| |
| 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) |
|
|
| |
| sparsity = 0.95 |
| u_mask = np.random.random(hypers.max_integer + 1) > sparsity |
| u_mask[0] = True |
|
|
| 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) |
|
|
| |
| 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 |
|
|
| |
| 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 |
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