globalbest

Global best, abbreviated gbest, is a concept in swarm intelligence and particle swarm optimization (PSO). It denotes the best position found by any particle in the entire swarm up to the current iteration. The gbest is used as the social component that guides particles toward regions of the search space that yielded high-quality solutions, contrasting with the local best, or lbest, which uses the best position found within a particle's neighborhood.

In standard PSO, each particle updates its velocity by combining inertia, cognitive attraction to its own best position (pbest), and social attraction toward the swarm's global best (gbest). A typical update is v_i = w*v_i + c1*r1*(pbest_i - x_i) + c2*r2*(gbest - x_i), and the position is updated accordingly. The use of gbest tends to converge quickly because all particles share the same guiding solution, but it can also lead to premature convergence on local optima.

Global best is central to PSO variants and is contrasted with neighborhood-based topologies where the best of a local group replaces gbest. The choice of topology affects exploration vs exploitation: gbest supports exploitation; ring or dynamic neighborhood topologies promote exploration and potentially better avoidance of local minima.

Origin and usage: PSO was introduced in 1995 by Kennedy and Eberhart as a population-based stochastic optimization method inspired by social behavior of birds and fish. Since then, gbest PSO has been applied to a wide range of optimization problems, including engineering design, neural network training, and parameter estimation.