R., Natale F. D., Donelli M., Massa A., and Zeni E., Optimized design of a multifunction/multiband antenna for automotive rescue systems, IEEE Transactions on Antennas and Propagation. (2006) 54, no. 2, 392–400, https://doi.org/10.1109/TAP.2005.863387.
10.1109/TAP.2005.863387
Web of Science® Google Scholar
16 Prez J. R. and Basterrechea J., Comparison of different heuristic optimization methods for near-field antenna measurements, IEEE Transactions on Antennas and Propagation. (2007) 55, no. 3 I, 549–555, https://doi.org/10.1109/TAP.2007.891508.
10.1109/TAP.2007.891508
Web of Science® Google Scholar
17 Selvan S., Xavier C., Karssemeijer N., Sequeira J., Cherian R., and Dhala B., Parameter estimation in stochastic mammogram model by heuristic optimization techniques, IEEE Transactions on Information Technology in Biomedicine. (2006) 10, no. 4, 685–695, https://doi.org/10.1109/TITB.2006.874197.
10.1109/TITB.2006.874197
PubMed Google Scholar
18 Veeramachaneni K., Osadciw L., and Varshney P., An adaptive multimodal biometric management algorithm, IEEE Transactions on Systems, Man and Cybernetics Part C: Applications and Reviews. (2005) 35, no. 3, 344–356, https://doi.org/10.1109/TSMCC.2005.848191.
10.1109/TSMCC.2005.848191
Web of Science® Google Scholar
19 Gaing Z.-L., A particle swarm optimization approach for optimum design of PID controller in AVR system, IEEE Transactions on Energy Conversion. (2004) 19, no. 2, 384–391.
10.1109/TEC.2003.821821
Web of Science® Google Scholar
20 Heo J., Lee K., and Garduno-Ramirez R., Multiobjective control of power plants using particle swarm optimization techniques, IEEE Transactions on Energy Conversion. (2006) 21, no. 2, 552–561, https://doi.org/10.1109/TEC.2005.858078.
10.1109/TEC.2005.858078
Web of Science® Google Scholar
21 Yoshida H., Kawata K., Fukuyama Y., Takayama S., and Nakanishi Y., A particle swarm optimization for reactive power and voltage control considering voltage security assessment, IEEE Transactions on Power Systems. (2000) 15, no. 4, 1232–1239.
10.1109/59.898095
Web of Science® Google Scholar
22 Park J., Choi K., and Allstot D., Parasitic-aware RF circuit design and optimization, IEEE Transactions on Circuits and Systems I: Regular Papers. (2004) 51, no. 10, 1953–1966, https://doi.org/10.1109/TCSI.2004.835691.
10.1109/TCSI.2004.835691
Web of Science® Google Scholar
23 Wang W., Lu Y., Fu J., and Xiong Y. Z., Particle swarm optimization and finite-element based approach for microwave filter design, IEEE Transactions on Magnetics. (2005) 41, no. 5, 1800–1803, https://doi.org/10.1109/TMAG.2005.846467.
10.1109/TMAG.2005.846467
Web of Science® Google Scholar
24 Liu W.-C., Design of a multiband CPW-fed monopole antenna using a particle swarm optimization approach, IEEE Transactions on Antennas and Propagation. (2005) 53, no. 10, 3273–3279, https://doi.org/10.1109/TAP.2005.856339.
10.1109/TAP.2005.856339
Web of Science® Google Scholar
25 Abido M., Optimal design of power-system stabilizers using particle swarm optimization, IEEE Transactions on Energy Conversion. (2002) 17, no. 3, 406–413, https://doi.org/10.1109/TEC.2002.801992.
10.1109/TEC.2002.801992
Web of Science® Google Scholar
26 Kannan S., Slochanal S., and Padhy N., Application and comparison of metaheuristic techniques to generation expansion planning problem, IEEE Transactions on Power Systems. (2005) 20, no. 1, 466–475, https://doi.org/10.1109/TPWRS.2004.840451.
10.1109/TPWRS.2004.840451
Web of Science® Google Scholar
27 Vlachogiannis J. and Lee K., Determining generator contributions to transmission system using parallel vector evaluated particle swarm optimization, IEEE Transactions on Power Systems. (2005) 20, no. 4, 1765–1774, https://doi.org/10.1109/TPWRS.2005.857014.
10.1109/TPWRS.2005.857014
Web of Science® Google Scholar
28 Gaing Z.-L., Particle swarm optimization to solving the economic dispatch considering the generator constraints, IEEE Transactions on Power Systems. (2003) 18, no. 3, 1187–1195, https://doi.org/10.1109/TPWRS.2003.814889.
10.1109/TPWRS.2003.814889
Web of Science® Google Scholar
29 Park J.-B., Lee K.-S., Shin J.-R., and Lee K., A particle swarm optimization for economic dispatch with nonsmooth cost functions, IEEE Transactions on Power Systems. (2005) 20, no. 1, 34–42, https://doi.org/10.1109/TPWRS.2004.831275.
10.1109/TPWRS.2004.831275
Web of Science® Google Scholar
30 Selvakumar A. I. and Thanushkodi K., A new particle swarm optimization solution to nonconvex economic dispatch problems, IEEE Transactions on Power Systems. (2007) 22, no. 1, 42–51, https://doi.org/10.1109/TPWRS.2006.889132.
10.1109/TPWRS.2006.889132
Web of Science® Google Scholar
31 Victoire T. and Jeyakumar A., Reserve constrained dynamic dispatch of units with valve-point effects, IEEE Transactions on Power Systems. (2005) 20, no. 3, 1273–1282, https://doi.org/10.1109/TPWRS.2005.851958.
10.1109/TPWRS.2005.851958
Web of Science® Google Scholar
32 Zhao B., Guo C., and Cao Y., A multiagent-based particle swarm optimization approach for optimal reactive power dispatch, IEEE Transactions on Power Systems. (2005) 20, no. 2, 1070–1078, https://doi.org/10.1109/TPWRS.2005.846064.
10.1109/TPWRS.2005.846064
Web of Science® Google Scholar
33 Juang C.-F. and Hsu C.-H., Temperature control by chip-implemented adaptive recurrent fuzzy controller designed by evolutionary algorithm, IEEE Transactions on Circuits and Systems I: Regular Papers. (2005) 52, no. 11, 2376–2384, https://doi.org/10.1109/TCSI.2005.854138.
10.1109/TCSI.2005.854138
Web of Science® Google Scholar
34 Adly A. and Abd-El-Hafiz S., Using the particle swarm evolutionary approach in shape optimization and field analysis of devices involving nonlinear magnetic media, IEEE Transactions on Magnetics. (2006) 42, no. 10, 3150–3152, https://doi.org/10.1109/TMAG.2006.880103.
10.1109/TMAG.2006.880103
Web of Science® Google Scholar
35 Grimaccia F., Mussetta M., and Zich R. E., Genetical swarm optimization: saelf-adaptive hybrid evolutionary algorithm for electromagnetics, IEEE Transactions on Antennas and Propagation. (2007) 55, no. 3 I, 781–785, https://doi.org/10.1109/TAP.2007.891561.
10.1109/TAP.2007.891561
Web of Science® Google Scholar
36 Ho S., Yang S., Ni G., and Wong H., A particle swarm optimization method with enhanced global search ability for design optimizations of electromagnetic devices, IEEE Transactions on Magnetics. (2006) 42, no. 4, 1107–1110, https://doi.org/10.1109/TMAG.2006.871426.
10.1109/TMAG.2006.871426
Web of Science® Google Scholar
37 Mikki S. and Kishk A., Quantum particle swarm optimization for electromagnetics, IEEE Transactions on Antennas and Propagation. (2006) 54, no. 10, 2764–2775, https://doi.org/10.1109/TAP.2006.882165.
10.1109/TAP.2006.882165
Web of Science® Google Scholar
38 Robinson J. and Rahmat-Samii Y., Particle swarm optimization in electromagnetics, IEEE Transactions on Antennas and Propagation. (2004) 52, no. 2, 397–407, https://doi.org/10.1109/TAP.2004.823969.
10.1109/TAP.2004.823969
Web of Science® Google Scholar
39 Shi X., Yeo K. S., Ma J.-G., Do M. A., and Li E., Scalable model of on-wafer interconnects for high-speed CMOS ICs, IEEE Transactions on Advanced Packaging. (2006) 29, no. 4, 770–776, https://doi.org/10.1109/TADVP.2006.884781.
10.1109/TADVP.2006.884781
CAS Web of Science® Google Scholar
