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Early results of the application of the PSO to type I environments (refer to Section A9) with small spatial severity showed that the PSO has an implicit ability to track changing optima [107, 228, 385] Each particle progressively converges on a point on the line that connects its personal best position with the global best position [863, 870] The trajectory of a particle can be described by a sinusoidal wave with diminishing amplitude around the global best position [651, 652] If there is a small change in the location of an optimum, it is likely that one of these oscillating particles will discover the new, nearby optimum, and will pull the other particles to swarm around the new optimum However, if the spatial severity is large, causing the optimum to be displaced outside the radius of the contracting swarm, the PSO will fail to locate the new optimum due to loss of diversity In such cases mechanisms need to be employed to increase the swarm diversity Consider spatial changes where the value of the optimum remains the same after the change, ie f (x (t)) = f (x (t + 1)), with x (t) = x (t + 1) Since the tness remains the same, the global best position does not change, and remains at the old optimum Similarly, if f (x (t)) > f (x (t+1)), assuming minimization, the global best position will also not change Consequently, the PSO will fail to track such a changing minimum This problem can be solved by re-evaluating the tness of particles at time t + 1 and updating global best and personal best positions However, keep in mind that the same problem as discussed above may still occur if the optimum is displaced outside the radius of the swarm One of the goals of optimization algorithms for dynamic environments is to locate the optimum and then to track it The self-adaptation ability of the PSO to track optima (as discussed above) assumes that the PSO did not converge to an equilibrium state in its rst goal to locate the optimum When the swarm reaches an equilibrium (ie converged to a solution), vi = 0 The particles have no momentum and the contributions from the cognitive and social components are zero The particles will remain in this stable state even if the optimum does change In the case of dynamic environments, it is possible that the swarm reaches an equilibrium if the temporal severity is low (in other words, the time between consecutive changes is large) It is therefore important to read the literature on PSO for dynamic environments with this aspect always kept in mind The next aspects to consider are the in uence of particle memory, velocity clamping and the inertia weight The question to answer is: to what extent do these parameters and characteristics of the PSO limit or promote tracking of changing optima These aspects are addressed next: Each particle has a memory of its best position found thus far, and velocity is adjusted to also move towards this position Similarly, each particle retains information about the global best (or local best) position When the nvironment changes this information becomes stale If, after an environment change, particles are still allowed to make use of this, now stale, information, they are.





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It is sensitive to the ordering of objectives, since optimization is biased towards improving the second objective Parsopoulos and Vrahatis [659, 660, 664, 665] developed the vector evaluated PSO (VEPSO), on the basis of the vector-evaluated genetic algorithm (VEGA) developed by Scha er [761] (also refer to Section 963) VEPSO uses two sub-swarms, where each sub-swarm optimizes a single objective This algorithm is therefore applicable to MOPs with only two objectives VEPSO follows a kind of coevolutionary approach The global best particle of the rst swarm is used in the velocity equation of the second swarm, while the second swarm s global best particle is sed in the velocity update of the rst swarm That is, S1 vij (t + 1) S2 vij (t + 1) = + = + wS1 vij (t) + c1 r1j (t)(S1 yij (t) S1 xij (t)) c2 r2j (t)(S2 i (t) S1 xij (t)) y wS2 vij (t) + c1 r1j (t)(S2 yij (t) S2 xij (t)) c2 rij (t)(S1 j (t) Sx2j (t)) y. the selection tness values The global guide for particle . ECC200 Generator In Java Using Barcode maker for Java .Related: Excel Interleaved 2 of 5 Generation , Create Intelligent Mail VB.NET , Generate ISBN VB.NET

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