The swarm and the queen: towards a deterministic and adaptive particle swarm optimization

A very simple particle swarm optimization iterative algorithm is presented, with just one equation and one social/confidence parameter. We define a "no-hope" convergence criterion and a "rehope" method so that, from time to time, the swarm re-initializes its position, according to some gradient estimations of the objective function and to the previous re-initialization (it means it has a kind of very rudimentary memory). We then study two different cases, a quite "easy" one (the Alpine function) and a "difficult" one (the Banana function), but both just in dimension two. The process is improved by taking into account the swarm gravity center (the "queen") and the results are good enough so that it is certainly worthwhile trying the method on more complex problems.