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.

[1]  H. Niederreiter,et al.  Localization of Search in Quasi-Monte Carlo Methods for Global Optimization , 1986 .

[2]  Russell C. Eberhart,et al.  A new optimizer using particle swarm theory , 1995, MHS'95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science.

[3]  Russell C. Eberhart,et al.  A discrete binary version of the particle swarm algorithm , 1997, 1997 IEEE International Conference on Systems, Man, and Cybernetics. Computational Cybernetics and Simulation.

[4]  Yue Shi,et al.  A modified particle swarm optimizer , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

[5]  Russell C. Eberhart,et al.  Parameter Selection in Particle Swarm Optimization , 1998, Evolutionary Programming.

[6]  J. Kennedy,et al.  Matching algorithms to problems: an experimental test of the particle swarm and some genetic algorithms on the multimodal problem generator , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

[7]  P. J. Angeline,et al.  Using selection to improve particle swarm optimization , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).