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. The number of parameters, N, is equal to len(x).
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 func. The total number of bounds is used to determine the number of parameters, N.
Any additional fixed parameters needed to completely specify the objective function.
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'
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 * N
A multiplier for setting the total population size. The population has popsize * N individuals. This keyword is overridden if an initial population is supplied via the init keyword. When using init='sobol' the population size is calculated as the next power of 2 after popsize * N.
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.
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.
Prints the evaluated func at every iteration.
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 True, then the minimization is halted (any polishing is still carried out).
If True (default), then scipy.optimize.minimize with the 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 trust-constr method is used instead. For large problems with many constraints, polishing can take a long time due to the Jacobian computations.
Set the maximum number of function evaluations. However, it probably makes more sense to set maxiter instead.
Specify which type of population initialization is performed. Should be one of:
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 * N. '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.
If '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 'deferred', the best solution vector is updated once per generation. Only 'deferred' is compatible with parallelization or vectorization, and the workers and vectorized keywords can over-ride this option.
If workers is an int the population is subdivided into workers sections and evaluated in parallel (uses multiprocessing.Pool <multiprocessing>). Supply -1 to use all cores available to the Process. Alternatively supply a map-like callable, such as multiprocessing.Pool.map for evaluating the population in parallel. This evaluation is carried out as workers(func, iterable). This option will override the updating keyword to updating='deferred' if workers != 1. Requires that func be pickleable.
Constraints on the solver, over and above those applied by the bounds kwd. Uses the approach by Lampinen.
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 init is given an initial population. x0.shape == (N,).
For each decision variable, a boolean value indicating whether the decision variable is constrained to integer values. The array is broadcast to (N,). If any decision variables are constrained to be integral, they will not be changed during polishing. Only integer values lying between the lower and upper bounds are used. If there are no integer values lying between the bounds then a ValueError is raised.
If vectorized is True, func is sent an x array with x.shape == (N, S), and is expected to return an array of shape (S,), where S is the number of solution vectors to be calculated. If constraints are applied, each of the functions used to construct a Constraint object should accept an x array with x.shape == (N, S), and return an array of shape (M, S), where M is the number of constraint components. This option is an alternative to the parallelization offered by workers, and may help in optimization speed. This keyword is ignored if workers != 1. This option will override the updating keyword to updating='deferred'.
This class implements the differential evolution solver
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