Analysis of the Publications on the Applications of  Particle Swarm Optimisation

Riccardo Poli

doi:10.1155/2008/685175

Analysis of the Publications on the Applications of Particle Swarm Optimisation

Poli, Riccardo 2008-02-14 00:00:00 Hindawi Publishing Corporation Journal of Artiﬁcial Evolution and Applications Volume 2008, Article ID 685175, 10 pages doi:10.1155/2008/685175 Review Article Analysis of the Publications on the Applications of Particle Swarm Optimisation Riccardo Poli Department of Computer Science, University of Essex, Colchester CO4 3SQ, UK Correspondence should be addressed to Riccardo Poli, rpoli@essex.ac.uk Received 24 July 2007; Accepted 30 November 2007 Recommended by Leonardo Vanneschi 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. Copyright © 2008 Riccardo Poli. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1. INTRODUCTION More precisely, in the canonical version of PSO, each par- ticle is moved by two elastic forces, one attracting it with ran- dom magnitude to the ﬁttest location so far encountered by The class of complex systems sometimes referred to as swarm the particle, and one attracting it with random magnitude to systems is a rich source of novel computational methods that can solve diﬃcult problems eﬃciently and reliably. When the best location encountered by any of the particle’s social neighbours in the swarm. If the problem is N dimensional, swarms solve problems in nature, their abilities are usually each particle’s position and velocity can be represented as a attributed to swarm intelligence; perhaps the best-known ex- amples are colonies of social insects such as termites, bees, vector with N components (one for each dimension). Start- ing with the velocity vector, v = (v ,... , v ), each compo- and ants. In recent years, it has proved possible to identify, 1 N nent, v ,isgiven by abstract, and exploit the computational principles underly- ing some forms of swarm intelligence, and to deploy them for v (t +1) = ωv (t)+ ψ R x − x (t) + ψ R x − x (t) , i i 1 s i 2 p i 1 i 2 i scientiﬁc and industrial purposes. One of the best-developed (1) techniquesofthistypeis particle swarm optimisation (PSO) [1]. where x is the ith component of the best point visited by si In PSOs, which are inspired by ﬂocks of birds and shoals the neighbours of the particle, x (t) is the ith component of of ﬁsh, a number of simple entities, the particles, are placed the particle’s current location, x is the ith component of its in the parameter space of some problem or function, and personal best, R and R are two independent random vari- 1 2 each evaluates the ﬁtness at its current location. Each par- ables uniformly distributed in [0, 1], ω is a constant known ticle then determines its movement through the parameter as the inertia weight [2], and ψ and ψ are two constants, 1 2 space by combining some aspect of the history of its own ﬁt- known as the acceleration coeﬃcients, which control the rel- ness values with those of one or more members of the swarm, ative proportion of cognition and social interaction in the and then moving through the parameter space with a veloc- swarm. The same formula is used independently for each di- ity determined by the locations and processed ﬁtness values mension of the problem, and synchronously for all particles. of those other members, along with some random perturba- The position of a particle is updated every time step using the tions. The members of the swarm that a particle can interact equation with are called its social neighbourhood. Together the social neighbourhoods of all particles form a PSOs social network. x (t +1) = x (t)+ v (t +1). (2) i i i 2 Journal of Artiﬁcial Evolution and Applications The next iteration takes place after all particles have been most) papers span more than one category. For examples, moved. Eventually, the swarm as a whole, like a ﬂock of birds many classiﬁers are hybrids of PSO and neural networks, collectively foraging for food, is likely to move close to the many applications involve some form of design, and so on. best location. We provide some conclusions in Section 4. The following alternative velocity-update equation was developed in [3] and is also widely used: 2. CATEGORY SELECTION AND CLASSIFICATION v (t +1) = κ v (t)+ ψ R x − x (t) + ψ R x − x (t) , i i 1 s i 2 p i i i 1 2 (3) Dividing PSO applications into areas is diﬃcult. So, as we mentioned in the previous section, we partially mechanised where κ is a constant called the constriction coeﬃcient.If ψ , the process. This was done through a number of programs in ψ ,and κ (or ω) are correctly chosen, the PSO is guaran- the Octave/Matlab language, Xemacs macros, and Unix util- teed to be stable without the need for special constraints (e.g., ities. bounding of velocities and positions). We started our analysis by searching the IEEE Xplore The topology of the social network used by a PSO is database for any papers matching the search phrase “particle at least as important in determining its behaviour and per- swarm optimization.” This produced around 1,100 hits. We formance as are the details of the velocity update equation. did not try to directly identify application papers. Instead, we Many variants of the canonical PSO and many topologies mechanically extracted all terms used in titles and abstracts. have been developed and tested in the last decade. We can- After manually excluding determiners, adjectives, and so on, not review them here. The interested reader, however, will be this produced well over 4,000 unique terms. These were then able to ﬁnd a comprehensive review of PSO techniques in [4]. manually checked for relevance from the point of view of ap- PSO can be and has been used across a wide range of ap- plications. 928 key terms remained after this ﬁltering process. plications. In general, we can say that areas where PSO has We then used the key terms to deﬁne a similarity rela- shown particular promise include multimodal problems and tionship between papers and used papers to deﬁne a simi- problems for which there is no specialised method available larity relationship between key terms, as follows. Each paper or all specialised methods give unsatisfactory results. How- was assigned a vector with 928 components (as many as our ever, it is hard to be much more speciﬁc that PSO applica- key terms). Each component represented how many times tions are so numerous and diverse that a whole book would the corresponding key term appeared in title and abstract of be necessary just to review the most paradigmatic ones, as- the paper. Given any two papers, we took the scalar product suming someone could identify them among the many hun- between the corresponding vectors as the similarity between dreds of applications reported in the literature, a really enor- the two papers. Similarly, each key term was assigned a vector mous task. with 1100 components (as many as the PSO papers in IEEE Here we have amuchmoremodestobjective:toidentify Xplore). Each component represented how many times the the main classes of applications where PSO has been success- key term appeared in title and abstract of the corresponding fully deployed. We have based our categorisation on an anal- paper. We then deﬁned the similarity between key terms as ysis of titles and abstracts of the over 1100 publications on the scalar product between the corresponding vectors. particle swarm optimisation stored, at the time of writing, in These two similarities relationships induce correspond- the IEEE Xplore database. Of these publications, around 350 ing graph structures on the paper and key term “spaces,” are proposals for improvements and specialisations of PSO. where each paper/term corresponds to a node and nodes Around 700 papers (55 of which are journal papers) can be are connected by edges wherever similarity between cor- classiﬁed as applications of PSO, although many of them in- responding papers/terms is above some preﬁxed threshold volve also the customisation or extension of the method to (e.g., zero). The edges are weighted by similarity. We can then best suit the speciﬁc application of interest. (The remaining make use of graph drawing packages to obtain pictorial rep- entries in the database are conference proceedings books and resentations of PSO application papers, PSO application ar- other miscellaneous entries.) eas, and their relationships. Although the analysis has been largely manual, because of For this purpose we used the open-source graph draw- the large size of this database, to speed up the work we have ing program neato (http://www.graphviz.org). In this pro- made use of several small computer programs which helped gram, the weights of the edges in a graph are interpreted us in the identiﬁcation of the main categories of applications as attractive forces between nodes. Starting from a random and gave us a ﬁrst rough classiﬁcation of papers. Categories placement, the program iteratively adjusts the position of the and class assignments were then checked and adjusted man- nodes in an attempt to minimise the energy in the system. At- ually one-by-one. We describe the process in more detail in tractive forces are balanced by a basic repulsive force between Section 2. nodes to prevent the graph from collapsing to a single point. As a result of this eﬀort we divide PSO applications into Figures 1 and 2 show two examples of the types of graphs one 26 diﬀerent categories. Categories and related applications obtains. are listed in alphabetical order in the subsections of Section 3. By zooming on areas where a high density of links are For each class of applications we indicate what fraction of all present, one can obtain semiquantitative evidence of which the application papers in the IEEE Xplore is devoted to that are the important application areas in PSO. See, for example, class. However, one should bear in mind that many (if not Figure 3 where we show a zoomed version of Figure 1.One Riccardo Poli 3 lagrange mammogram assignment congregation graphics school bacteria chemo relaxation ultrawideband job_shop shields wideband combustion concurrent passiv e switc h aging risk preventive ancient multimedia imaging drive capacitiv e battery areas floorplan shop navigation integration plane cooling knapsack chess disturb avoidance cable valve shapes electronic pong obstacle partner augmentation taxis placement layout unmanned breast geometric near_field nuclear semiconductor high_speed policy assembly car odor capture broadband stress relationship reflector memory charge sonar aerial scattering steel on_wafer salesman producer player station harmonic drug sources oxide furnace estimator enterprise inheritance oscillato r scalabl e wide_band geometry spiral target travel cmos coke heating leakage demand clea r oven hydro transport route eeg inductor manufacturing microstrip microwave track emission implanted ocean case fractal thermal city plant camera chip checkers multiband combinatorial spectra play construction friction shape motor on_chip board inverse scheduling product properties hydrothermal wafer monitoring inventory robot circuit virtual radiation band simulation embedded landmark plan cubic conductors reconfigurable layer stabilizer industrial reflectance casting standard flo w economic planning dominance magnet vehicl e folded multi_objective dispatch heat circle urban sensor engine transform hardware dipole media model antenna miniaturised multilayer mobile parasitic docking constraint space area_control collisio n cast patch chondrogenesis market cost pack fis h environment mission filte r fusion color ward train stability servo protein quantum electric amplifie r game music forecast sea proportional reliability structure line load design area surface dielectric multi_agent device transcription transmission damping torque control compensation segment estimation channel traffic format power face binding database multiclass fuzzy fuel finite_element packing complex mechanism discrete expansion acoustic grid frequency collaborative customer identification induction capacitor energy wireless excitation predict neural simulate multi_machine coalition detect on_line recognition binary chaotic array quality cell blind agent incident network gene voltage absorber identify electromagnetic landing thyristor polarization security cognition support fault recognizing transient frame regulatory texture image class reactive coding compensator micro_grid synthesis deformable rule digital allocation routing visual regulator gate analog temperature cluster strategy acces s quantizer pattern theory scene bandwidth software regression beamforming service wavele t signal multicast neuron wind decay backpropagation plate merchant template border intrusion miniature defec t management chaos diagnostic error investment speech cellula r medical wiener motif water discovery wavelengt h air video platform logistic s manipulator entropy annealing supervised gabor focus noise diagnosis delay reconfiguration visio n failure inference beam congestion encoding protocol feedforward attention b_spline biomedical neuro_fuzzy industry knowledge companies defensive cognitive proton survival microarray underwater cascading oxyge n cancer stock feed_forward bluetooth technologies multimodal pricing treatment flicker snake architecture corporate photo balancing expressway cutting kernel low_contrast acquisition organisms membrane decision incorporate turbine predator denoising unsupervised spatial pixel portfolio biologica l chain contour radar ubiquitous k_means biometric proprietors supply compression suppliers strategic assets photograph tumor investor financial Figure 1: 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 toneato. can clearly see there that some terms, such as design, control, All PSO papers in the IEEE Xplore database were then power, and antenna, act as “hubs” in PSO applications. mechanically provisionally assigned to one of the most fre- After performing this information gathering exercise, we quent keywords. Then we manually analysed each publi- proceeded to do a more formal analysis. The key terms were cation and either conﬁrmed the mechanical classiﬁcation, scored on the basis of how many papers in the database used movedthe papertoadiﬀerent category, deleted the paper such terms in title and abstract. This further helped identify if it was not an application paper, or, occasionally, created a important application categories. Indeed, the most frequent new category for that paper. terms were “network,” “control,” “model,” “design,” “power,” The result of this process is reported in the next section. “neural,” “plan,” “fuzzy,” “class,” “cluster,” “antenna,” “im- age,” “planning,” and “scheduling,” but many others were 3. PSO APPLICATIONS identiﬁed as important. Based on this analysis, we created provisional categories (the headings of the subsections in In our search for PSO application papers, we eventually iden- Section 3). tiﬁed around 650 which deserved citation. 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_aggregation_city_contract_customer_electric_industry_load_power_price_purchase_reconfiguratio _control_cost_discrete_flow_fuel_power_train n _chaos_chaotic_control_detect_discrete_gate_gene _cutting_face_milling_model_predict_surface _cost_cubic_dispatch_economic_fuel_patch _chaotic_multi_objective_plan_planning_preventive_product_relationship_schedulin g _compensator_control_damping_design_power_stabilit y _area_control_design_excitation_gene_power_signal_stabilizer _car_control_gene_industrial_model_simulatio n _attention_cost_dispatch_economic_emission_energy_fuel_mission_patch_penetration_power_risk_sources_wind _area_control_electric_identification_model_power_space _control_frequency_gene_load_power _array_battery_collector_control_grid_load_photo_photovoltaic_storage_strategy _analog_array_control_model_platform_power_proportional_reconfigurable _contour_detect_gabor_image_wavelet _area_areas_constraint_navigation_sea_train_unmanned_vehicl e 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_model_pack_packages_sea_simulation _patch_sea_synthesis_texture_transfer _patch_sea_synthesis_texture _analog_image_pixel_synthesis_texture Figure 2: Example of graph representation of PSO application papers and their relationships. Papers are labelled with the list of key terms appearing in their title and abstract. The rest length for repulsive forces between nodes was set to 9. Only links (similarities) with strength greater than 9 were passed to neato. diﬃcult for any journal to publish a paper including so many database covering this area. Applications include (see [6]) references. To circumvent the problem, in this paper we only the optimal control [7] and design [8, 9] of phased arrays, cite journal papers, but provide an online technical report broadband antenna design [10, 11] and modelling, design of [5] (available from http://www.essex.ac.uk/dces/research/ Yagi-Uda arrays [12], array failure correction, optimisation publications/technicalreports/2007/tr-csm469.pdf)withall of proﬁled corrugated horn antennas, optimisation of a re- citations and references. The BibTeX bibliography used for ﬂectarray antenna, far-ﬁeld radiation pattern reconstruction these papers is available at http://cswww.essex.ac.uk/staﬀ/ [13], antenna modelling, design of planar antennas, confor- rpoli/ieeepso.bib. mal antenna array design [14], design of patch antennas, an- tenna miniaturisation, design of multiband antennas [15], design of aperiodic antenna arrays, near-ﬁeld antenna mea- 3.1. Antennas surements [16], synthesis of antenna arrays, reﬂector anten- The area of antenna design is extremely popular with approx- nas, adaptive array antennas, design of implantable anten- imately 5.8% of all application papers in the IEEE Xplore nas. Riccardo Poli 5 antenna mobile patch market cost ronment mission filter electric quantum design load area transmission control power expansion ency energy wireless predict simulate Figure 3: Zoomed version of Figure 1. 