This module implements a global optimization algorithm called Differential Evolution.

Consider the following optimization problem: \(min ~ f(\mathbf{x}) ~~ s.t. ~~ \mathbf{x} \\in D\), where \(D \\in \mathbb{R}^d\) and \(f: D \mapsto \mathbb{R}\). Class DifferentialEvolutionAlgorithm solves this optimization problem using the differential evolution algorithm. No further assumptions on the function \(f\) are needed. Thus it can be non-convex, noisy etc.

The domain \(D\) is implicitly specified by passing the function filtern_fn() to DifferentialEvolutionAlgorithm.

Some information related to Differential Evolution can be found in the following papers:

  1. Tvrdik 2008: http://www.proceedings2008.imcsit.org/pliks/95.pdf
  2. Fleetwood: http://www.maths.uq.edu.au/MASCOS/Multi-Agent04/Fleetwood.pdf
  3. Piyasatian: http://www-personal.une.edu.au/~jvanderw/DE_1.pdf

evolve_fn() is an adaptation of the following MATLAB code: http://www.icsi.berkeley.edu/~storn/DeMat.zip hosted on http://www.icsi.berkeley.edu/~storn/code.html#deb1.

class gc3libs.optimizer.dif_evolution.DifferentialEvolutionAlgorithm(initial_pop, de_strategy='DE_rand', de_step_size=0.85, prob_crossover=1.0, exp_cross=False, itermax=100, dx_conv_crit=None, y_conv_crit=None, in_domain=None, seed=None, logger=None, after_update_opt_state=[])

Differential Evolution Algorithm class. DifferentialEvolutionAlgorithm explicitly allows for an another process to control the optimization. Driver classes can be found in gc3libs.optimizer.drivers.py.

  • initial_pop – Initial population for the optimization. Value can be any sequence that can be passed to the np.array() constructor.
  • de_strategy (str) – e.g. DE_rand_either_or_algorithm. Allowed are:
  • de_step_size (float) – Differential Evolution step size.
  • prob_crossover (float) – Probability new population draws will replace old members.
  • exp_cross (bool) – Set True to use exponential crossover.
  • itermax (int) – Maximum # of iterations.
  • dx_conv_crit (float) – Abort optimization if all population members are within a certain distance to each other.
  • y_conv_crit (float) – Declare convergence when the target function is below a y_conv_crit.
  • in_domain (fun) – Optional function that implements nonlinear constraints.
  • seed (float) – Seed to initialize NumPy’s random number generator.
  • logger (obj) – Configured logger to use.
  • after_update_opt_state – List of Functions that are called at the end of DifferentialEvolutionAlgorithm.after_update_opt_state(). Use this list to provide problem-specific printing and plotting routines. Examples can be found in gc3libs.optimizer.extra.

The de_strategy value must be chosen from the dif_evolution.strategies enumeration. Allowed values are (description of the strategies taken from http://www.icsi.berkeley.edu/~storn/DeMat.zip):

  1. 'DE_rand': The classical version of DE.
  2. 'DE_local_to_best': A version which has been used by quite a number of
    scientists. Attempts a balance between robustness # and fast convergence.
  3. 'DE_best_with_jitter': Taylored for small population sizes and fast
    convergence. Dimensionality should not be too high.
  4. 'DE_rand_with_per_vector_dither': Classical DE with dither to become even more robust.
  5. 'DE_rand_with_per_generation_dither': Classical DE with dither to become even more robust.
    Choosing de_step_size = 0.3 is a good start here.
  6. 'DE_rand_either_or_algorithm': Alternates between differential mutation and three-point- recombination.

Generates a new population fullfilling in_domain.

Return type:list of population members
static evolve_fn(population, prob_crossover, de_step_size, dim, best_iter, de_strategy, exp_cross)

Return new population, evolved according to de_strategy.

  • population – Population generating offspring from.
  • prob_crossover – Probability new population draws will replace old members.
  • de_step_size – Differential Evolution step size.
  • dim – Dimension of each population member.
  • best_iter – Best population member of the current population.
  • de_strategy – Differential Evolution strategy. See DifferentialEvolutionAlgorithm.
  • bool (exp_cross) – Set True to use exponential crossover.
select(new_pop, new_vals)

Perform a one-on-one battle by index, keeping the member with lowest corresponding value.