c2r2gbest

c2r2gbest is a variant of particle swarm optimization (PSO) that emphasizes the global-best guidance and the use of a social learning factor with a random component. In this variant, the cognitive term associated with a particle’s personal best is typically omitted, making the swarm’s movement primarily influenced by the best position found so far by the collective.

The velocity update is usually expressed as v_i(t+1) = w v_i(t) + c2 r2 (gbest(t) - x_i(t)), and the position update is x_i(t+1) = x_i(t) + v_i(t+1). Here w is the inertia weight, c2 is the social learning coefficient, r2 is a random number drawn from a uniform distribution in [0,1], gbest(t) is the best position found by the swarm up to time t, and x_i(t) is the current position of particle i. The absence of the cognitive term (pbest) differentiates c2r2gbest from many standard PSO variants.

Purpose and behavior: By relying on the global best and a stochastic social term, c2r2gbest tends to exploit the region around the best solution while the random component and inertia help sustain exploration. This can lead to faster convergence in smooth landscapes but may reduce diversity in complex, multimodal problems.

Applications and considerations: c2r2gbest is applicable to continuous optimization tasks where rapid convergence to a promising region is desired. Its performance depends on parameter settings (w, c2, and the handling of r2) and may require tuning or adaptive strategies to mitigate premature convergence.

See also: Particle swarm optimization; global-best PSO.