# Explorations and explanations and exploitations

324Chapter Seven—The Particle Swarm

**Summary**

The No Free Lunch theorem argues that no single algorithm can opti-mize better than any other, if we compare them on all possible objective functions. But it turns out that most “possible” functions are uninterest-ing; they fail to qualify to be considered problems. Given the subset of situations that researchers really do concern themselves with, it

ispossi-ble to demonstrate that one algorithm has the advantage over another. One way to find these differences is by trying the algorithms on sets of problems that are known to be difficult, for different reasons; one may

The particle swarm algorithm imitates human social behavior. Indi-viduals interact with one another while learning from their own experi-ence, and gradually the population members move into better regions of the problem space. The algorithm is extremely simple—it can be de-scribed in one straightforward formula—but it is able to surmount many of the obstacles that optimization problems commonly present. In Chapter 8 we will see that the simple formula generates rich and com-plex effects. Researchers have investigated numerous ways to manipulate the search trajectories of the particles, and some of these ways have re-sulted in improvements and insights.