Entropy-based Memetic Particle Swarm Optimization for computing periodic orbits of nonlinear mappings

The computation of periodic orbits of nonlinear mappings is very important for studying and better understanding the dynamics of complex systems. Evolutionary algorithms have shown to be an efficient alternative for the computation of periodic orbits in cases where the inherent properties of the problem at hand render gradient-based methods invalid. Such cases usually involve nondifferentiable mappings or poorly behaved partial derivatives. We propose a Memetic Particle Swarm Optimization algorithm that exploits Shannon´s information entropy for decision making in swarm level, as well as a probabilistic decision making scheme in particle level, for determining when and where local search is applied. These decisions have a significant impact on the required number of function evaluations, especially in cases where high accuracy is desirable. Experimental results are performed on well-known problems and useful conclusions are derived.