optimatic.optimisers package

Submodules

optimatic.optimisers.differential_evolution module

Implements Differential Evolution to find the minimum of a function \(f:\mathbb{R}^n \rightarrow \mathbb{R}\). See https://en.wikipedia.org/wiki/Differential_evolution

class optimatic.optimisers.differential_evolution.Agent(dims, search, parent)

Bases: object

class optimatic.optimisers.differential_evolution.Optimiser(f, search, cr, F, NP, precision=1e-07, steps=10000)

Bases: optimatic.optimisers.optimiser_base.Optimiser

Parameters:

• f – The function being optimised
• search – The min/max value in each dimension to search in. This should be provided as a nummpy array of the format [[x_min, x_max], [y_min, y_max], ..], where \([x_{min}, x_{max}]\) is the search space in the \(x\) dimension, etc. This should be of length \(n\).
• cr – Crossover probability
• F – Differential weight
• NP – Number of agents to use
• precision – Algorithm will stop when \(||\mathbf{x}_n - \mathbf{x}_{n-1}|| < \text{precision}\), where \(\mathbf{x}_n\) and \(\mathbf{x}_{n-1}\) are the positions of the two agents closest to the minimum.
• steps – Max number of iterations to perform

optimise()

step()

optimatic.optimisers.grad_desc module

Gradient descent optimisation

Implements gradient descent to optimise a function \(f:\mathbb{R}^n \rightarrow \mathbb{R}\).

Uses the reccurence relation:

\[\mathbf{x}_n = \mathbf{x}_{n-1} - \gamma_n \nabla f(\mathbf{x}_{n-1})\]

Where

\[\gamma_n = \frac{(\mathbf{x}_n - \mathbf{x}_{n-1}) \cdot (\mathbf{\nabla}f(\mathbf{x}_n) - \mathbf{\nabla} f(\mathbf{x}_{n-1}))}{||\mathbf{\nabla}f(\mathbf{x}_n) - \mathbf{\nabla}f(\mathbf{x}_{n-1})||^2}\]

class optimatic.optimisers.grad_desc.Optimiser(f, x0, df=None, gamma=0.1, precision=1e-07, steps=10000)

Bases: optimatic.optimisers.optimiser_base.Optimiser

Parameters:

• f – The function to optimise
• x0 – The starting position for the algorithm
• df – The derivative of the function to optimise. If this isn’t provided, it will be estimated from \(f\) using central_diff()
• precision – The precision to calculate the minimum to
• gamma – The starting value for \(\gamma\)
• steps – The max number of iterations of the algorithm to run

step()

optimatic.optimisers.optimiser_base module

Optimiser base class

All optimiser classes should inherit from this class

class optimatic.optimisers.optimiser_base.Optimiser(f, x0, precision=1e-07, steps=10000)

Bases: object

Parameters:

• f – The function to optimise
• x0 – The starting position for the algorithm
• precision – The precision to calculate the minimum to
• steps – The max number of iterations of the algorithm to run

optimise()

Runs step() the specified number of times

step()

Runs one iteration of the algorithm

Module contents