Particle Swarm Optimization

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(PSO). This is an evolutionary algorithm based on swarm behavior of animals, like bird flocking. A move from a state is influenced by directions of states in its neighborhood. A consensus function is used to average neighbors' best fitness values, and this is combined with the original state's fitness to obtain a new position for the state. It applies to continuous variables, using a velocity term to derive state increments. The fundamental equation that governs state evolution is

LaTeX: 
v_p = wv_p + A r (x^*_p - x_p) + B r' (g^* - x_p)

where p is a particle, or state, and

LaTeX: v_p = velocity vector of particle LaTeX: p
LaTeX: x_p = position vector of particle LaTeX: p
LaTeX: x^*_p = previous position of particle LaTeX: p giving best fitness value
LaTeX: g^*_p = position of globally best fitness value
LaTeX: w = parameter, called "inertia weight"
LaTeX: r, r' are pseudo-random numbers in LaTeX: [0,1]
LaTeX: A, B = positive parameters, generally in LaTeX: [1,2]


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