Particle Swarm Optimization
Particle swarm optimization (PSO) was first described by J. Kennedy and R. Eberhart in 1995. The algorithm was originally conceived as a way of simulating social behaviour. A common analogy is of a flock of birds, flying over a field with varying concentrations of food. Each "bird" has a memory of the best food source it has found so far ("local best"), as well as the best food source that the flock has found ("global best"). Each bird tends to fly toward a randomly weighted average of the "local best" and the "global best". Each bird has momentum, so they will not make sharp or sudden changes in direction. After a number of iterations, the flock has made a thorough search of the area, and most of the flock is converging on the best available food source in the area.
In order to apply PSO to capital works optimization projects in the water industry, an "objective function" is formulated. The objective function is made up of real capital and operating costs, and artificial costs engineered to cause the optimization to steer away from undesirable solutions. During the optimization, the particles (or "birds") fly through "n"-dimensional space, where "n" is the number of decision variables available. Beginning with an initial population scattered randomly across the problem space (or "field"), the swarm (or "flock") will begin to converge on the lowest point on the objective function after a number of iterations.
