The Particle SwarmOptimization AlgorithmDecision Support2010-2011Andry PintoHugo AlvesIns DominguesLus !ochaSusana "ruzSummaryIntroduction to Particle Swarm Optimization #PSO$Origins"oncept PSO AlgorithmPSO %or the &in Pac'ing Pro(lem #&PP$Pro(lem )ormulationAlgorithmSimulation !esultsIntroduction to the PSO* Origins Inspired %rom the nature social (ehavior and dynamic movements with communications o% insects+ (irds and ,shIntroduction to the PSO* Origins In -./0+ "raig !eynolds descri(ed this process in 1 simple (ehaviors*Separationavoid crowding local 2oc'mates Alignmentmove towards the average heading o% local 2oc'mates Cohesionmove toward the average position o% local 2oc'mates Introduction to the PSO* OriginsApplication to optimization*Particle Swarm OptimizationProposed (y 3ames 4ennedy 5 !ussell 6(erhart #-..7$"om(ines sel%8e9periences with social e9periencesIntroduction to the PSO* Concept:ses a num(er o% agents #particles$ that constitute a swarm moving around in the search space loo'ing %or the (est solution6ach particle in search space ad;usts its ovement towards a promising area to get the glo(al optimum6ach particle 'eeps trac'*its (est solution+ personal (est+ pbestthe (est value o% any particle+ glo(al (est+ gbestIntroduction to the PSO* Concept6ach particle ad;usts its travelling speed dynamically corresponding to the 2ying e9periences o% itsel% and its colleagues6ach particle modi,es its position according to*its current positionits current velocitythe distance (etween its current position and pbestthe distance (etween its current position and gbestIntroduction to the PSO* Algorithm - NeighborhoodgeographicalsocialIntroduction to the PSO* Algorithm - Neighborhoodglo(alIntroduction to the PSO* Algorithm - ParameterssAlgorithm parametersA * Population o% agentspi * Position o% agent ai in the solution spacef * O(;ective %unction vi * ?elocity o% agent@s ai V(ai) * Aeigh(orhood o% agent ai#,9ed$The neigh(orhood concept in PSO is not the same as the one used in other meta8heuristics search+ since in PSO each particle@s neigh(orhood never changes #is ,9ed$Introduction to the PSO* AlgorithmB9CD E PSO#$P E ParticleFInitialization#$G)or iE- to it_max )or each particle p in P dofp E %#p$G I% fp is (etter than %#pBest$ pBest E pGend end gBest E (est p in PG )or each particle p in P dov E v I c1CrandC#pBest J p$ I c2CrandC#gBest J p$Gp E p I vG endendIntroduction to the PSO* AlgorithmParticle update rulep E p I v withv E v I c1 C rand C #pBest J p$ I c2 C rand C #gBest J p$wherep* particle@s positionv* path direction c1* weight o% local in%ormation c2* weight o% glo(al in%ormationpBest* (est position o% the particlegBest* (est position of the swarmrand* random varia(leIntroduction to the PSO* Algorithm - ParametersAum(er o% particles usually (etween -K and 7KC1 is the importance o% personal (est valueC2 is the importance o% neigh(orhood (est value:sually C1 I C2 E L #empirically chosen value$I% velocity is too low algorithm too slowI% velocity is too high algorithm too unsta(leIntroduction to the PSO* Algorithm-M "reate a Npopulation@ o% agents #particles$ uni%ormly distri(uted over O PM 6valuate each particle@s position according to the o(;ective %unction1M I% a particle@s current position is (etter than its previous (est position+ update itLM Determine the (est particle #according to the particle@s previous (est positions$Introduction to the PSO* Algorithm7M :pdate particles@ velocities*0M >ove particles to their new positions*QM Ro to step P until stopping criteria are satis,edIntroduction to the PSO* AlgorithmParticle@s velocity* Makes the particle moe in the same direction and !ith the same elocit"1# $nertia2# Personal $n%uence Social $n%uence $mproes the indiidual Makes the particle return to a preious position' better