Whale Optimization Algorithm (WOA)

A module for the Whale Optimization Algorithm with parallel computing support.

Original paper: Mirjalili, S., Lewis, A. (2016). The whale optimization algorithm. Advances in engineering software, 95, 51-67.

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What can you use?

  • Multi processing: ✔️

  • Discrete spaces: ✔️

  • Continuous spaces: ✔️

  • Mixed Discrete/Continuous spaces: ✔️

Parameters

class neorl.evolu.woa.WOA(mode, bounds, fit, nwhales=5, a0=2, b=1, int_transform='nearest_int', ncores=1, seed=None)[source]

Whale Optimization 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

  • nwhales – (int): number of whales in the population

  • a0 – (float): initial value for coefficient a, which is annealed from a0 to 0 (see Notes below for more info).

  • b – (float): constant for defining the shape of the logarithmic spiral

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

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

  • seed – (int) random seed for sampling

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

This function evolutes the WOA algorithm for number of generations.

Parameters

  • ngen – (int) number of generations to evolute

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

  • verbose – (bool) print statistics to screen

Returns

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

Example

from neorl import WOA
import matplotlib.pyplot as plt

#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]

nwhales=20
#setup and evolute WOA
woa=WOA(mode='min', bounds=BOUNDS, fit=FIT, nwhales=nwhales, a0=1.5, b=1, ncores=1, seed=1)
x_best, y_best, woa_hist=woa.evolute(ngen=100, verbose=1)

plt.figure()
plt.plot(woa_hist['a'], label='a')
plt.plot(woa_hist['A'], label='A')
plt.xlabel('generation')
plt.ylabel('coefficient')
plt.legend()
plt.show()

Notes

  • WOA mimics the social behavior of humpback whales, which is inspired by the bubble-net hunting strategy.

  • The whale leader is controlled by multiple coefficients, where a is considered the most important. The coefficient a balances WOA exploration and exploitation. The value of a is annealed “linearly” from a0 > 0 to 0 over the course of ngen. Typical values for a0 are 1, 1.5, 2, and 4.

  • Therefore, the user should notice that ngen value used within the .evolute function has an impact on the a value and hence on WOA overall performance.

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

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

  • Total number of cost evaluations for WOA is nwhales * (ngen + 1).