3.2. Biomedical tial databases, dynamic clustering, dimensionality reduc- tion, genetic-programming-based classiﬁcation, fuzzy clus- Biological, medical, and pharmaceutical applications are also tering, cascading classiﬁers, classiﬁcation threshold optimi- very popular with approximately 4.3% of all application pa- sation, classiﬁcation of hierarchical biological data, electrical pers in the IEEE Xplore database covering these areas. Appli- wafer sort classiﬁcation, document and information cluster- cations include human tremor analysis for the diagnosis of ing, data mining, feature selection. Parkinson’s disease, inference of gene regulatory networks, human movement biomechanics optimisation, phylogenetic 3.5. Combinatorial optimisation tree reconstruction, cancer classiﬁcation [17], and survival prediction, DNA motif detection, gene clustering, identiﬁca- Around 24 papers (3.5%) in the database deal with combina- tion of transcription factor binding sites in DNA, biomarker torial optimisation problems. These include applications on selection, protein structure prediction and docking, drug de- ﬂoorplanning, travelling-sales man problems, packing and sign, radiotherapy planning, analysis of brain magnetoen- knapsack, minimum spanning trees, satisﬁability, path op- cephalography data, RNA secondary structure determina- timisation, knights cover problem, n-queens problem, layout tion, electroencephalogram analysis, biometrics [18]. optimisation, vehicle routing, urban planning, FPGA place- ment and routing. 3.3. Communication networks 3.6. Control The design and optimisation of communication networks is the subject of around 30 papers (4.4%) in the ap- Control applications have one of the largest shares (7.0%) of plications database. Applications include bluetooth net- application papers in the IEEE Xplore database. Application works, autotuning for universal mobile telecommunication areas include automatic generation control tuning, design system networks, optimal equipment placement in mo- of controllers, traﬃc ﬂow control, adaptive inverse control, bile communication, routing, radar networks, wavelength- predictive control, PI and PID controllers [19], strip ﬂatness division-multiplexed network, peer-to-peer networks, TCP control, ultrasonic motor control, power plants and systems network control, bandwidth and channel allocation, WDM control [20, 21], control of chaotic systems, process control, telecommunication networks, wireless networks, grouped- adaptive PMD compensation in WDM networks, fractional and-delayed broadcasting, bandwidth reservation. order controllers, combustion control, inertia system con- trol, automatic landing control. 3.4. Clustering and classiﬁcation 3.7. Design Clustering, classiﬁcation, and data mining are the top- ics of approximately 29 papers (4.3%) in the bibliogra- Around 4.4% of the bibliography is devoted to design appli- phy. Applications include clustering, clustering in large spa- cations. These include conceptual design, induction heating 6 Journal of Artiﬁcial Evolution and Applications cooker design, VLSI design, RF circuit synthesis [22], worst in the bibliography. Topics include fault diagnosis of steam- case electronic design, ﬁlter design [23], antenna design [24], turbine generators, circuits that automatically recover from CMOS wideband ampliﬁer design, motor design, logic cir- component failure, gearbox fault diagnosis, automatic defect cuits design, power systems [25], transmission lines, me- classiﬁcation in semiconductor wafers, service restoration chanical design, electromagnetics, case library search. in power distribution, fault-tolerant power systems, miss- ing sensors restoration, fault diagnosis in digital circuits, test pattern generation for circuits, software fault detection, de- 3.8. Distribution networks fensive islanding of power system, power transformers fault Design and restructuring of electricity networks and load diagnosis, optimisation of repairable systems, diagnosis of dispatching are among the problems most frequently at- faults in motors. tacked with PSO, occupying around 7.1% of the applica- tions bibliography. Applications include transmission net- 3.13. Financial work planning, network reconﬁguration and expansion [26], distributed generation [27], microgrids, economic dispatch Around 1.0% of the papers in the bibliography have to do problem [28–32], voltage regulation, congestion manage- with ﬁnance and economics. Topics include ﬁnancial risk ment. early warning, investment decision-making, option pricing, investment portfolio selection, electricity market. 3.9. Electronics and electromagnetics A substantial proportion of the papers in the IEEE database 3.14. Fuzzy and neurofuzzy describe applications in the areas of electronics and elec- tromagnetics. Here we list further applications representing Around 26 papers (3.8% of the bibliography) attack prob- approximately 5.8% of the database. These include on-chip lems in the area of fuzzy and neurofuzzy systems and control. inductors, fuel cells, FPGA-based temperature control [33], These include design of neurofuzzy networks, fuzzy rule ex- AC transmission system control, electromagnetic shape de- traction, fuzzy control, membership functions optimisation, sign [34], microwave ﬁlters, generic electromagnetics design fuzzy modelling, fuzzy classiﬁcation, design of hierarchical and optimisation applications [35–38], linear array antenna fuzzy systems, fuzzy queue management. synthesis, RF IC design and optimisation, semiconductor optimisation, high-speed CMOS [39], conductors [40], fre- quency selective surface and absorber design [41], CMOS RF 3.15. Graphics and visualisation wideband ampliﬁer design, voltage ﬂicker measurement, cir- cuit synthesis, shielding, conﬁguration of FPGAs and parallel Applications in the areas of computer graphics and visu- processor arrays, digital circuit design. alisation also have a share of the applications bibliogra- phy (1.7%). Speciﬁc topics include graphic presentation 3.10. Engines and motors of networks, dimensionality reduction, collision detection in graphic models, texture synthesis, interactive particle Around 10 papers (1.4%) in the applications bibliography swarms, 3D graphics. deal with the design or optimisation of engines and electrical motors. Topics include engine data classiﬁcation, locomotive 3.16. Image and video torque control, motor control in electric and hybrid vehicles, induction motor speed control, direct motor torque control, fault and parameter estimation in induction motors, optimi- A large proportion of the applications bibliography (7.6%) sation of internal combustion engines, optimisation of nu- of PSO applications is devoted to image and video analysis clear electric propulsion systems. applications. Image analysis applications include iris recog- nition, fruit quality grading, face detection and recognition, image segmentation, synthetic aperture radar imaging, lo- 3.11. Entertainment cating treatment planning landmarks in orthodontic x-ray Music generation and games have also a small niche in PSO images, image classiﬁcation, inversion of ocean colour re- applications, occupying approximately (1.3%) in the appli- ﬂectance measurements [43], image fusion, traﬃc stop-sign cations publication database. In the area of games, applica- detection, defect detection, image retrieval, human detection tions include analysis of leaf nodes in game trees [42], learn- in infrared imagery, image registration [44], pixel classiﬁca- ing to play board games, iterated prisoner dilemma, learning tion, detection of objects, pedestrian detection and tracking, to play solo Pong. In the area of music, swarms have been texture synthesis, microwave imaging [45, 46], scene match- used for interactive music improvisation. ing, photo time-stamp recognition, contrast enhancement, 3D recovery with structured beam matrix, autocropping for digital photographs, character recognition, shape matching, 3.12. Faults image noise cancellation. Video applications include MPEG The detection or diagnosis of faults and the recovery from optimisation, motion estimation, object tracking, body pos- them occupy approximately (2.3%) of the application papers ture tracking, traﬃc incident detection. Riccardo Poli 7 3.17. Metallurgy 3.22. Robotics About 9 papers (1.3% of the bibliography) deal with applica- Numerous papers describing PSO applications in robotics tions in metallurgy. These include optimisation of steelmak- are present in the literature. These cover about 3.4% of ing process and modelling in sintering process. the applications bibliography. Topics include control of robotic manipulators and arms, motion planning and con- 3.18. Modelling trol, robot running, collective robotic search, unsupervised robotic learning, path planning, obstacle avoidance, swarm Many papers in the bibliography involve some form of mod- robotics, unmanned vehicle navigation, soccer playing, robot elling. Several that have not been described under other vision, transport robots, odour source localisation, environ- headings are listed here. These