How to Optimize a Function with the Mixed (Continuous and Discrete) Search Space

In some cases, search space consists of both continuous subspace and discrete subspace. ZOOpt can solve this kind of mixed optimization problem easily.

We define a variant of Sphere function in fx.py for minimization.

def sphere_mixed(solution):
    """Sphere function for mixed optimization"""
    x = solution.get_x()
    value = sum([i*i for i in x])
    return value

Then, define corresponding objective and parameter.

Finally, use ZOOpt to optimize.

from fx import sphere_mixed
from zoopt import Dimension, Objective, Parameter, ExpOpt


# mixed optimization
def minimize_sphere_mixed():
    """
    Mixed optimization example of minimizing sphere function, which has mixed search search space.

    :return: no return
    """

    # setup optimization problem
    dim_size = 100
    dim_regs = []
    dim_tys = []
    # In this example, the search space is discrete if this dimension index is odd, Otherwise, the search space
    # is continuous.
    for i in range(dim_size):
        if i % 2 == 0:
            dim_regs.append([0, 1])
            dim_tys.append(True)
        else:
            dim_regs.append([0, 100])
            dim_tys.append(False)
    dim = Dimension(dim_size, dim_regs, dim_tys)
    objective = Objective(sphere_mixed, dim)  # form up the objective function

    budget = 100 * dim_size  # number of calls to the objective function
    parameter = Parameter(budget=budget)

    ExpOpt.min(objective, parameter, repeat=1, plot=True)

For a few seconds, the optimization is done. Visualized optimization progress looks like

More concrete examples are available in the example/simple_functions/mixed_opt.py file .