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Hence, particles will have di erent global guides This ensures that particles are attracted to di erent solutions The local guide of each particle is simply the personal best position of the particle Personal best positions are only updated if the new position, xi (t + 1) yi (t) The global guide replaces the global best, and the local guide replaces the personal best in the velocity update equation In addition to the normal position update, a mutation operator (also referred to as a craziness operator in the context of PSO) is applied to the particle positions The degree of mutation decreases over time, and the probability of mutation also decreases over time That is, xij (t + 1) = N (0, (t))xij (t) + vij (t + 1) where, for example with (0) an initial large variance The MOPSO developed by Coello Coello and Lechuga is summarized in Algorithm 1614 Algorithm 1614 Coello Coello and Lechuga MOPSO Create and initialize an nx -dimensional swarm S; Let A = and Ans = 0; Evaluate all particles in the swarm; for all non-dominated xi do A = A {xi }; end Generate hypercubes; Let yi = xi for all particles; repeat Select global guide, y; Select local guide, yi ; Update velocities using equation (162); Update positions using equation (1696); Check boundary constraints; Evaluate all particles in the swarm; Update the repository, A; until stopping condition is true; (t) = (0) e t (1696) (1697) asp.net pdf editor component ASP.NET PDF Editor: view, create, convert, annotate, redact, edit ...
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CuteEditor - A powerful ASP . NET Wysiwyg Editor . ... This example demonstrates you can use Cute Editor to create industry standard PDF files on the fly. In the ... 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 environment changes this information becomes stale If, after an environment change, particles are still allowed to make use of this, now stale, information, they are. asp.net core pdf editor RAD PDF - The ASP.NET AJAX PDF Viewer and PDF Editor
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