form about 2.8% of the bib- ment mapping, voice control of robots [55]. liography. Topics include inversion of underwater acoustic models, modelling MIDI music, customer satisfaction mod- els, thermal process system identiﬁcation, friction models, 3.23. Scheduling ultrawideband channel modelling, chaotic time series mod- elling, identifying ARMAX models [47], nonlinear model About 5.6% of the bibliography deals with scheduling ap- identiﬁcation, nonlinear system identiﬁcation, model selec- plications. These include generator and transmission main- tion, power plants and systems, model order reduction. tenance scheduling, ﬂow shop scheduling [56], hydrother- mal scheduling, optimal operational planning of energy plants, blending scheduling, power generation scheduling, 3.19. Neural networks tasks scheduling in distributed computer system, scheduling Neural networks are used in combination with PSO in many in battery energy storage systems [57], jobshop scheduling, applications. Some have already been listed under a diﬀer- radar time management, project scheduling, train schedul- ent heading elsewhere. Here we list further PSO applica- ing, timetable scheduling, production scheduling, assembly tions to neural networks (3.8% of the bibliography). Topics scheduling, holonic manufacturing scheduling. include inversion of neural networks, neural network con- trol for nonlinear processes [48], design of radial basis func- 3.24. Security and military tion networks [49], product unit networks, neural gas net- works, feedforward neural network training, design of recur- About 1.3% of the bibliography is devoted to security rent neural networks [50], cellular neural networks, wavelet and military applications. These include network security, neural networks, neuron controllers. security-constrained power generation, intrusion detection, cryptography and cryptanalysis, security border identiﬁca- 3.20. Prediction and forecasting tion in power systems [58], weapon-target assignment, mis- sile eﬀectiveness optimisation. About 2.9% of the papers on applications in the bibliogra- phy have to do with prediction and forecasting. Topics in- clude water quality prediction and classiﬁcation, prediction 3.25. Sensor networks of chaotic systems, ecological models, meteorological predic- tions, electric load forecasting, battery pack state of charge 13 papers (1.9%) are devoted to sensors and, particularly, estimation, time series prediction, predictions of elephant sensor networks. Applications include wireless sensor net- migrations, prediction of the ﬂow stress in steel, prediction work sink node optimisation, ad hoc sensor networks node of surface roughness in end milling, streamﬂow forecast, ur- clustering, wireless sensor network design [59], estimation ban traﬃc ﬂow forecasting. of target position in wireless sensor networks, cluster forma- tion in wireless sensor networks, multicast routing in wireless 3.21. Power systems and plants sensor networks, odour source localisation, wireless video sensor networks optimisation, swarm-based mobile sensor A large proportion (5.8%) of the application papers in the networks, sensor scheduling for target tracking, distributed bibliography deals with power generation and power sys- sensor placement, and topology planning. tems. Speciﬁc applications include (see also [51]) automatic generation control, power transformer protection, load fore- casting, STATCOM power system, fault-tolerant control of 3.26. Signal processing compensators, optimal power dispatch, power system perfor- mance optimisation [52], secondary voltage control, power Approximately 3.8% of the bibliography is devoted to ap- control and optimisation, design of power system stabilisers, plications of PSO in signal processing. These include pat- control of photovoltaic systems, large-scale power plant con- tern recognition of ﬂatness signal, design of IIR ﬁlters, par- trol, operational planning for cogeneration systems, analysis ticle ﬁlter optimisation, nonlinear adaptive ﬁlters, Costas of power quality signals, generation planning and restructur- arrays, wavelets, blind detection, blind source separation, ing, hybrid power generation systems [53], optimal strate- analogue ﬁlter tuning, localisation of acoustic sources, dis- gies for electricity production [54], power loss minimisation, tributed odour source localisation, speech coding [60], 2D production costing, and operations planning. IIR ﬁlters. 8 Journal of Artiﬁcial Evolution and Applications The reader interested in advanced PSO techniques and Year IEEE Xplore open questions in PSO algorithms and theory should refer to 1995 (0) [4] for an extensive treatment. 1996 (0) 1997 (2) 1998 (3) REFERENCES 1999 (6) (10) [1] J.Kennedy andR.C.Eberhart, Swarm Intelligence,Morgan 2001 (13) Kaufmann Publishers, San Francisco, Calif, USA, 2001. (36) [2] Y. Shi and R. C. Eberhart, “A modiﬁed particle swarm op- (86) timizer,” in Proceedings of the IEEE Congress on Evolutionary (270) Computation (CEC ’99), pp. 69–73, Piscataway, NJ, USA, 1999. (425) [3] M. Clerc and J. Kennedy, “The particle swarm-explosion, sta- (687) bility, and convergence in a multidimensional complex space,” IEEE Transactions on Evolutionary Computation,vol. 6, no.1, Figure 4: PSO papers by year. pp. 58–73, 2002. [4] R. Poli, J. Kennedy, and T. Blackwell, “Particle swarm optimi- sation: an overview,” Swarm Intelligence Journal,vol. 1, no.1, 4. CONCLUSIONS [5] R. Poli, “An analysis of publications on particle swarm op- This paper presents a bird’s eye view of PSO applications. timization applications,” Tech. Rep. CSM-469, Department This has been obtained by identifying and analysing around of Computing and Electronic Systems, University of Essex, 700 PSO application papers stored in IEEE Xplore database Colchester, Essex, UK, May–November 2007. at the time of writing. [6] N. Jin and Y. Rahmat-Samii, “Advances in particle swarm op- The picture we obtain is that of a technique with an im- timization for antenna designs: real-number, binary, single- mense scope of applications, ranging from biological and objective and multiobjective implementations,” IEEE Transac- medical to electrical, electronic, and electromagnetic, to tions on Antennas and Propagation, vol. 55, no. 3 I, pp. 556– practical computational intelligence applications, to combi- 567, 2007. natorial problem solving, to image analysis, signal process- [7] M. Donelli, R. Azaro, F. D. Natale, and A. Massa, “An innova- ing and graphics, to robotics. What is particularly amaz- tive computational approach based on a particle swarm strat- ing is the rate of growth of PSO publications (see Figure 4), egy for adaptive phased-arrays control,” IEEE Transactions on most of which are in fact about applications of the technique. Antennas and Propagation, vol. 54, no. 3, pp. 888–898, 2006. The number of publications reporting PSO applications has [8] D. Boeringer and D. Werner, “Particle swarm optimization grown nearly exponential for the last few years, and seems to versus genetic algorithms for phased array synthesis,” IEEE show no sign of slowing down at the present moment. Transactions on Antennas and Propagation,vol. 52, no.3,pp. What makes PSO so attractive to practitioners? Clearly, 771–779, 2004. the algorithm shines for its simplicity and for the ease with [9] M. Khodier and C. Christodoulou, “Linear array geometry synthesis with minimum sidelobe level and null control using which it can be adapted to diﬀerent application domains and particle swarm optimization,” IEEE Transactions on Antennas hybridised with other techniques. This is perhaps what most and Propagation, vol. 53, no. 8, pp. 2674–2679, 2005. people want from a practical problem solver: being able to [10] N. Jin and Y. Rahmat-Samii, “Parallel particle swarm opti- learn the basics of a new technique quickly, and being able mization and ﬁnite-diﬀerence time-domain (PSO/FDTD) al- to use it as a building block to be mixed and matched with gorithm for multiband and wide-band patch antenna de- whatever tools they are already familiar with. Also, the PSO signs,” IEEE Transactions on Antennas and Propagation, vol. 53, routinely delivers good optimisation results. Most people will no. 11, pp. 3459–3468, 2005. not care as to whether their new tool is guaranteed to give [11] Y. Kim, S. Keely, J. Ghosh, and H. Ling, “Application of artiﬁ- the absolute best performance on a problem. What they want cial neural networks to broadband antenna design based on a is something simple and reliable. Finally, probably the PSO parametric frequency model,” IEEE Transactions on Antennas has, at the moment, in the mind of many people the sort of and Propagation, vol. 55, no. 3 I, pp. 669–674, 2007. magical black box ﬂavour that attracted so many researchers [12] M. Migliore, D. Pinchera, and F. Schettino, “A simple and ro- to other areas of artiﬁcial/computational intelligence (such as bust adaptive parasitic antenna,” IEEE Transactions on Anten- neural network, genetic algorithms, or fuzzy systems) before. nas and Propagation, vol. 53, no. 10, pp. 3262–3272, 2005. What application areas should we expect PSO to do well [13] X. Wu, A. Kishk, and A. Glisson, “A transmission line method in? It is very hard to make speciﬁc suggestions. The PSO to compute the far-ﬁeld radiation of arbitrarily directed seemstohaveworkedverywellinalmostall areaswhere it Hertzian dipoles in a multilayer dielectric structure: theory has been applied, with perhaps the exception of combinato- and applications,” IEEE Transactions on Antennas and Propa- rial optimisation problems where further improvements to gation, vol. 54, no. 10, pp. 2731–2741, 2006. PSO techniques may still be needed before the PSO can com- [14] D. Boeringer and D. Werner, “Eﬀciency-constrained particle pete on par with other techniques. Naturally, the best pre- swarm optimization of a modiﬁed bernstein polynomial for dictor of future performance is the past. All of the 26 areas conformal array excitation amplitude synthesis,” IEEE Trans- identiﬁed in this paper appear to be still very fertile. actions on Antennas and Propagation, vol. 53, 2005. Riccardo Poli 9 [15] R. Azaro, F. D. Natale, M. Donelli, A. Massa, and E. Zeni, “Op- [31] T. Victoire and A. Jeyakumar, “Reserve constrained dynamic timized design of a multifunction/multiband antenna for au- dispatch of units with valve-point eﬀects,” IEEE Transactions tomotive rescue systems,” IEEE Transactions on Antennas and on Power Systems, vol. 20, no. 3, pp. 1273–1282, 2005. Propagation, vol. 54, no. 2, pp. 392–400, 2006. [32] B. Zhao, C. Guo, and Y. Cao, “A multiagent-based particle swarm optimization approach for optimal reactive power dis- [16] J. R. Prez and J. Basterrechea, “Comparison of diﬀerent patch,” IEEE Transactions on Power Systems,vol. 20, no.2,pp. heuristic optimization methods for near-ﬁeld antenna mea- 1070–1078, 2005. surements,” IEEE Transactions on Antennas and Propagation, vol. 55, no. 3 I, pp. 549–555, 2007. [33] C.-F. Juang and C.-H. Hsu, “Temperature control by chip- implemented adaptive recurrent fuzzy controller designed by [17] S. Selvan, C. Xavier, N. Karssemeijer, J. Sequeira, R. Cherian, evolutionary algorithm,” IEEE Transactions on Circuits and and B. 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Publisher: Hindawi Publishing Corporation
Copyright: Copyright © 2008 Riccardo Poli. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
ISSN: 1687-6229
DOI: 10.1155/2008/685175
Publisher site: See Article on Publisher Site

Abstract

Hindawi Publishing Corporation Journal of Artiﬁcial Evolution and Applications Volume 2008, Article ID 685175, 10 pages doi:10.1155/2008/685175 Review Article Analysis of the Publications on the Applications of Particle Swarm Optimisation Riccardo Poli Department of Computer Science, University of Essex, Colchester CO4 3SQ, UK Correspondence should be addressed to Riccardo Poli, rpoli@essex.ac.uk Received 24 July 2007; Accepted 30 November 2007 Recommended by Leonardo Vanneschi 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. Copyright © 2008 Riccardo Poli. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1. INTRODUCTION More precisely, in the canonical version of PSO, each par- ticle is moved by two elastic forces, one attracting it with ran- dom magnitude to the ﬁttest location so far encountered by The class of complex systems sometimes referred to as swarm the particle, and one attracting it with random magnitude to systems is a rich source of novel computational methods that can solve diﬃcult problems eﬃciently and reliably. When the best location encountered by any of the particle’s social neighbours in the swarm. If the problem is N dimensional, swarms solve problems in nature, their abilities are usually each particle’s position and velocity can be represented as a attributed to swarm intelligence; perhaps the best-known ex- amples are colonies of social insects such as termites, bees, vector with N components (one for each dimension). Start- ing with the velocity vector, v = (v ,... , v ), each compo- and ants. In recent years, it has proved possible to identify, 1 N nent, v ,isgiven by abstract, and exploit the computational principles underly- ing some forms of swarm intelligence, and to deploy them for v (t +1) = ωv (t)+ ψ R x − x (t) + ψ R x − x (t) , i i 1 s i 2 p i 1 i 2 i scientiﬁc and industrial purposes. One of the best-developed (1) techniquesofthistypeis particle swarm optimisation (PSO) [1]. where x is the ith component of the best point visited by si In PSOs, which are inspired by ﬂocks of birds and shoals the neighbours of the particle, x (t) is the ith component of of ﬁsh, a number of simple entities, the particles, are placed the particle’s current location, x is the ith component of its in the parameter space of some problem or function, and personal best, R and R are two independent random vari- 1 2 each evaluates the ﬁtness at its current location. Each par- ables uniformly distributed in [0, 1], ω is a constant known ticle then determines its movement through the parameter as the inertia weight [2], and ψ and ψ are two constants, 1 2 space by combining some aspect of the history of its own ﬁt- known as the acceleration coeﬃcients, which control the rel- ness values with those of one or more members of the swarm, ative proportion of cognition and social interaction in the and then moving through the parameter space with a veloc- swarm. The same formula is used independently for each di- ity determined by the locations and processed ﬁtness values mension of the problem, and synchronously for all particles. of those other members, along with some random perturba- The position of a particle is updated every time step using the tions. The members of the swarm that a particle can interact equation with are called its social neighbourhood. Together the social neighbourhoods of all particles form a PSOs social network. x (t +1) = x (t)+ v (t +1). (2) i i i 2 Journal of Artiﬁcial Evolution and Applications The next iteration takes place after all particles have been most) papers span more than one category. For examples, moved. Eventually, the swarm as a whole, like a ﬂock of birds many classiﬁers are hybrids of PSO and neural networks, collectively foraging for food, is likely to move close to the many applications involve some form of design, and so on. best location. We provide some conclusions in Section 4. The following alternative velocity-update equation was developed in [3] and is also widely used: 2. CATEGORY SELECTION AND CLASSIFICATION v (t +1) = κ v (t)+ ψ R x − x (t) + ψ R x − x (t) , i i 1 s i 2 p i i i 1 2 (3) Dividing PSO applications into areas is diﬃcult. So, as we mentioned in the previous section, we partially mechanised where κ is a constant called the constriction coeﬃcient.If ψ , the process. This was done through a number of programs in ψ ,and κ (or ω) are correctly chosen, the PSO is guaran- the Octave/Matlab language, Xemacs macros, and Unix util- teed to be stable without the need for special constraints (e.g., ities. bounding of velocities and positions). We started our analysis by searching the IEEE Xplore The topology of the social network used by a PSO is database for any papers matching the search phrase “particle at least as important in determining its behaviour and per- swarm optimization.” This produced around 1,100 hits. We formance as are the details of the velocity update equation. did not try to directly identify application papers. Instead, we Many variants of the canonical PSO and many topologies mechanically extracted all terms used in titles and abstracts. have been developed and tested in the last decade. We can- After manually excluding determiners, adjectives, and so on, not review them here. The interested reader, however, will be this produced well over 4,000 unique terms. These were then able to ﬁnd a comprehensive review of PSO techniques in [4]. manually checked for relevance from the point of view of ap- PSO can be and has been used across a wide range of ap- plications. 