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 (note pso maximizes fitness, so we negate the function):

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:

space_min = [-1.5, -3]
space_max = [4, 4]

Finally, we run our particle swarm optimization. We choose to run the algorithm for 10 iterations, with a swarm size of 50 particles, alongside the default inertia, cognitive, and social weights, as well as the default velocity clamping of 0.1:

from quickopt.pso import pso
result = pso(funct=objective, space_min=space_min, space_max=space_max, iterations=10, swarm_size=50, verbose=1)

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