Grey Wolf Optimizer (GWO)

A module for the Grey Wolf Optimizer with parallel computing support.

Original paper: Mirjalili, S., Mirjalili, S. M., & Lewis, A. (2014). Grey wolf optimizer. Advances in engineering software, 69, 46-61.

What can you use?

• Multi processing: ✔️

• Discrete spaces: ✔️

• Continuous spaces: ✔️

• Mixed Discrete/Continuous spaces: ✔️

Parameters

class neorl.evolu.gwo.GWO(mode, bounds, fit, nwolves=5, int_transform='nearest_int', ncores=1, seed=None)

Grey Wolf Optimizer

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

• nwolves – (int): number of the grey wolves in the group

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

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

• seed – (int) random seed for sampling

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

This function evolutes the GWO algorithm for number of generations.

Parameters

• ngen – (int) number of generations to evolute

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

• verbose – (bool) print statistics to screen

Returns

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

Example

from neorl import GWO
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]

nwolves=5
gwo=GWO(mode='min', fit=FIT, bounds=BOUNDS, nwolves=nwolves, ncores=1, seed=1)
x_best, y_best, gwo_hist=gwo.evolute(ngen=100, verbose=1)

#-----
#or with fixed initial guess for all wolves (uncomment below)
#-----
#x0=[[-90, -85, -80, 70, 90] for i in range(nwolves)]
#x_best, y_best, gwo_hist=gwo.evolute(ngen=100, x0=x0)

plt.figure()
plt.plot(gwo_hist['alpha_wolf'], label='alpha_wolf')
plt.plot(gwo_hist['beta_wolf'], label='beta_wolf')
plt.plot(gwo_hist['delta_wolf'], label='delta_wolf')
plt.plot(gwo_hist['fitness'], label='best')
plt.xlabel('Generation')
plt.ylabel('Fitness')
plt.legend()
plt.show()

Notes

• GWO assigns the best fitness to the first wolf (called Alpha), second best fitness to Beta wolf, third best fitness to Delta wolf, while the remaining wolves in the group are called Omega, which follow the leadership and position of Alpha, Beta, and Delta.

• ncores argument evaluates the fitness of all wolves in the group in parallel. Therefore, set ncores <= nwolves for most optimal resource allocation.

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

• Total number of cost evaluations for GWO is nwolves * ngen.