40 Genovesi S., Monorchio A., Mittra R., and Manara G., A sub-boundary approach for enhanced particle swarm optimization and its application to the design of artificial magnetic conductors, IEEE Transactions on Antennas and Propagation. (2007) 55, no. 3 I, 766–770, https://doi.org/10.1109/TAP.2007.891559.
10.1109/TAP.2007.891559
Web of Science® Google Scholar
41 Cui S. and Weile D., Application of a parallel particle swarm optimization scheme to the design of electromagnetic absorbers, IEEE Transactions on Antennas and Propagation. (2005) 53, no. 11, 3616–3624, https://doi.org/10.1109/TAP.2005.858866.
10.1109/TAP.2005.858866
Web of Science® Google Scholar
42 Messerschmidt L. and Engelbrecht A., Learning to play games using a PSO-based competitive learning approach, IEEE Transactions on Evolutionary Computation. (2004) 8, no. 3, 280–288, https://doi.org/10.1109/TEVC.2004.826070.
10.1109/TEVC.2004.826070
Web of Science® Google Scholar
43 Slade W., Ressom H., Musavi M., and Miller R., Inversion of ocean color observations using particle swarm optimization, IEEE Transactions on Geoscience and Remote Sensing. (2004) 42, no. 9, 1915–1923, https://doi.org/10.1109/TGRS.2004.833389.
10.1109/TGRS.2004.833389
Web of Science® Google Scholar
44 Wachowiak M., Smolikova R., Zheng Y., Zurada J., and Elmaghraby A., An approach to multimodal biomedical image registration utilizing particle swarm optimization, IEEE Transactions on Evolutionary Computation. (2004) 8, no. 3, 289–301, https://doi.org/10.1109/TEVC.2004.826068.
10.1109/TEVC.2004.826068
Web of Science® Google Scholar
45 Donelli M. and Massa A., Computational approach based on a particle swarm optimizer for microwave imaging of two-dimensional dielectric scatterers, IEEE Transactions on Microwave Theory and Techniques. (2005) 53, no. 5, 1761–1776, https://doi.org/10.1109/TMTT.2005.847068.
10.1109/TMTT.2005.847068
Web of Science® Google Scholar
46 Huang T. and Mohan A. S., A microparticle swarm optimizer for the reconstruction of microwave images, IEEE Transactions on Antennas and Propagation. (2007) 55, no. 3 I, 568–576, https://doi.org/10.1109/TAP.2007.891545.
10.1109/TAP.2007.891545
Web of Science® Google Scholar
47 Huang C.-M., Huang C.-J., and Wang M.-L., A particle swarm optimization to identifying the ARMAX model for short-term load forecasting, IEEE Transactions on Power Systems. (2005) 20, no. 2, 1126–1133, https://doi.org/10.1109/TPWRS.2005.846106.
10.1109/TPWRS.2005.846106
Web of Science® Google Scholar
48 Song Y., Chen Z., and Yuan Z., New chaotic PSO-based neural network predictive control for nonlinear process, IEEE Transactions on Neural Networks. (2007) 18, no. 2, 595–601, https://doi.org/10.1109/TNN.2006.890809.
10.1109/TNN.2006.890809
PubMed Web of Science® Google Scholar
49 Huang C.-M. and Wang F.-L., An RBF network with OLS and EPSO algorithms for real-time power dispatch, IEEE Transactions on Power Systems. (2007) 22, no. 1, 96–104, https://doi.org/10.1109/TPWRS.2006.889133.
10.1109/TPWRS.2006.889133
Web of Science® Google Scholar
50 Juang C.-F., A hybrid of genetic algorithm and particle swarm optimization for recurrent network design, IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics. (2004) 34, no. 2, 997–1006, https://doi.org/10.1109/TSMCB.2003.818557.
10.1109/TSMCB.2003.818557
PubMed Web of Science® Google Scholar
51 Alrashidi M. R. and El-Hawary M. E., A survey of particle swarm optimization applications in electric power systems, to appear in IEEE Transactions on Evolutionary Computationhttps://doi.org/10.1109/TEVC.2006.880326.
10.1109/TEVC.2006.880326
Google Scholar
