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import numpy as np
from dataclasses import dataclass
@dataclass
class Hyperparameters:
max_integer: int = 250
num_restarts: int = 5
num_search_steps: int = 1000
initial_temperature: float = 0.01
def compute_c6(u_set: np.ndarray) -> float:
"""Compute the C6 lower bound for a given set U."""
if len(u_set) < 2:
return -1.0
U = np.array(u_set, dtype=int)
u_plus_u = np.unique(U[:, None] + U[None, :])
u_minus_u = np.unique(U[:, None] - U[None, :])
size_U_plus_U = len(u_plus_u)
size_U_minus_U = len(u_minus_u)
max_U = np.max(U)
if max_U == 0:
return -1.0
ratio = size_U_minus_U / size_U_plus_U
c6_bound = 1 + np.log(ratio) / np.log(2 * max_U + 1)
return c6_bound
def run_single_trial(hypers: Hyperparameters, seed: int):
"""Run one trial of simulated annealing search."""
np.random.seed(seed)
# Initialize a random sparse set, ensuring 0 is included
sparsity = 0.95
u_mask = np.random.random(hypers.max_integer + 1) > sparsity
u_mask[0] = True # Ensure 0 is included
current_set = np.where(u_mask)[0]
current_c6 = compute_c6(current_set)
best_set = current_set.copy()
best_c6 = current_c6
for step in range(hypers.num_search_steps):
temp = hypers.initial_temperature * (1 - step / hypers.num_search_steps)
temp = max(temp, 1e-6)
# Propose a random mutation: flip a random element (except 0)
idx = np.random.randint(1, hypers.max_integer + 1)
new_mask = u_mask.copy()
new_mask[idx] = not new_mask[idx]
new_set = np.where(new_mask)[0]
if len(new_set) < 2:
continue
new_c6 = compute_c6(new_set)
delta = new_c6 - current_c6
# Accept if better, or probabilistically if worse
if delta > 0 or np.random.random() < np.exp(delta / temp):
u_mask = new_mask
current_set = new_set
current_c6 = new_c6
if current_c6 > best_c6:
best_c6 = current_c6
best_set = current_set.copy()
return best_set, best_c6
def run():
hypers = Hyperparameters()
best_c6 = -float("inf")
best_set = None
for i in range(hypers.num_restarts):
u_set, c6 = run_single_trial(hypers, seed=42 + i)
if c6 > best_c6:
best_c6 = c6
best_set = u_set
print(f"Search complete. Best C6 lower bound found: {best_c6:.8f}")
return best_set, best_c6
# EVOLVE-BLOCK-END
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