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Reinitialize the entire swarm While this approach does neglect the swarm s memory and breaks the swarm out of a current optimum, it has the disadvantage that the swarm needs to search all over again If changes are not severe, the consequence is an unnecessary increase in computational complexity due to an increase in the number of iterations to converge to the new optimum The danger is also that the swarm may converge on a worse local optimum Reinitialization of the entire swarm is more e ective under severe environment changes Reinitialize only parts of the swarm, but make sure to retain the global best position The reinitialization of a percentage of the particle positions injects more diversity, and also preserves memory of the search space by keeping potentially good particles (existing particles may be close to the changed optimum) Hu and Eberhart experimented with a number of reinitialization percentages [386], and observed that lower reinitialization is preferred for smaller changes Larger changes require more particles to be reinitialized for e cient tracking It was also found empirically that total reinitialization is not e cient Particles memory of previous best positions is a major cause of the ine ciency of the PSO in tracking changing optima This statement is con rmed by the results of Carlisle and Dozier [107], where it was found that the cognition-only model showed poor performance The cognitive component promotes the nostalgic tendency to return to previously found best positions However, after a change in the environment, these positions become stale since they do not necessarily re ect the search space for the changed environment The consequence is that particles are attracted to outdated positions Carlisle and Dozier [107], and Hu and Eberhart [385] proposed that the personal best positions of all particles be reset to the current position of the particle when a change is detected This action e ectively clears the memory of all particles Resetting of the personal best positions is only e ective when the swarm has not yet converged to a solution [386] If this is the case, w(t)v(t) 0 and the contribution of the cognitive component will be zero for all particles, since (yi (t) xi (t)) = 0, i = 1, , ns Furthermore, the contribution of the social component will also e approximately zero, since, at convergence, all particles orbit around the same global best position (with an approximately zero swarm radius) Consequently, velocity updates are very small, as is the case for position updates To address the above problem, resetting of the personal best positions can be combined with partial reinitialization of the swarm [386] In this case, reinitialization increases diversity while resetting of the personal best positions prevents return to out-of-date positions Looking more carefully at the resetting of personal best positions, it may not always be a good strategy to simply reset all personal best positions Remember that by doing so, all particles forget any experience that they have gained about the search space during the search process It might just be that after an environment change, the personal best position of a particle is closer to the new goal than the current position Under less severe changes, it is possible that the personal best position remains the best position for that particle Carlisle and Dozier proposed that the personal best.

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3/9 Printer In Java Using Barcode generator for .Figure 161 Geometrical Illustration of Velocity and Position Updates for Single Two-Dimensional Particle The social component, c2 r2 ( xi ), in the case of the gbest PSO or, c2 r2 ( i y y xi ), in the case of the lbest PSO, which quanti es the performance of particle i relative to a group of particles, or neighbors Conceptually, the social component resembles a group norm or standard that individuals seek to attain The e ect of the social component is that each particle is also drawn towards the best position found by the particle s neighborhood The contribution of the cognitive and social components are weighed by a stochastic amount, c1 r1 or c2 r2 , respectively The e ects of these weights are discussed in more detail in Section 164. Dimensional Particle The social component, c2 r2 .Related: VB.NET Interleaved 2 of 5 Generating , PDF417 Printing .NET WinForms , .NET WinForms EAN-13 Generator

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positions will cause the swarm never to reach an equilibrium state While not all the methods discussed below consider this fact, all of the methods can address the problem by reducing the amount of chaos over time Kennedy and Eberhart [449] were the rst to mention the advantages of randomly reinitializing particles, a process referred to as craziness Although Kennedy mentioned the potential advantages of a craziness operator, no evaluation of such operators was given Since then, a number of researchers have proposed di erent approaches to implement a craziness operator for PSO When considering any method to add randomness to the swarm, a number of aspects need to be considered, including what should be randomized, when should randomization occur, how should it be done, and which members of the swarm will be a ected Additionally, thought should be given to what should be done with personal best positions of a ected particles These aspects are discussed next The diversity of the swarm can be increased by randomly initializing position vectors [534, 535, 863, 874, 875, 922, 923] and/or velocity vectors [765, 766, 922, 923, 924] By initializing positions, particles are physically relocated to a di erent, random position in the search space If velocity vectors are randomized and positions kept constant, particles retain their memory of their current and previous best solutions, but are forced to search in di erent random directions If a better solution is not found due to random initialization of the velocity vector of a particle, the particle will again be attracted towards its personal best position If position vectors are initialized, thought should be given to what should be done with personal best positions and velocity vectors Total reinitialization will have a particle s personal best also initialized to the new random position [534, 535, 923] This e ectively removes the particle s memory and prevents the particle from moving back towards its previously found best position (depending on when the global best position is updated) At the rst iteration after reinitialization the new particle is attracted only towards the previous global best position of the swarm Alternatively, reinitialized particles may retain their memory of previous best positions It should be noted that the latter may have less diversity than removing particle memories, since particles are immediately moving back towards their previous personal best positions It may, of course, happen that a new personal best position is found en route When positions are reinitialized, velocities are usually initialized to zero, to have a zero momentum at the rst iteration after reinitialization Alternatively, velocities can be initialized to small random values [923] Venter and Sobieszczanski-Sobieski [874, 875] initialize velocities to the cognitive component before reinitialization This ensures a momentum back towards the personal best position The next mportant question to consider is when to reinitialize If reinitialization happens too soon, the a ected particles may not have had su cient time to explore their current regions before being relocated If the time to reinitialization is too long, it may happen that all particles have already converged This is not really a problem, other than wasted computational time since no improvements are seen in this state Several approaches have been identi ed to decide when to reinitialize:.

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