Cuckoo Search (CS)

A module for the Cuckoo Search Algorithm with parallel computing support.

Original paper: Yang, X. S., & Deb, S. (2009, December). Cuckoo search via Lévy flights. In 2009 World congress on nature & biologically inspired computing (NaBIC) (pp. 210-214). IEEE.

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What can you use?

  • Multi processing: ✔️

  • Discrete spaces: ✔️

  • Continuous spaces: ✔️

  • Mixed Discrete/Continuous spaces: ✔️

Parameters

class neorl.evolu.cs.CS(mode, bounds, fit, ncuckoos=15, pa=0.25, int_transform='nearest_int', ncores=1, seed=None)[source]

Cuckoo Search Algorithm

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

  • ncuckoos – (int) number of cuckoos or nests in the population: one cuckoos per nest. Default value is 15.

  • pa – (float) a scalar value for the coefficient that controls exploration/exploitation, i.e. fraction of the cuckoos/nests that will be replaced by the new cuckoos/nests.

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

  • ncores – (int) number of parallel processors (must be <= ncuckoos)

  • seed – (int) random seed for sampling

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

This function evolutes the CS algorithm for number of generations

Parameters

  • ngen – (int) number of generations to evolute

  • x0 – (list of lists) initial position of the cuckoos (must be of same size as ncuckoos)

  • verbose – (bool) print statistics to screen

Returns

(tuple) (best individual, best fitness, and dictionary containing major search results)

Example

from neorl import CS

#Define the fitness function
def Sphere(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]

#setup and evolute CS
cs = CS(mode = 'min', bounds = BOUNDS, fit = Sphere, ncuckoos = 40, pa = 0.25, seed=1)
x_best, y_best, cs_hist=cs.evolute(ngen = 200, verbose=True)

Notes

  • CS algorithm is based on the obligate brood parasitic behavior of some cuckoo species in combination with the Levy flight behavior of some birds and fruit flies. CS assumes each cuckoo lays one egg at a time, and dump its egg in randomly chosen nest. Also, the best nests with high quality of eggs will carry over to the next generations.

  • pa controls exploration/exploitation of the algorithm, it is the fraction of the cuckoos/nests that will be replaced by new cuckoos/nests. In this case, the host bird can either throw the egg away or abandon the nest, and build a completely new nest.

  • ncores argument evaluates the fitness of all cuckoos in the population in parallel. Therefore, set ncores <= ncuckoos for most optimal resource allocation.

  • Look for an optimal balance between ncuckoos and ngen, it is recommended to minimize the number of ncuckoos to allow for more updates and more generations.

  • Total number of cost evaluations for CS is 2*ncuckoos * (ngen + 1).