2Introduction : Swarm Intelligence Study of collective behavior in decentralized, self- organized systems.Originated from the study of colonies, or swarms of social organisms.Collective intelligence arises from interactions.
3Introduction Particle Swarm Optimization: Introduced by Kennedy & Eberhart 1995Inspired by social behavior of birds and shoals of fishSwarm intelligence-based optimizationNondeterministicPopulation-based optimizationPerformance comparable to Genetic algorithms
4Particle Swarm Optimization Swarm : a set of particles (S)Particle: a potential solutionPosition,Velocity ,Each particle maintainsIndividual best position:Swarm maintains its global best:
5PSO Algorithm Basic algorithm of PSO: Initialize the swarm from the solution spaceEvaluate fitness of each particleUpdate individual and global bestsUpdate velocity and position of each particleGo to step 2, and repeat until termination condition
6PSO Algorithm (cont.) Original velocity update equation: with : acceleration constantInertiaCognitive ComponentSocial Component
8PSO Algorithm - Parameters Acceleration constantSmall values limit the movement of the particlesLarge values : tendency to explode toward infinityIn generalMaximum velocityVelocity is a stochastic variable => uncontrolled trajectory
9Initialize swarm and evaluate fitness (t=0) Simple 1D ExampleInitialize swarm and evaluate fitness (t=0)gbest
10Update velocity and position (t=1) Simple 1D ExampleUpdate velocity and position (t=1)gbest
11Update personal and global best (t=2) Simple 1D ExampleEvaluate fitnessUpdate personal and global best (t=2)gbest
12Update personal and global best (t=2) Simple 1D ExampleEvaluate fitnessUpdate personal and global best (t=2)gbest
13Update velocity and position (t=2) Simple 1D ExampleUpdate velocity and position (t=2)gbestInertiaPersonalSocialTotal
14Rate of Convergence Improvement Inertia weight:Scaling the previous velocityControl search behaviorHigh values explorationLow values exploitation
15PSO with Inertia weight can be decreased over time:Linear [0.9 to 0.4]Nonlinearmain disadvantage:once the inertia weight is decreased, the swarm loses its ability to search new areas (can not recover its exploration mode).
16Rate of Convergence Improvement Constriction Factor:Canonical PSOTypically ,Can converge without using Vmax (velocity clamping)Improve the convergence by damping the oscillations
17Swarm Topologies Two general types of neighborhoods: Global best (gbest) : fully connected networkLocal best (lbest) : according to a topologyRingWheelVon Neumanngbestlbest
18Lbest vs. GbestGbest converges fast but may be trapped in a local optima.Lbest is slower in convergence but has more chances to find an optimal solution.Most efficient neighborhood structure, in general, depends on the type of problem.Fully Informed PSO (FIPS):Each individual is influenced by successes of all its neighbors.
19Diversity Improvement Based on lbest model.Usually slow down the convergence rate.Spatial Neighborhoods:Partition particles based on spatial location.Calculate the largest distance between any two particles.Select neighboring particles according to ratio:Selection threshold can be varied over time.Start with small ratio (lbest) and gradually increase the ratio.
20Diversity Improvement Neighborhood Topologies:In lbest model, all particles can exchange information indirectly.Average path length depends on the topology.Topology significantly affects the performance (experimentally).Randomly change some connections can change average path length.i i i+2
21Diversity Improvement Subpopulations:Previously used in GA.Original swarm is partitioned to subpopulations.PSO is applied to each subpopulation.An interaction scheme is used for information sharing between subpopulations.Each subpopulation can search the smaller region of search space.
22Discrete PSO Binary PSO: Introduces by kennedy and Eberhart. Each individual (particle) has to take a binary decision.Predisposition is derived based on individual and group performance:Previous statepredisposition
23Binary PSO (cont.)determines a threshold in the probability function and therefore should be bounded in the range of [0.0, 1.0].state of the dth position in the string at time t:Where is a random number with a uniform distribution.1Vid
24PSO Variants Hybrid PSO Adaptive PSO PSO in complex environments Incorporate the capabilities of other evolutionary computation techniques.Adaptive PSOAdaptation of PSO parameters for a better performance.PSO in complex environmentsMultiobjective or constrained optimization problems or tracking dynamic systems.Other variantsvariations to the original formulation to improve its performance.
25Hybrid PSOGA-PSO:combines the advantages of swarm intelligence and a natural selection mechanism.jump from one area to another by the selection mechanism accelerating the convergence speed.capability of “breeding”.replacing agent positions with low fitness values, with those with high fitness, according to a selection rate
26Hybrid PSO EPSO: The particle movement is defined as: Evolutionary PSO Incorporates a selection procedureSelf-adapting of parametersThe particle movement is defined as:
27Hybrid PSO : EPSO Mutation of weights and global best: Learning parameters can be either fixed or dynamically changing as strategic parameters.Survival Selection:Stochastic tournament.
29Hybrid PSO : DEPSO Hybrid of Differential Evolution and PSO. A DE operator applied to the particle’s best position to eliminate the particles falling into local minima.Alternation:Original PSO algorithm at the odd iterations.DE operator at the even iterations.
30Hybrid PSO : DEPSO DE mutation on particle’s best positions: where k is a random integer value within [1,n] which ensures the mutation in at least one dimension.Trial point:For each dth dimention:
32Dynamic Tracking in PSO The classical PSO is very effective in solving static optimization problems but is not as efficient when applied to a dynamic system in which the optimal value may change repeatedly.An adaptive approach has been introduced for this problem:Detection of environmental changes:changed-gbest-valuefixed-gbest-valuesrerandomizing a certain number of particles
33ApplicationsConvenience of realization, properties of low constraint on the continuity of objective function and joint of search space, and ability of adapting to dynamic environment, make PSO be applied in more and more fields.Some PSO applications:Electronics and electromagneticSignal, Image and video processingNeural networksCommunication networks…