Category: Tutorials
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Applications of Particle Swarm Optimization
Particle swarm optimization can be used in a variety of different applications. A few examples involving nonconvex, multi-objective, discontinuous search spaces and applications in neural networks and support vector machines are mentioned.
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In-depth 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.
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An Overview of Particle Swarm Optimization
Particle swarm optimization is often used to optimize functions in rather unfriendly non-convex, non-continuous spaces. The idea behind the algorithm involves a swarm of particles flying through a space both collaboratively and independently.
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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.
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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.
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Inverted Delayed Henon Map
Inverting the delayed Henon map yields a repellor whose sensitivities can be explored.
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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.