Differential Evolution (DE)

A module for differential evolution (DE) that optimizes a problem by iteratively trying to improve a candidate solution. DE maintains the population of candidate solutions and creating new candidate solutions by combining existing ones according to simple combination methods. The candidate solution with the best score/fitness is reported by DE.

Original paper: Storn, Rainer, and Kenneth Price. “Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces.” Journal of global optimization 11.4 (1997): 341-359.

What can you use?

  • Multi processing: ✔️

  • Discrete spaces: ✔️

  • Continuous spaces: ✔️

  • Mixed Discrete/Continuous spaces: ✔️

Parameters

class neorl.evolu.de.DE(mode, bounds, fit, npop=50, F=0.5, CR=0.3, int_transform='nearest_int', ncores=1, seed=None, **kwargs)[source]

Parallel Differential Evolution

Parameters

  • mode – (str) problem type, either “min” for minimization problem or “max” for maximization

  • bounds – (dict) input parameter type and lower/upper bounds in dictionary form. Example: bounds={'x1': ['int', 1, 4], 'x2': ['float', 0.1, 0.8], 'x3': ['float', 2.2, 6.2]}

  • fit – (function) the fitness function

  • npop – (int) number of individuals in the population

  • F – (float) differential/mutation weight between [0,2]

  • CR – (float) crossover probability between [0,1]

  • int_transform – (str): method of handling int/discrete variables, choose from: nearest_int, sigmoid, minmax.

  • ncores – (int) number of parallel processors

  • seed – (int) random seed for sampling

evolute(ngen, x0=None, verbose=False)[source]

This function evolutes the DE algorithm for number of generations.

Parameters

  • ngen – (int) number of generations to evolute

  • x0 – (list of lists) the initial individuals of the population

  • verbose – (bool) print statistics to screen

Returns

(tuple) (best individual, best fitness, and a list of fitness history)

Example

from neorl import DE

#Define the fitness function
def FIT(individual):
    """Sphere test objective function.
            F(x) = sum_{i=1}^d xi^2
            d=1,2,3,...
            Range: [-100,100]
            Minima: 0
    """
    y=sum(x**2 for x in individual)
    return y

#Setup the parameter space (d=5)
nx=5
BOUNDS={}
for i in range(1,nx+1):
    BOUNDS['x'+str(i)]=['float', -100, 100]

de=DE(mode='min', bounds=BOUNDS, fit=FIT, npop=60, F=0.5, CR=0.7, ncores=1, seed=1)
x_best, y_best, de_hist=de.evolute(ngen=100, verbose=1)

Notes

  • Start with a crossover probability CR considerably lower than one (e.g. 0.2-0.3). If no convergence is achieved, increase to higher levels (e.g. 0.8-0.9)

  • F is usually chosen between [0.5, 1].

  • The higher the population size npop, the lower one should choose the weighting factor F

  • You may start with npop =10*d, where d is the number of input parameters to optimise (degrees of freedom).

  • Total number of cost evaluations for DE is 2 * npop * ngen.