than the current Conseratie Makes the particle (ollo! the best neighbors directionIntroduction to the PSO* AlgorithmIntensi,cation* e9plores the previous solutions+ ,nds the (est solution o% a given regionDiversi,cation* searches new solutions+ ,nds the regions with potentially the (est solutionsIn PSO*Introduction to the PSO* Algorithm - )*ampleIntroduction to the PSO* Algorithm - )*ampleIntroduction to the PSO* Algorithm - )*ampleIntroduction to the PSO* Algorithm - )*ampleIntroduction to the PSO* Algorithm - )*ampleIntroduction to the PSO* Algorithm - )*ampleIntroduction to the PSO* Algorithm - )*ampleIntroduction to the PSO* Algorithm - )*ampleIntroduction to the PSO* Algorithm CharacteristicsAdantagesInsensitive to scaling o% design varia(lesSimple implementation6asily parallelized %or concurrent processingDerivative %ree?ery %ew algorithm parameters?ery eScient glo(al search algorithmDisadantagesTendency to a %ast and premature convergence in mid optimum pointsSlow convergence in re,ned search stage #wea' local search a(ility$Introduction to the PSO* Di+erent ApproachesSeeral approaches2-D Otsu PSOActive Target PSOAdaptive PSOAdaptive Mutatin PSOAdaptive PSO !uided b" Acce#eratin $nfrmatin Attractive %epu#sive Partic#e S&arm Optimi'atinBinar" PSOCperative Mu#tip#e PSOD"namic and Ad(ustab#e PSO)xtended Partic#e S&arms *Davoud Sedighizadeh and 6llips >asehian+ ethods+ Ta9onomy and Applications=MInternational 3ournal o% "omputer Theory and 6ngineering+ ?olM -+ AoM 7+ Decem(er PKK. On s#ving Mu#tib(ective Bin Pac+ing Prb#em ,sing Partic#e S&arm Optimi'atin DMS Liu+ 4M"M Tan+ "M4M Roh and TM4M HoPKK0 8 I666 "ongress on 6volutionary "omputation)irst implementation o% PSO %or &PPPSO %or the &PP*$ntroductionPSO %or the &PP*Problem ,ormulation>ulti8O(;ective PD &PP>a9imum o% $ (ins with width - and height .3 items with &( / -+ 0( / . and weight jO(;ectives>inimize the num(er o% (ins used 4>inimize the average deviation (etween the overall centre o% gravity and the desired onePSO %or the &PP*$nitiali-ation:sually generated randomlyIn this wor'*Solution %rom &ottom Le%t )ill #&L)$ heuristicTo sort the rectangles %or &L)*!andomAccording to a criteria #width+ weight+ area+ perimeterMM$PSO %or the &PP* $nitiali-ation ./,Item moved to the right i% intersection detected at the topItem moved to the top i% intersection detected at the rightItem moved i% there is a lower availa(le space %or insertionPSO %or the &PP*Algorithm ?elocity depends on either pbest or gbest* never (oth at the same time O!PSO %or the &PP* Algorithm-st Stage*Partial Swap (etween P (ins>erge P (insSplit - (inPnd Stage* !andom rotation1rd Stage* !andom shuUe >utation modes %or a single particlePSO %or the &PP* AlgorithmThe 2owchart o% H>OPSOH hy(ridM multiS swarmO objectiveP particleO optimizationPSO %or the &PP* Problem ,ormulation0 classes with PK instances randomly generatedSize range*"lass -* BK+ -KKD"lass P* BK+ P7D"lass 1* BK+ 7KD"lass L* BK+ Q7D"lass 7* BP7+ Q7D"lass 0* BP7+ 7KD"lass P* small items V more diScult to pac'PSO %or the &PP*Simulation 0esults"omparison with P other methods>OPSO #>ultio(;ective PSO$ %rom B-D>O6A #>ultio(;ective 6volutionary Algorithm$ %rom BPDDe,nition o% parameters*B-D Tang+ 4M PM+ Huang+ LM+ Whou "M RM and Pang+ TM+ OPSO o(tained in%erior results compared to the other twoPSO %or the &PP*ConclusionsPresentation o% a mathematical model %or >O&PP8PD>O&PP8PD solved (y the proposed H>OPSO&L) chosen as the decoding heuristicH>OPSO is a ro(ust search optimization algorithm"reation o% varia(le length data structureSpecialized mutation operatorH>OPSO per%orms consistently well with the (est average per%ormance on the per%ormance metricOutper%orms >OPSO and >O6A in most o% the test cases used in this paperThe Particle SwarmOptimization Algorithm11