OneMax

Description:

Optimization (max)

Single-objective

Constraints (no)

The general problem statement is given by:

We have a state vector \(\mathbf{x} \in [0, 1]^M\) of bits, such as: \(\mathbf{x} = (0, 0, 1, 1, 0, ..., 1)\).

The optimal solution is the one where each variable has the value of ‘1’.

\[f(\mathbf{x}) = \sum_{i=1}^{M} x_i, \text{ with } x_i \in \{0, 1\}\]
Global maximum is found at:

\[f(1, 1, ..., 1) = M\]

Step 1: Import python libraries and StarPSO classes

import numpy as np
from star_pso.population.swarm import Swarm
from star_pso.population.particle import Particle
from star_pso.engines.binary_pso import BinaryPSO
from star_pso.utils.auxiliary import cost_function

Step 2: Define the objective function

@cost_function
def fun_one_max(x: np.ndarray, **kwargs) -> tuple[float, bool]:

    # Compute the function value.
    f_val = np.sum(x)

    # Condition for termination.
    solution_found = f_val == len(x)

    # Return the solution tuple.
    return f_val, solution_found

Step 3: Set the PSO parameters

# Set a seed for reproducible initial population.
SEED = 1821

# Random number generator.
rng = np.random.default_rng(SEED)

# Define the number of optimizing variables.
n_dim = 30

# Define the number of particles.
n_pop = 60

# Sample the initial points randomly.
X_t0 = rng.integers(low=0, high=1, endpoint=True, size=(n_pop, n_dim))

# Initial population (swarm).
swarm_t0 = Swarm([Particle(x) for x in X_t0])

# Create a BinaryPSO object that will perform the optimization.
test_PSO = BinaryPSO(initial_swarm = swarm_t0, obj_func = fun_one_max)

Step 4: Run the optimization

test_PSO.run(max_it = 1000,
             options = {"w0": 0.70, "c1": 1.50, "c2": 1.50, "mode": "g_best"},
             reset_swarm = False, verbose = False, adapt_params = False)

Step 5: Final output

# Get the optimal solution from the PSO.
i_opt, f_opt, x_opt = test_PSO.get_optimal_values()

# Display the (final) optimal value.
print(f"Optimum Found: {f_opt} / {D}, at iteration {i_opt}.\n")

# Display each particle position value.
print(f"Optimum position: {x_opt}")