Parameters

func : callable

The objective function to be minimized. Must be in the form f(x, *args) , where x is the argument in the form of a 1-D array and args is a tuple of any additional fixed parameters needed to completely specify the function.

bounds : sequence or `Bounds`

Bounds for variables. There are two ways to specify the bounds: 1. Instance of Bounds class. 2. (min, max) pairs for each element in x , defining the finite lower and upper bounds for the optimizing argument of :None:None:`func`. It is required to have len(bounds) == len(x) . len(bounds) is used to determine the number of parameters in x .

args : tuple, optional

Any additional fixed parameters needed to completely specify the objective function.

strategy : str, optional

The differential evolution strategy to use. Should be one of:

• 'best1bin'

• 'best1exp'

• 'rand1exp'

• 'randtobest1exp'

• 'currenttobest1exp'

• 'best2exp'

• 'rand2exp'

• 'randtobest1bin'

• 'currenttobest1bin'

• 'best2bin'

• 'rand2bin'

• 'rand1bin'

The default is 'best1bin'

maxiter : int, optional

The maximum number of generations over which the entire population is evolved. The maximum number of function evaluations (with no polishing) is: (maxiter + 1) * popsize * len(x)

popsize : int, optional

A multiplier for setting the total population size. The population has popsize * len(x) individuals. This keyword is overridden if an initial population is supplied via the :None:None:`init` keyword. When using init='sobol' the population size is calculated as the next power of 2 after popsize * len(x) .

tol : float, optional

Relative tolerance for convergence, the solving stops when np.std(pop) <= atol + tol * np.abs(np.mean(population_energies)) , where and atol and :None:None:`tol` are the absolute and relative tolerance respectively.

mutation : float or tuple(float, float), optional

The mutation constant. In the literature this is also known as differential weight, being denoted by F. If specified as a float it should be in the range [0, 2]. If specified as a tuple (min, max) dithering is employed. Dithering randomly changes the mutation constant on a generation by generation basis. The mutation constant for that generation is taken from U[min, max). Dithering can help speed convergence significantly. Increasing the mutation constant increases the search radius, but will slow down convergence.

recombination : float, optional

The recombination constant, should be in the range [0, 1]. In the literature this is also known as the crossover probability, being denoted by CR. Increasing this value allows a larger number of mutants to progress into the next generation, but at the risk of population stability.

seed : {None, int, `numpy.random.Generator`,

numpy.random.RandomState }, optional

If seed is None (or :None:None:`np.random`), the numpy.random.RandomState singleton is used. If seed is an int, a new RandomState instance is used, seeded with seed . If seed is already a Generator or RandomState instance then that instance is used. Specify seed for repeatable minimizations.

disp : bool, optional

Prints the evaluated :None:None:`func` at every iteration.

callback : callable, `callback(xk, convergence=val)`, optional

A function to follow the progress of the minimization. xk is the current value of x0 . val represents the fractional value of the population convergence. When val is greater than one the function halts. If callback returns :None:None:`True`, then the minimization is halted (any polishing is still carried out).

polish : bool, optional

If True (default), then scipy.optimize.minimize with the :None:None:`L-BFGS-B` method is used to polish the best population member at the end, which can improve the minimization slightly. If a constrained problem is being studied then the :None:None:`trust-constr` method is used instead.

maxfun : int, optional

Set the maximum number of function evaluations. However, it probably makes more sense to set :None:None:`maxiter` instead.

init : str or array-like, optional

Specify which type of population initialization is performed. Should be one of:

• 'latinhypercube'

• 'sobol'

• 'halton'

• 'random'

• array specifying the initial population. The array should have shape (M, len(x)) , where M is the total population size and len(x) is the number of parameters. :None:None:`init` is clipped to :None:None:`bounds` before use.

The default is 'latinhypercube'. Latin Hypercube sampling tries to maximize coverage of the available parameter space.

'sobol' and 'halton' are superior alternatives and maximize even more the parameter space. 'sobol' will enforce an initial population size which is calculated as the next power of 2 after popsize * len(x) . 'halton' has no requirements but is a bit less efficient. See scipy.stats.qmc for more details.

'random' initializes the population randomly - this has the drawback that clustering can occur, preventing the whole of parameter space being covered. Use of an array to specify a population could be used, for example, to create a tight bunch of initial guesses in an location where the solution is known to exist, thereby reducing time for convergence.

atol : float, optional

Absolute tolerance for convergence, the solving stops when np.std(pop) <= atol + tol * np.abs(np.mean(population_energies)) , where and atol and :None:None:`tol` are the absolute and relative tolerance respectively.

updating : {'immediate', 'deferred'}, optional

If :None:None:`immediate` the best solution vector is continuously updated within a single generation. This can lead to faster convergence as trial vectors can take advantage of continuous improvements in the best solution. With :None:None:`deferred` the best solution vector is updated once per generation. Only :None:None:`deferred` is compatible with parallelization, and the :None:None:`workers` keyword can over-ride this option.

workers : int or map-like callable, optional

If :None:None:`workers` is an int the population is subdivided into :None:None:`workers` sections and evaluated in parallel (uses :None:None:`multiprocessing.Pool <multiprocessing>`). Supply :None:None:`-1` to use all cores available to the Process. Alternatively supply a map-like callable, such as :None:None:`multiprocessing.Pool.map` for evaluating the population in parallel. This evaluation is carried out as workers(func, iterable) . This option will override the :None:None:`updating` keyword to :None:None:`updating='deferred'` if :None:None:`workers != 1`. Requires that :None:None:`func` be pickleable.

constraints : {NonLinearConstraint, LinearConstraint, Bounds}

Constraints on the solver, over and above those applied by the :None:None:`bounds` kwd. Uses the approach by Lampinen.

x0 : None or array-like, optional

Provides an initial guess to the minimization. Once the population has been initialized this vector replaces the first (best) member. This replacement is done even if :None:None:`init` is given an initial population.

This class implements the differential evolution solver

Examples

See :

Local connectivity graph

Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.

Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)

SVG is more flexible but power hungry; and does not scale well to 50 + nodes.

All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them

---

GitHub : /scipy/optimize/_differentialevolution.py#334
type: <class 'type'>
Commit: