Category: Tutorials

Applications of Particle Swarm Optimization
Particle swarm optimization can be used in a variety of different applications. A few examples involving nonconvex, multiobjective, discontinuous search spaces and applications in neural networks and support vector machines are mentioned.

Indepth details of Particle Swarm Optimization
I explain and show code to construct the Particle Swarm Optimization in Python. I conclude by optimizing on the Rastrigin function, a function that researchers use to test optimization algorithms on.

An Overview of Particle Swarm Optimization
Particle swarm optimization is often used to optimize functions in rather unfriendly nonconvex, noncontinuous spaces. The idea behind the algorithm involves a swarm of particles flying through a space both collaboratively and independently.

Lyapunov spectra of inverted discrete dynamical systems
One can estimate the lyapunov spectrum of dynamical systems and their inverted counterparts using local Jacobian matrices and Wolf’s algorithm.

Modelling Sensitivity using Neural Networks
Artificial neural networks can be applied to the delayed Henon map and shown to replicate the sensitivities of the map surprisingly well.

Inverted Delayed Henon Map
Inverting the delayed Henon map yields a repellor whose sensitivities can be explored.

Delayed Henon Map Sensitivities
Partial derivatives can be used to explore how sensitive the output of a function is to perturbations in each of the time lags.