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11 Mar 2019 ... If you are looking for a free Mac PDF editor so you can add or ... of a PDF , and even convert PDFs to Word, Excel and other file formats, we have ... a PDF tool that will let you import a PDF into Word (or Pages) and edit it there. 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:. pdf editor software free download: Free PDF Editor - Download pdf editor application for windows 10 Win PDF Editor : Edit PDF Content, Remove PDF Text - Downloada
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