928 key terms remained after this ﬁltering process. plications. In general, we can say that areas where PSO has We then used the key terms to deﬁne a similarity rela- shown particular promise include multimodal problems and tionship between papers and used papers to deﬁne a simi- problems for which there is no specialised method available larity relationship between key terms, as follows. Each paper or all specialised methods give unsatisfactory results. How- was assigned a vector with 928 components (as many as our ever, it is hard to be much more speciﬁc that PSO applica- key terms). Each component represented how many times tions are so numerous and diverse that a whole book would the corresponding key term appeared in title and abstract of be necessary just to review the most paradigmatic ones, as- the paper. Given any two papers, we took the scalar product suming someone could identify them among the many hun- between the corresponding vectors as the similarity between dreds of applications reported in the literature, a really enor- the two papers. Similarly, each key term was assigned a vector mous task. with 1100 components (as many as the PSO papers in IEEE Here we have amuchmoremodestobjective:toidentify Xplore). Each component represented how many times the the main classes of applications where PSO has been success- key term appeared in title and abstract of the corresponding fully deployed. We have based our categorisation on an anal- paper. We then deﬁned the similarity between key terms as ysis of titles and abstracts of the over 1100 publications on the scalar product between the corresponding vectors. particle swarm optimisation stored, at the time of writing, in These two similarities relationships induce correspond- the IEEE Xplore database. Of these publications, around 350 ing graph structures on the paper and key term “spaces,” are proposals for improvements and specialisations of PSO. where each paper/term corresponds to a node and nodes Around 700 papers (55 of which are journal papers) can be are connected by edges wherever similarity between cor- classiﬁed as applications of PSO, although many of them in- responding papers/terms is above some preﬁxed threshold volve also the customisation or extension of the method to (e.g., zero). The edges are weighted by similarity. We can then best suit the speciﬁc application of interest. (The remaining make use of graph drawing packages to obtain pictorial rep- entries in the database are conference proceedings books and resentations of PSO application papers, PSO application ar- other miscellaneous entries.) eas, and their relationships. Although the analysis has been largely manual, because of For this purpose we used the open-source graph draw- the large size of this database, to speed up the work we have ing program neato (http://www.graphviz.org). In this pro- made use of several small computer programs which helped gram, the weights of the edges in a graph are interpreted us in the identiﬁcation of the main categories of applications as attractive forces between nodes. Starting from a random and gave us a ﬁrst rough classiﬁcation of papers. Categories placement, the program iteratively adjusts the position of the and class assignments were then checked and adjusted man- nodes in an attempt to minimise the energy in the system. At- ually one-by-one. We describe the process in more detail in tractive forces are balanced by a basic repulsive force between Section 2. nodes to prevent the graph from collapsing to a single point. As a result of this eﬀort we divide PSO applications into Figures 1 and 2 show two examples of the types of graphs one 26 diﬀerent categories. Categories and related applications obtains. are listed in alphabetical order in the subsections of Section 3. By zooming on areas where a high density of links are For each class of applications we indicate what fraction of all present, one can obtain semiquantitative evidence of which the application papers in the IEEE Xplore is devoted to that are the important application areas in PSO. See, for example, class. However, one should bear in mind that many (if not Figure 3 where we show a zoomed version of Figure 1.One Riccardo Poli 3 lagrange mammogram assignment congregation graphics school bacteria chemo relaxation ultrawideband job_shop shields wideband combustion concurrent passiv e switc h aging risk preventive ancient multimedia imaging drive capacitiv e battery areas floorplan shop navigation integration plane cooling knapsack chess disturb avoidance cable valve shapes electronic pong obstacle partner augmentation taxis placement layout unmanned breast geometric near_field nuclear semiconductor high_speed policy assembly car odor capture broadband stress relationship reflector memory charge sonar aerial scattering steel on_wafer salesman producer player station harmonic drug sources oxide furnace estimator enterprise inheritance oscillato r scalabl e wide_band geometry spiral target travel cmos coke heating leakage demand clea r oven hydro transport route eeg inductor manufacturing microstrip microwave track emission implanted ocean case fractal thermal city plant camera chip checkers multiband combinatorial spectra play construction friction shape motor on_chip board inverse scheduling product properties hydrothermal wafer monitoring inventory robot circuit virtual radiation band simulation embedded landmark plan cubic conductors reconfigurable layer stabilizer industrial reflectance casting standard flo w economic planning dominance magnet vehicl e folded multi_objective dispatch heat circle urban sensor engine transform hardware dipole media model antenna miniaturised multilayer mobile parasitic docking constraint space area_control collisio n cast patch chondrogenesis market cost pack fis h environment mission filte r fusion color ward train stability servo protein quantum electric amplifie r game music forecast sea proportional reliability structure line load design area surface dielectric multi_agent device transcription transmission damping torque control compensation segment estimation channel traffic format power face binding database multiclass fuzzy fuel finite_element packing complex mechanism discrete expansion acoustic grid frequency collaborative customer identification induction capacitor energy wireless excitation predict neural simulate multi_machine coalition detect on_line recognition binary chaotic array quality cell blind agent incident network gene voltage absorber identify electromagnetic landing thyristor polarization security cognition support fault recognizing transient frame regulatory texture image class reactive coding compensator micro_grid synthesis deformable rule digital allocation routing visual regulator gate analog temperature cluster strategy acces s quantizer pattern theory scene bandwidth software regression beamforming service wavele t signal multicast neuron wind decay backpropagation plate merchant template border intrusion miniature defec t management chaos diagnostic error investment speech cellula r medical wiener motif water discovery wavelengt h air video platform logistic s manipulator entropy annealing supervised gabor focus noise diagnosis delay reconfiguration visio n failure inference beam congestion encoding protocol feedforward attention b_spline biomedical neuro_fuzzy industry knowledge companies defensive cognitive proton survival microarray underwater cascading oxyge n cancer stock feed_forward bluetooth technologies multimodal pricing treatment flicker snake architecture corporate photo balancing expressway cutting kernel low_contrast acquisition organisms membrane decision incorporate turbine predator denoising unsupervised spatial pixel portfolio biologica l chain contour radar ubiquitous k_means biometric proprietors supply compression suppliers strategic assets photograph tumor investor financial Figure 1: 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 toneato. can clearly see there that some terms, such as design, control, All PSO papers in the IEEE Xplore database were then power, and antenna, act as “hubs” in PSO applications. mechanically provisionally assigned to one of the most fre- After performing this information gathering exercise, we quent keywords. Then we manually analysed each publi- proceeded to do a more formal analysis. The key terms were cation and either conﬁrmed the mechanical classiﬁcation, scored on the basis of how many papers in the database used movedthe papertoadiﬀerent category, deleted the paper such terms in title and abstract. This further helped identify if it was not an application paper, or, occasionally, created a important application categories. Indeed, the most frequent new category for that paper. terms were “network,” “control,” “model,” “design,” “power,” The result of this process is reported in the next section. “neural,” “plan,” “fuzzy,” “class,” “cluster,” “antenna,” “im- age,” “planning,” and “scheduling,” but many others were 3. PSO APPLICATIONS identiﬁed as important. Based on this analysis, we created provisional categories (the headings of the subsections in In our search for PSO application papers, we eventually iden- Section 3). tiﬁed around 650 which deserved citation. 