optimization

Trials and errors (grid search)

Implementation of a grid search optimization.

It should be used for reference only as the search space will almost certainly be too big.

pylinkage.optimization.grid_search.fast_variator(divisions, bounds)

Return an iterable of elements’ all possibles variations.

Number of variations: ((max_dim - 1 / min_dim) / delta_dim) ** len(ite).

Here the order in the variations is not important.

Parameters:

• divisions (int) – Number of subdivisions between bounds.

• bounds (tuple[tuple[float], tuple[float]]) – 2-uple of minimal then maximal bounds.

Returns:

An iterable of all the dimension combinations.

Return type:

Generator[float]

pylinkage.optimization.grid_search.sequential_variator(center, divisions, bounds)

Return an iterable of each possible variation for the elements.

Number of variations: ((max_dim - 1 / min_dim) / delta_dim) ** len(ite).

Because linkage is not tolerant to violent changes, the order of output for the coefficients is very important.

The coefficient is in order: middle → min (step 2), min → middle (step 2), middle → max (step 1), so that there is no huge variation.

Parameters:

• center (Iterable[float]) – Elements that should vary.

• divisions (int) – Number of subdivisions between bounds.

• bounds (tuple[tuple[float], tuple[float]]) – 2-uple of minimal then maximal bounds.

Returns:

An iterable of all the dimension combinations.

Return type:

Generator[float]

pylinkage.optimization.grid_search.tqdm_verbosity(iterable, verbose=True, *args, **kwargs)

Wrapper for tqdm, that let you specify if you want verbosity.

Deprecated since version 0.6.0: tqdm_verbosity will be removed in pylinkage 0.7.0, as tqdm can be disabled with the argument disable=True.

Parameters:

• iterable –

• verbose – (Default value = True)

• args – Ordered args to pass to tqdm

• kwargs – Keyword args for tqdm

pylinkage.optimization.grid_search.trials_and_errors_optimization(eval_func, linkage, parameters=None, n_results=10, divisions=5, **kwargs)

Return the list of dimensions optimizing eval_func.

Each dimension set has a score, which is added in an array of n_results results, contains the linkages with the best scores in a maximization problem by default.

Parameters:

• eval_func (Callable) – Evaluation function. Input: (linkage, num_constraints, initial_coordinates). Output: score (float)

• linkage (pylinkage.linkage.Linkage) – Linkage to evaluate.

• parameters (list) – Parameters that will be modified. Geometric constraints. If not, it will be assigned tuple(linkage.get_num_constraints()). The default is None.

• n_results (int) – Number of the best candidates to return. The default is 10.

• divisions (int) – Number of subdivisions between bounds. The default is 5.

• kwargs (dict) –

  • Extra arguments for the optimization.

  • boundsA 2-uple (tuple of two elements), containing the minimal and maximal bounds.

    If None, we will use parameters as a center. (Default value = None).

  • order_relationA function of two arguments, should return the best score of two

    scores. Common examples are min, max, abs. (Default value = max()).

  • verboseThe number of combinations will be printed in console if True.

    (Default value = True).

  • sequential : If True, two consecutive linkages will have a small variation.

Returns:

3-uplet of score, dimensions and initial position for each Linkage to return. Its size is {n_results}.

Return type:

list[MutableAgent]

Particle Swarm Optimization

Implementation of a particle swarm optimization.

Created on Fri Mar 8, 13:51:45 2019.

@author: HugoFara

pylinkage.optimization.particle_swarm.particle_swarm_optimization(eval_func, linkage, center=None, dimensions=None, n_particles=100, leader=3.0, follower=0.1, inertia=0.6, neighbors=17, iters=200, bounds=None, order_relation=<built-in function max>, verbose=True, **kwargs)

Particle Swarm Optimization wrapper for pyswarms.

This function is a simple wrapper to optimize a linkage using PSO. It will mainly call the LocalBestPSO function from pyswarms.single.

Parameters:

• eval_func (Callable -> float) – The evaluation function. Input: (linkage, num_constraints, initial_coordinates). Output: score (float). The swarm will look for the HIGHEST score.

• linkage (pylinkage.linkage.Linkage) – Linkage to be optimized. Make sure to give an optimized linkage for better results

• center (list) – A list of initial dimensions. If None, dimensions will be generated randomly between bounds. The default is None.

• dimensions (int) – Number of dimensions of the swarm space, number of parameters. If None, it takes the value len(tuple(linkage.get_num_constraints())). The default is None.

• n_particles (float) – Number of particles in the swarm. The default is 100.

• inertia (float) – Inertia of each particle, w in pyswarms. The default is .3.

• leader (float) – Learning coefficient of each particle, c1 in pyswarms. The default is .2.

• follower (float) – Social coefficient, c2 in pyswarms. The default is .5.

• neighbors (int) – Number of neighbors to consider. The default is 17.

• iters (int) – Number of iterations to describe. The default is 200.

• bounds (sequence of two list of float) – Bounds to the space, in format (lower_bound, upper_bound). (Default value = None)

• order_relation (Callable(float, float) -> float) – How to compare scores. There should not be anything else than the built-in max and min functions. The default is max.

• verbose (bool) – The optimization state will be printed in the console if True. (Default value = True).

• kwargs (dict) – keyword arguments to pass to pyswarm.local.single.LocalBestPSO.

Returns:

List of 3 elements: best score, best dimensions and initial positions.

Return type:

Agent

Utility

Utility for optimization.

pylinkage.optimization.utils.generate_bounds(center, min_ratio=5, max_factor=5)

Simple function to generate bounds from a linkage.

Parameters:

• center (Iterable) – 1-D sequence, often in the form of linkage.get_num_constraints().

• min_ratio (float) – Minimal compression ratio for the bounds. Minimal bounds will be of the shape center[x] / min_ratio. (Default value = 5)

• max_factor (float) – Dilation factor for the upper bounds. Maximal bounds will be of the shape center[x] * max_factor. (Default value = 5)