lam: int = 10

budget_factor = 5

seed = 42

rng = None

def sample_conditional_binomial(self, p: float, n: int) -> int:

"""Sample Binomial(n, p), but ensure in [1, n]."""

k = sum(1 for _ in range(n) if self.rng.random() < p)

if k < 1:

k = 1

elif k > n:

k = n

return

def __call__(self, f, seed = 1) -> tuple[float, np.ndarray]:

"""

self.seed = seed

self.rng = np.random.default_rng(self.seed)

n = f.meta_data.n_variables

budget = self.budget_factor * n * n

# Initialize x within bounds (PBO: binary {0,1})

x = self.rng.integers(0,2,n)

fx = f(x)

mutation_rate = 0.2

while f.state.evaluations < budget:

# Generate λ offspring

best_y = None

best_fy = None

for _ in range(self.lam):

tmp_mr = 1.0 / (1.0 + (((1.0 - mutation_rate) / mutation_rate) * math.exp(0.22 * rng.normal(0,1))))

ell = self.sample_conditional_binomial(tmp_mr,n)

idx = self.rng.choice(n, size=ell, replace=False)

y = x.copy()

# bit flip for {0,1}: new = lb + ub - old (works for 0/1 bounds)

y[idx] = 1 - y[idx]

fy = f(y)

if best_y is None:

best_y, best_fy, win_r = y, fy, tmp_mr

else:

if fy > best_fy:

best_y, best_fy, win_r = y, fy, tmp_mr

if best_fy >= fx:

x, fx = best_y, best_fy

if best_fy >= f.optimum.y:

break

mutation_rate = win_r