Bat Algorithm (BAT)

A module for the bat optimization algorithm with differential operator, Levy flights trajectory, and parallel computing support.

Original papers:

• Xie, J., Zhou, Y., Chen, H. (2013). A novel bat algorithm based on differential operator and Lévy flights trajectory. Computational intelligence and neuroscience, 2013.

• Yang, X. S. (2010). A new metaheuristic bat-inspired algorithm. In Nature inspired cooperative strategies for optimization (NICSO 2010) (pp. 65-74). Springer, Berlin, Heidelberg.

What can you use?

• Multi processing: ✔️

• Discrete spaces: ✔️

• Continuous spaces: ✔️

• Mixed Discrete/Continuous spaces: ✔️

Parameters

class neorl.evolu.bat.BAT(mode, bounds, fit, nbats=50, fmin=0, fmax=1, A=0.5, r0=0.5, alpha=1.0, gamma=0.9, levy='False', int_transform='nearest_int', ncores=1, seed=None)

BAT 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': ['float', 0.1, 0.8], 'x2': ['float', 2.2, 6.2]}

• fit – (function) the fitness function

• nbats – (int): number of bats in the population

• fmin – (float): minimum value of the pulse frequency

• fmax – (float): maximum value of the pulse frequency

• A – (float) initial value of the loudness rate

• r0 – (float) asymptotic value of the pulse rate

• alpha – (float) decay factor of loudness A, i.e. A approaches 0 by the end of evolution if alpha < 1

• gamma – (float) exponential factor of the pulse rate r, i.e. r increases abruptly at the beginning and then converges to r0 by the end of evolution

• levy – (bool): a flag to activate Levy flight steps of the bat to increase bat diversity

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

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

• seed – (int) random seed for sampling

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

This function evolutes the BAT algorithm for number of generations.

Parameters

• ngen – (int) number of generations to evolute

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

• verbose – (bool) print statistics to screen

Returns

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

Example

from neorl import BAT

#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]

#setup and evolute BAT
bat=BAT(mode='min', bounds=BOUNDS, fit=FIT, nbats=40, 
        fmin=0, fmax=1, A=1.0, r0=0.7,
        ncores=1, seed=1)
x_best, y_best, bat_hist=bat.evolute(ngen=100, verbose=1)

Notes

• BAT mimics the echolocation behavior of bats in nature. The bats emit a very loud and short sound pulse; the echo that reflects back from the surrounding objects is received by their big ears. This feedback information of echo is analyzed by the bats, which reveals the direction of the flight pathway. The echo also helps the bats to distinguish different insects and obstacles to hunt prey, where the search for the prey here is analogous to the search for global optima.

• The bats start with loudness value of A, and decay it by a factor of alpha. If the user chooses alpha=1, fixed value of A is used.

• Bats fly randomly to search for the prey with frequency varying between fmin and fmax.

• The bats emit pulses with emission rate represented by the asymptotic value (r0). The value of emission rate is updated in generation i according to \(r_i = r_0(1-exp(-\gamma i))\), where gamma is the exponential factor of the pulse rate. r typically decreases abruptly at the beginning and then converges back to r0 by the end of the evolution.

• We provide a flexible BAT implemetation that can handle continuous (float), discrete (int), and categorical (grid) spaces and their mix. The user can control the type of discrete transformation via the argument int_transform.

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

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

• Total number of cost evaluations for BAT is 3*nbats * (ngen + 1).