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_diagnosis_fault_line_power_recognized_support_theory_transform _chemo_design_disease_drug_face_format_industry_pharmaceutical_quality_sea _design_digital_filter_quantum_train _aging_bacteria_bacterial_flow_foraging_load_powe r _cell_circuit_detect_floorplan_placement_plan_planning _flow_line_power _array_cost_cryptography_gene_graph_sea_signal _array_curve_excitation_line_pattern_plan_synthesis_technologies_train _design_filter_low_dispersion _constraint_power_survival_train_transfer _mobile_robot_sea _biology_congregation_flow_passive_power_standar d _environment_odor_track _environment_mobile_obstacle_plan_planning_robot _cost_customer_electric_face_industry_power_quality_reconfiguration_service_supply _agent_coalition_multi_agent_sea_structure _commission_mission_robot_technologies _complex_space _cost_emission_energy_management_mission_plan _area_attention_comprehensive_coverage_electric_power_sea _estimation_regulator_voltage _antenna_car_reflector_shape _cluster_partner_perception_perceptual_robot_visua l _city_fuzzy_power_relaxation_stabilizer _diagnosis_fault_magnet_motor_reliability _antenna_electronic_gate_load_parasitic_switch _class_filter_structure _environment_fusion_mobile_odor_robot _amplifier_annealing_circuit_design_line_parasitic_power_simulate_synthesis_tunneling _cell_environment_graph_graphics_layout_manufacturing_mobile_reconfigurable_robot_simulation_station _allocation_cell_environment_graph_graphics_layout_manufacturing_reconfigurable_robot_simulation_station_transport _canceling_channel_design_error_face_filter_identification_quantum_surface _algebraic_complex_discrete_sea_space_stability _convolution_crystal_defect_design_detect_display_embedded_face_filter_focus_image_low_contrast_manufacturing_play_surface_textu re _design_filter_friction_gene_line_microstrip_microwave_sort _corporate_estimation_filter_gene_incorporate_line _assets_city_decision_financial_investment_investor_portfolio_theory _filter_gene_structure _assets_decision_financial_investment_investor_portfolio_theory_train _design_filter_gene_microwave_model_plan_se a _alphabet_binary_blind_channel_constraint_detect_discrete_mission_mobile_signal_train_transmissio n _gene_kernel_regression_spatial_technology_theory _annealing_circuit_design_parasitic_simulate_synthesis _blind_format_recover_signal_transform _collective_environment_filter_gene_kernel_organisms_sensor_sensory _aperture_array_directional_excitation_gene_radiating_train _annealing_coding_encoding_gene_routing_simulate_vehicle _construction_image_microwave_standard _chaotic_embedded_mechanism_sea_standard _annealing_gene_routing_simulate_vehicle _construction_image_microwave _chaotic_standard _annealing_circuit_design_gene_parasitic_simulate_sort_sorting_synthesis_tunnelin g _corporate_incorporate_inheritance_multi_objectiv e _analog_image_patch_photo_synthesis_texture _deliver_model_product_sea_simulation _inheritance_multi_objective _model_pack_packages_sea_simulation _patch_sea_synthesis_texture_transfer _patch_sea_synthesis_texture _analog_image_pixel_synthesis_texture Figure 2: Example of graph representation of PSO application papers and their relationships. Papers are labelled with the list of key terms appearing in their title and abstract. The rest length for repulsive forces between nodes was set to 9. Only links (similarities) with strength greater than 9 were passed to neato. diﬃcult for any journal to publish a paper including so many database covering this area. Applications include (see [6]) references. To circumvent the problem, in this paper we only the optimal control [7] and design [8, 9] of phased arrays, cite journal papers, but provide an online technical report broadband antenna design [10, 11] and modelling, design of [5] (available from http://www.essex.ac.uk/dces/research/ Yagi-Uda arrays [12], array failure correction, optimisation publications/technicalreports/2007/tr-csm469.pdf)withall of proﬁled corrugated horn antennas, optimisation of a re- citations and references. The BibTeX bibliography used for ﬂectarray antenna, far-ﬁeld radiation pattern reconstruction these papers is available at http://cswww.essex.ac.uk/staﬀ/ [13], antenna modelling, design of planar antennas, confor- rpoli/ieeepso.bib. mal antenna array design [14], design of patch antennas, an- tenna miniaturisation, design of multiband antennas [15], design of aperiodic antenna arrays, near-ﬁeld antenna mea- 3.1. Antennas surements [16], synthesis of antenna arrays, reﬂector anten- The area of antenna design is extremely popular with approx- nas, adaptive array antennas, design of implantable anten- imately 5.8% of all application papers in the IEEE Xplore nas. Riccardo Poli 5 antenna mobile patch market cost ronment mission filter electric quantum design load area transmission control power expansion ency energy wireless predict simulate Figure 3: Zoomed version of Figure 1. 3.2. Biomedical tial databases, dynamic clustering, dimensionality reduc- tion, genetic-programming-based classiﬁcation, fuzzy clus- Biological, medical, and pharmaceutical applications are also tering, cascading classiﬁers, classiﬁcation threshold optimi- very popular with approximately 4.3% of all application pa- sation, classiﬁcation of hierarchical biological data, electrical pers in the IEEE Xplore database covering these areas. Appli- wafer sort classiﬁcation, document and information cluster- cations include human tremor analysis for the diagnosis of ing, data mining, feature selection. Parkinson’s disease, inference of gene regulatory networks, human movement biomechanics optimisation, phylogenetic 3.5. Combinatorial optimisation tree reconstruction, cancer classiﬁcation [17], and survival prediction, DNA motif detection, gene clustering, identiﬁca- Around 24 papers (3.5%) in the database deal with combina- tion of transcription factor binding sites in DNA, biomarker torial optimisation problems. These include applications on selection, protein structure prediction and docking, drug de- ﬂoorplanning, travelling-sales man problems, packing and sign, radiotherapy planning, analysis of brain magnetoen- knapsack, minimum spanning trees, satisﬁability, path op- cephalography data, RNA secondary structure determina- timisation, knights cover problem, n-queens problem, layout tion, electroencephalogram analysis, biometrics [18]. optimisation, vehicle routing, urban planning, FPGA place- ment and routing. 3.3. Communication networks 3.6. Control The design and optimisation of communication networks is the subject of around 30 papers (4.4%) in the ap- Control applications have one of the largest shares (7.0%) of plications database. Applications include bluetooth net- application papers in the IEEE Xplore database. Application works, autotuning for universal mobile telecommunication areas include automatic generation control tuning, design system networks, optimal equipment placement in mo- of controllers, traﬃc ﬂow control, adaptive inverse control, bile communication, routing, radar networks, wavelength- predictive control, PI and PID controllers [19], strip ﬂatness division-multiplexed network, peer-to-peer networks, TCP control, ultrasonic motor control, power plants and systems network control, bandwidth and channel allocation, WDM control [20, 21], control of chaotic systems, process control, telecommunication networks, wireless networks, grouped- adaptive PMD compensation in WDM networks, fractional and-delayed broadcasting, bandwidth reservation. order controllers, combustion control, inertia system con- trol, automatic landing control. 3.4. Clustering and classiﬁcation 3.7. Design Clustering, classiﬁcation, and data mining are the top- ics of approximately 29 papers (4.3%) in the bibliogra- Around 4.4% of the bibliography is devoted to design appli- phy. Applications include clustering, clustering in large spa- cations. These include conceptual design, induction heating 6 Journal of Artiﬁcial Evolution and Applications cooker design, VLSI design, RF circuit synthesis [22], worst in the bibliography. Topics include fault diagnosis of steam- case electronic design, ﬁlter design [23], antenna design [24], turbine generators, circuits that automatically recover from CMOS wideband ampliﬁer design, motor design, logic cir- component failure, gearbox fault diagnosis, automatic defect cuits design, power systems [25], transmission lines, me- classiﬁcation in semiconductor wafers, service restoration chanical design, electromagnetics, case library search. in power distribution, fault-tolerant power systems, miss- ing sensors restoration, fault diagnosis in digital circuits, test pattern generation for circuits, software fault detection, de- 3.8. Distribution networks fensive islanding of power system, power transformers fault Design and restructuring of electricity networks and load diagnosis, optimisation of repairable systems, diagnosis of dispatching are among the problems most frequently at- faults in motors. tacked with PSO, occupying around 7.1% of the applica- tions bibliography. Applications include transmission net- 3.13. Financial work planning, network reconﬁguration and expansion [26], distributed generation [27], microgrids, economic dispatch Around 1.0% of the papers in the bibliography have to do problem [28–32], voltage regulation, congestion manage- with ﬁnance and economics. Topics include ﬁnancial risk ment. early warning, investment decision-making, option pricing, investment portfolio selection, electricity market. 