Examples

McCormick Function

The McCormick function is a multimodal function that is commonly used to test optimization algorithms. It is defined as f(x,y) = sin(x + y) + (x - y)**2 - 1.5*x + 2.5*y + 1 along the domain [-1.5, 4] x [-3, 4]. The global minimum of this function is located at f(-0.54719, -1.54719) = -1.9133.

We implement the McCormick function as follows:

import numpy as np
def objective(params):
    x, y = params
    return np.sin(x + y) + (x - y)**2 - 1.5*x + 2.5*y + 1

We then define our search space:

lower_bounds = [-1.5, -3]
upper_bounds = [4, 4]

Finally, we run our bayesian optimization algorithm. We choose to run the algorithm for only 20 iterations, with 50 initial samples:

from quickopt.bayesopt_tpe import bayesopt_tpe
result = bayesopt_tpe(funct=objective, space_min=lower_bounds, space_max=upper_bounds, iterations=20, samples=50, verbose=1)

The following is a heatmap of the optimization process, with each point representing a new optimal solution found by the algorithm: