partikelsvärmoptimering

Particle swarm optimization (PSO) is a population-based stochastic optimization technique inspired by the collective behavior of birds flocking or fish schooling. It searches for optima by adjusting the trajectories of a group of candidate solutions, called particles, in a continuous search space.

Introduced by Kennedy and Eberhart in 1995, PSO has become widely used for function optimization, neural network training, and engineering design. It is valued for its simplicity, few parameters, and ability to handle nonlinear, multimodal landscapes.

In a PSO run, each particle has a position x_i and a velocity v_i in D dimensions. Each particle remembers its best position pbest_i found so far, and the swarm remembers the best position gbest found by any particle. At each iteration, velocities are updated by v_i ← w v_i + c1 r1 (pbest_i − x_i) + c2 r2 (gbest − x_i), and positions by x_i ← x_i + v_i, where w is an inertia weight, c1 and c2 are cognitive and social coefficients, and r1, r2 are random factors in [0,1].

Variants include using a constriction factor to guarantee convergence, modifying topology from global best (gbest) to local best (lbest) where neighborhoods influence updates, and adapting PSO to discrete or mixed search spaces. Discrete PSO variants are used for combinatorial problems, while multi-objective and hybrid PSO approaches combine PSO with other optimization techniques.

Applications span continuous optimization problems, engineering design, control, parameter tuning, neural network training, feature selection, and scheduling. PSO is praised for fast convergence and ease of implementation, but can suffer from premature convergence and sensitivity to parameter settings in complex or high-dimensional landscapes.