Particle swarm optimization

In computational science, particle swarm optimization (PSO) is a computational method that optimizes a problem by iteratively trying to improve a population of candidate solutions with regard to a given measure of quality. It solves a problem through interactions among a population of candidate solutions, dubbed particles, moving the particles around in the search-space according to simple mathematical formulae that adjust each particle's position and velocity. Each particle's movement is influenced by its own best known position so far, and by the best known position in its topological neighborhood (which may include the entire population if so specified); vectors are updated as better positions are found. This is expected to move the swarm toward good solutions. PSO is originally attributed to Kennedy and Eberhart and was first intended for simulating social behaviour, as a stylized representation of the movement of organisms in a bird flock or fish school, or the evolution of attitudes in a human population. Simulation of principles of social behavior was observed to be capable of solving hard mathematical problems. The book by Kennedy and Eberhart describes many philosophical aspects of PSO and swarm intelligence. An extensive survey of PSO applications is made by Poli. In 2017, a comprehensive review on theoretical and experimental works on PSO was published by Bonyadi and Michalewicz. PSO is a metaheuristic as it makes few or no assumptions about the problem being optimized and can search very large spaces of candidate solutions. Also, PSO does not use the gradient of the problem being optimized, which means PSO does not require that the optimization problem be differentiable as is required by classic optimization methods such as gradient descent and quasi-newton methods. However, metaheuristics such as PSO do not guarantee an optimal solution is ever found.