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drawn to the old optimum an optimum that may no longer exist in the changed environment It can thus be seen that particle memory (from which the global best is selected) is detrimental to the ability of PSO to track changing optima A solution to this problem is to reinitialize or to re-evaluate the personal best positions (particle memory) The inertia weight, together with the acceleration coe cients balance the exploration and exploitation abilities of the swarm The smaller w, the less the swarm explores Usually, w is initialized with a large value that decreases towards a small value (refer to Section 1632) At the time that a change occurs, the value of w may have reduced too much, thereby limiting the swarm s exploration ability and its chances of locating the new optimum To alleviate this problem, the value of w should be restored to its initial large value when a change in the environment is detected This also needs to be done for the acceleration coe cients if adaptive accelerations are used Velocity clamping also has a large in uence on the exploration ability of PSO (refer to 1631) Large velocity clamping (ie small Vmax,j values) limits the step sizes, and more rapidly results in smaller momentum contributions than lesser clamping For large velocity clamping, the swarm will have great di culty in escaping the old optimum in which it may nd itself trapped To facilitate tracking of changing objectives, the values of Vmax,j therefore need to be chosen carefully When a change in environment is detected, the optimization algorithm needs to react appropriately to adapt to these changes To allow timeous and e cient tracking of optima, it is important to correctly and timeously detect if the environment did change The task is easy if it is known that changes occur periodically (with the change frequency known), or at predetermined intervals It is, however, rarely the case that prior information about when changes occur is available An automated approach is needed to detect changes based on information received from the environment Carlisle and Dozier [106, 109] proposed the use of a sentry particle, or more than one sentry particle The task of the sentry is to detect any change in its local environment If only one sentry is used, the same particle can be used for all iterations However, feedback from the environment will then only be from one small part of the environment Around the sentry the environment may be static, but it may have changed elsewhere A better strategy is to select the particle randomly from the swarm for each iteration Feedback is then received from di erent areas of the environment A sentry particle stores a copy of its most recent tness value At the start of the next iteration, the tness of the sentry particle is re-evaluated and compared with its previously stored value If there is a di erence in the tness, a change has occurred More sentries allow simultaneous feedback from more parts of the environment If multiple sentries are used detection of changes is faster and more reliable However, the tness of a sentry particle is evaluated twice per iteration If tness evaluation is costly, multiple sentries will signi cantly increase the computational complexity of the search algorithm As an alternative to using randomly selected sentry particles, Hu and Eberhart [385].

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Taxpayer Identification Number (TIN)

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proposed to monitor changes in the tness of the global best position By monitoring the tness of the global best particle, change detection is based on globally provided information To increase the accuracy of change detection, Hu and Eberhart [386] later also monitored the global second-best position Detection of the second-best and global best positions limits the occurrence of false alarms Monitoring of these global best positions is based on the assumption that if the optimum location changes, then the optimum value of the current location also changes One of the rst studies in the application of PSO to dynamic environments came from Carlisle and Dozier [107], where the e ciency of di erent velocity models (refer to Section 1635) has been evaluated Carlisle and Dozier observed that the social-only model is faster in tracking changing objectives than the full model However, the reliability of the social-only model deteriorates faster than the full model for larger update frequencies The sel ess and cognition-only models do not perform well on changing environments Keep in mind that these observations were without changing the original velocity models, and should be viewed under the assumption that the swarm had not yet reached an equilibrium state Since this study, a number of other studies have been done to investigate how the PSO should be changed to track dynamic optima These studies are summarized in this section From these studies in dynamic environments, it became clear that diversity loss is the major reason for the failure of PSO to achieve more e cient tracking Eberhart and Shi [228] proposed using the standard PSO, but with a dynamic, randomly selected inertia coe cient For this purpose, equation (1624) is used to select a new w(t) for each time step In their implementation, c1 = c2 = 1494, and velocity clamping was not done As motivation for this change, recall from Section 1631 that velocity clamping restricts the exploration abilities of the swarm Therefore, removal of velocity clamping facilitates larger exploration, which is highly bene cial Furthermore, from Section 1632, the inertia coe cient controls the exploration exploitation trade-o Since it cannot be predicted in dynamically changing environments if exploration or exploitation is preferred, the randomly changing w(t) ensures a good mix of focusing on both exploration and exploitation While this PSO implementation presented promising results, the e ciency is limited to type I environments with a low severity and type II environments where the value of the optimum is better after the change in the environment This restriction is mainly due to the memory of particles (ie the personal best positions and the global best selected from the personal best positions), and that changing the inertia will not be able to kick the swarm out of the current optimum when vi (t) 0, i = 1, , ns A very simple approach to increase diversity is to reinitialize the swarm, which means that all particle positions are set to new random positions, and the personal best and neighborhood best positions are recalculated Eberhart and Shi [228] suggested the following approaches: Do not reinitialize the swarm, and just continue to search from the current position This approach only works for small changes, and when the swarm has not yet reached an equilibrium state.

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Enter your TIN in the appropriate box For individuals, this is your social security number (SSN) However, for a resident alien, sole proprietor, or disregarded entity, see the Part I instructions on page 3 For other entities, it is your employer identification number (EIN) If you do not have a number, see How to get a TIN on page 3 Note: If the account is in more than one name, see the chart on page 4 for guidelines on whose number to enter

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