3.9. Electronics and electromagnetics A substantial proportion of the papers in the IEEE database 3.14. Fuzzy and neurofuzzy describe applications in the areas of electronics and elec- tromagnetics. Here we list further applications representing Around 26 papers (3.8% of the bibliography) attack prob- approximately 5.8% of the database. These include on-chip lems in the area of fuzzy and neurofuzzy systems and control. inductors, fuel cells, FPGA-based temperature control [33], These include design of neurofuzzy networks, fuzzy rule ex- AC transmission system control, electromagnetic shape de- traction, fuzzy control, membership functions optimisation, sign [34], microwave ﬁlters, generic electromagnetics design fuzzy modelling, fuzzy classiﬁcation, design of hierarchical and optimisation applications [35–38], linear array antenna fuzzy systems, fuzzy queue management. synthesis, RF IC design and optimisation, semiconductor optimisation, high-speed CMOS [39], conductors [40], fre- quency selective surface and absorber design [41], CMOS RF 3.15. Graphics and visualisation wideband ampliﬁer design, voltage ﬂicker measurement, cir- cuit synthesis, shielding, conﬁguration of FPGAs and parallel Applications in the areas of computer graphics and visu- processor arrays, digital circuit design. alisation also have a share of the applications bibliogra- phy (1.7%). Speciﬁc topics include graphic presentation 3.10. Engines and motors of networks, dimensionality reduction, collision detection in graphic models, texture synthesis, interactive particle Around 10 papers (1.4%) in the applications bibliography swarms, 3D graphics. deal with the design or optimisation of engines and electrical motors. Topics include engine data classiﬁcation, locomotive 3.16. Image and video torque control, motor control in electric and hybrid vehicles, induction motor speed control, direct motor torque control, fault and parameter estimation in induction motors, optimi- A large proportion of the applications bibliography (7.6%) sation of internal combustion engines, optimisation of nu- of PSO applications is devoted to image and video analysis clear electric propulsion systems. applications. Image analysis applications include iris recog- nition, fruit quality grading, face detection and recognition, image segmentation, synthetic aperture radar imaging, lo- 3.11. Entertainment cating treatment planning landmarks in orthodontic x-ray Music generation and games have also a small niche in PSO images, image classiﬁcation, inversion of ocean colour re- applications, occupying approximately (1.3%) in the appli- ﬂectance measurements [43], image fusion, traﬃc stop-sign cations publication database. In the area of games, applica- detection, defect detection, image retrieval, human detection tions include analysis of leaf nodes in game trees [42], learn- in infrared imagery, image registration [44], pixel classiﬁca- ing to play board games, iterated prisoner dilemma, learning tion, detection of objects, pedestrian detection and tracking, to play solo Pong. In the area of music, swarms have been texture synthesis, microwave imaging [45, 46], scene match- used for interactive music improvisation. ing, photo time-stamp recognition, contrast enhancement, 3D recovery with structured beam matrix, autocropping for digital photographs, character recognition, shape matching, 3.12. Faults image noise cancellation. Video applications include MPEG The detection or diagnosis of faults and the recovery from optimisation, motion estimation, object tracking, body pos- them occupy approximately (2.3%) of the application papers ture tracking, traﬃc incident detection. Riccardo Poli 7 3.17. Metallurgy 3.22. Robotics About 9 papers (1.3% of the bibliography) deal with applica- Numerous papers describing PSO applications in robotics tions in metallurgy. These include optimisation of steelmak- are present in the literature. These cover about 3.4% of ing process and modelling in sintering process. the applications bibliography. Topics include control of robotic manipulators and arms, motion planning and con- 3.18. Modelling trol, robot running, collective robotic search, unsupervised robotic learning, path planning, obstacle avoidance, swarm Many papers in the bibliography involve some form of mod- robotics, unmanned vehicle navigation, soccer playing, robot elling. Several that have not been described under other vision, transport robots, odour source localisation, environ- headings are listed here. These form about 2.8% of the bib- ment mapping, voice control of robots [55]. liography. Topics include inversion of underwater acoustic models, modelling MIDI music, customer satisfaction mod- els, thermal process system identiﬁcation, friction models, 3.23. Scheduling ultrawideband channel modelling, chaotic time series mod- elling, identifying ARMAX models [47], nonlinear model About 5.6% of the bibliography deals with scheduling ap- identiﬁcation, nonlinear system identiﬁcation, model selec- plications. These include generator and transmission main- tion, power plants and systems, model order reduction. tenance scheduling, ﬂow shop scheduling [56], hydrother- mal scheduling, optimal operational planning of energy plants, blending scheduling, power generation scheduling, 3.19. Neural networks tasks scheduling in distributed computer system, scheduling Neural networks are used in combination with PSO in many in battery energy storage systems [57], jobshop scheduling, applications. Some have already been listed under a diﬀer- radar time management, project scheduling, train schedul- ent heading elsewhere. Here we list further PSO applica- ing, timetable scheduling, production scheduling, assembly tions to neural networks (3.8% of the bibliography). Topics scheduling, holonic manufacturing scheduling. include inversion of neural networks, neural network con- trol for nonlinear processes [48], design of radial basis func- 3.24. Security and military tion networks [49], product unit networks, neural gas net- works, feedforward neural network training, design of recur- About 1.3% of the bibliography is devoted to security rent neural networks [50], cellular neural networks, wavelet and military applications. These include network security, neural networks, neuron controllers. security-constrained power generation, intrusion detection, cryptography and cryptanalysis, security border identiﬁca- 3.20. Prediction and forecasting tion in power systems [58], weapon-target assignment, mis- sile eﬀectiveness optimisation. About 2.9% of the papers on applications in the bibliogra- phy have to do with prediction and forecasting. Topics in- clude water quality prediction and classiﬁcation, prediction 3.25. Sensor networks of chaotic systems, ecological models, meteorological predic- tions, electric load forecasting, battery pack state of charge 13 papers (1.9%) are devoted to sensors and, particularly, estimation, time series prediction, predictions of elephant sensor networks. Applications include wireless sensor net- migrations, prediction of the ﬂow stress in steel, prediction work sink node optimisation, ad hoc sensor networks node of surface roughness in end milling, streamﬂow forecast, ur- clustering, wireless sensor network design [59], estimation ban traﬃc ﬂow forecasting. of target position in wireless sensor networks, cluster forma- tion in wireless sensor networks, multicast routing in wireless 3.21. Power systems and plants sensor networks, odour source localisation, wireless video sensor networks optimisation, swarm-based mobile sensor A large proportion (5.8%) of the application papers in the networks, sensor scheduling for target tracking, distributed bibliography deals with power generation and power sys- sensor placement, and topology planning. tems. Speciﬁc applications include (see also [51]) automatic generation control, power transformer protection, load fore- casting, STATCOM power system, fault-tolerant control of 3.26. Signal processing compensators, optimal power dispatch, power system perfor- mance optimisation [52], secondary voltage control, power Approximately 3.8% of the bibliography is devoted to ap- control and optimisation, design of power system stabilisers, plications of PSO in signal processing. These include pat- control of photovoltaic systems, large-scale power plant con- tern recognition of ﬂatness signal, design of IIR ﬁlters, par- trol, operational planning for cogeneration systems, analysis ticle ﬁlter optimisation, nonlinear adaptive ﬁlters, Costas of power quality signals, generation planning and restructur- arrays, wavelets, blind detection, blind source separation, ing, hybrid power generation systems [53], optimal strate- analogue ﬁlter tuning, localisation of acoustic sources, dis- gies for electricity production [54], power loss minimisation, tributed odour source localisation, speech coding [60], 2D production costing, and operations planning. 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Analysis of the Publications on the Applications of Particle Swarm Optimisation

Analysis of the Publications on the Applications of Particle Swarm Optimisation

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Analysis of the Publications on the Applications of Particle Swarm Optimisation

Analysis of the Publications on the Applications of Particle Swarm Optimisation

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