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At xed intervals, as is done in the mass extinction PSO developed by Xie et al [923, 924] As discussed above, xed intervals may prematurely reinitialize a particle Probabilistic approaches, where the decision to reinitialize is based on a probability In the dissipative PSO, Xie et al [922] reinitialize velocities and positions based on chaos factors that serve as probabilities of introducing chaos in the system Let cv and cl , with cv , cl [0, 1], be respectively the chaos factors for velocity and location Then, for each particle, i, and each dimension, j, if rij U (0, 1) < cv , then the velocity component is reinitialized to vij (t + 1) = U (0, 1)Vmax,j Also, if rij U (0, 1) < cl , then the position component is initialized to xij (t + 1) U (xmin,j , xmax,j ) A problem with this approach is that it will keep the swarm from reaching an equilibrium state To ensure that an equilibrium can be reached, while still taking advantage of chaos injection, start with large chaos factors that reduce over time The initial large chaos factors increase diversity in the rst phases of the search, allowing particles to converge in the nal stages A similar probabilistic approach to reinitializing velocities is followed in [765, 766] Approaches based on some convergence condition, where certain events trigger reinitialization Using convergence criteria, particles are allowed to rst exploit their local regions before being reinitialized Venter and Sobieszczanski-Sobieski [874, 875] and Xie et al [923] initiate reinitialization when particles do not improve over time Venter and SobieszczanskiSobieski evaluate the variation in particle tness of the current swarm If the variation is small, then particles are centered in close proximity to the global best position Particles that are two standard deviations away from the swarm center are reinitialized Xie et al count for each xi = y the number of times that f (xi ) f ( ) < When this count exceeds a given threshold, the corresponding y particle is reinitialized Care should be taken in setting values for and the count threshold If is too large, particles will be reinitialized before having any chance of exploiting their current regions Clerc [133] de nes a hope and re-hope criterion If there is still hope that the objective can be reached, particles are allowed to continue in their current search directions If not, particles are reinitialized around the global best position, taking into consideration the local shape of the objective function Van den Bergh [863] de ned a number of convergence tests for a multi-start PSO, namely the normalized swarm radius condition, the particle cluster condition and the objective function slope condition (also refer to Section 1616 for a discussion on these criteria) L vberg and Krink [534, 535] use self-organized criticality (SOC) to determine when to reinitialize particles Each particle maintains an additional variable, Ci , referred to as the criticality of the particle If two particles are closer than a threshold distance, , from one another, then both have their criticality increased by one The larger the criticality of all particles, the more uniform the swarm becomes To prevent criticality from building up, each Ci is reduced by a fraction in each iteration As soon as Ci > C, where C is the global criticality limit, particle i is reinitialized Its criticality is distributed to its immediate neighbors. azure pdf Azure – Integration of PDF Acrobat Reader with Azure Information ...
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