52 Vlachogiannis J. and Lee K., A comparative study on particle swarm optimization for optimal steady-state performance of power systems, IEEE Transactions on Power Systems. (2006) 21, no. 4, 1718–1728, https://doi.org/10.1109/TPWRS.2006.883687.
10.1109/TPWRS.2006.883687
Web of Science® Google Scholar
53 Esmin A., Lambert-Torres G., and De Souza A. Z., A hybrid particle swarm optimization applied to loss power minimization, IEEE Transactions on Power Systems. (2005) 20, no. 2, 859–866, https://doi.org/10.1109/TPWRS.2005.846049.
10.1109/TPWRS.2005.846049
Web of Science® Google Scholar
54 Ma Y., Jiang C., Hou Z., and Wang C., The formulation of the optimal strategies for the electricity producers based on the particle swarm optimization algorithm, IEEE Transactions on Power Systems. (2006) 21, no. 4, 1663–1671, https://doi.org/10.1109/TPWRS.2006.883676.
10.1109/TPWRS.2006.883676
Web of Science® Google Scholar
55 Chatterjee A., Pulasinghe K., Watanabe K., and Izumi K., A particle-swarm-optimized fuzzy-neural network for voice-controlled robot systems, IEEE Transactions on Industrial Electronics. (2005) 52, no. 6, 1478–1489, https://doi.org/10.1109/TIE.2005.858737.
10.1109/TIE.2005.858737
Web of Science® Google Scholar
56 Liu B., Wang L., and Jin Y.-H., An effective PSO-based memetic algorithm for flow shop scheduling, IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics. (2007) 37, no. 1, 18–27, https://doi.org/10.1109/TSMCB.2006.883272.
10.1109/TSMCB.2006.883272
PubMed Web of Science® Google Scholar
57 Lee T.-Y., Operating schedule of battery energy storage system in a time-of-use rate industrial user with wind turbine generators: a multipass iteration particle swarm optimization approach, IEEE Transactions on Energy Conversion. (2007) 22, no. 3, 774–782, https://doi.org/10.1109/TEC.2006.878239.
10.1109/TEC.2006.878239
Web of Science® Google Scholar
58 Kassabalidis I., El-Sharkawi M., MarksR. J.II, Moulin L. S., and Da Silva A. A., Dynamic security border identification using enhanced particle swarm optimization, IEEE Transactions on Power Systems. (2002) 17, no. 3, 723–729, https://doi.org/10.1109/TPWRS.2002.800942.
10.1109/TPWRS.2002.800942
Web of Science® Google Scholar
59 Yuan Y., He Z., and Chen M., Virtual MIMO-based cross-layer design for wireless sensor networks, IEEE Transactions on Vehicular Technology. (2006) 55, no. 3, 856–864, https://doi.org/10.1109/TVT.2006.873837.
10.1109/TVT.2006.873837
Web of Science® Google Scholar
60 Venayagamoorthy G. K. and Zha W., Comparison of nonuniform optimal quantizer designs for speech coding with adaptive critics and particle swarm, IEEE Transactions on Industry Applications. (2007) 43, no. 1, 238–244, https://doi.org/10.1109/TIA.2006.885897.
10.1109/TIA.2006.885897
Web of Science® Google Scholar

Citing Literature

All articles

Analysis of the Publications on the Applications of Particle Swarm Optimisation

Abstract

1. Introduction

2. Category Selection and Classification

3. PSO Applications

3.1. Antennas

3.2. Biomedical

3.3. Communication Networks

3.4. Clustering and Classification

3.5. Combinatorial Optimisation

3.6. Control

3.7. Design

3.8. Distribution Networks

3.9. Electronics and Electromagnetics

3.10. Engines and Motors

3.11. Entertainment

3.12. Faults

3.13. Financial

3.14. Fuzzy and Neurofuzzy

3.15. Graphics and Visualisation

3.16. Image and Video

3.17. Metallurgy

3.18. Modelling

3.19. Neural Networks

3.20. Prediction and Forecasting

3.21. Power Systems and Plants

3.22. Robotics

3.23. Scheduling

3.24. Security and Military

3.25. Sensor Networks

3.26. Signal Processing

4. Conclusions

References

Citing Literature

Figures

References

Related

Information