added the best_prgoram for reference

Author: codelion

examples/circle_packing/best_program.py

@@ -0,0 +1,138 @@
+# EVOLVE-BLOCK-START
+"""Advanced circle packing for n=26 circles in a unit square"""
+import numpy as np
+from scipy.optimize import minimize
+
+def construct_packing():
+    """
+    Construct an optimized arrangement of 26 circles in a unit square
+    using mathematical principles and optimization techniques.
+    
+    Returns:
+        Tuple of (centers, radii, sum_of_radii)
+        centers: np.array of shape (26, 2) with (x, y) coordinates
+        radii: np.array of shape (26) with radius of each circle
+        sum_of_radii: Sum of all radii
+    """
+    n = 26
+    
+    # Initial guess: Strategic placement with some randomness
+    centers = np.zeros((n, 2))
+    radii = np.zeros(n)
+
+    # Heuristic placement for better initial guess: place larger circles in center
+    radii[:] = np.linspace(0.12, 0.05, n) # Linear distribution of radii
+    
+    # Initial placement: approximate hexagonal grid
+    grid_x = int(np.sqrt(n))
+    grid_y = int(n / grid_x)
+    
+    x_coords = np.linspace(0.15, 0.85, grid_x)
+    y_coords = np.linspace(0.15, 0.85, grid_y)
+    
+    count = 0
+    for i in range(grid_x):
+        for j in range(grid_y):
+            if count < n:
+                centers[count] = [x_coords[i] + 0.05 * (j % 2), y_coords[j]]
+                count += 1
+    
+    # Place remaining circles randomly
+    while count < n:
+        centers[count] = np.random.rand(2) * 0.7 + 0.15
+        count += 1
+
+    # Objective function: Negative sum of radii (to maximize)
+    def objective(x):
+        centers = x[:2*n].reshape(n, 2)
+        radii = x[2*n:]
+        return -np.sum(radii)
+
+    # Constraint: No overlaps and circles stay within the unit square
+    def constraint(x):
+        centers = x[:2*n].reshape(n, 2)
+        radii = x[2*n:]
+        
+        # Overlap constraint
+        overlap_constraints = []
+        for i in range(n):
+            for j in range(i + 1, n):
+                dist = np.sqrt(np.sum((centers[i] - centers[j])**2))
+                overlap_constraints.append(dist - (radii[i] + radii[j]))
+        
+        # Boundary constraints
+        boundary_constraints = []
+        for i in range(n):
+            boundary_constraints.append(centers[i, 0] - radii[i])  # x >= radius
+            boundary_constraints.append(1 - centers[i, 0] - radii[i]) # x <= 1 - radius
+            boundary_constraints.append(centers[i, 1] - radii[i])  # y >= radius
+            boundary_constraints.append(1 - centers[i, 1] - radii[i]) # y <= 1 - radius
+        
+        return np.array(overlap_constraints + boundary_constraints)
+
+    # Initial guess vector
+    x0 = np.concatenate([centers.flatten(), radii])
+
+    # Bounds: Circles stay within the unit square and radii are positive
+    bounds = [(0, 1)] * (2*n) + [(0.03, 0.2)] * n # radii are positive, up to 0.2
+
+    # Constraints dictionary
+    constraints = {'type': 'ineq', 'fun': constraint}
+
+    # Optimization using SLSQP
+    result = minimize(objective, x0, method='SLSQP', bounds=bounds, constraints=constraints, options={'maxiter': 1000, 'ftol': 1e-8})
+
+    # Extract optimized centers and radii
+    optimized_centers = result.x[:2*n].reshape(n, 2)
+    optimized_radii = result.x[2*n:]
+
+    # Ensure radii are not negative (numerical stability)
+    optimized_radii = np.maximum(optimized_radii, 0.001)
+
+    # Calculate the sum of radii
+    sum_radii = np.sum(optimized_radii)
+
+    return optimized_centers, optimized_radii, sum_radii
+# EVOLVE-BLOCK-END
+
+# This part remains fixed (not evolved)
+def run_packing():
+    """Run the circle packing constructor for n=26"""
+    centers, radii, sum_radii = construct_packing()
+    return centers, radii, sum_radii
+
+def visualize(centers, radii):
+    """
+    Visualize the circle packing
+    
+    Args:
+        centers: np.array of shape (n, 2) with (x, y) coordinates
+        radii: np.array of shape (n) with radius of each circle
+    """
+    import matplotlib.pyplot as plt
+    from matplotlib.patches import Circle
+    
+    fig, ax = plt.subplots(figsize=(8, 8))
+    
+    # Draw unit square
+    ax.set_xlim(0, 1)
+    ax.set_ylim(0, 1)
+    ax.set_aspect('equal')
+    ax.grid(True)
+    
+    # Draw circles
+    for i, (center, radius) in enumerate(zip(centers, radii)):
+        circle = Circle(center, radius, alpha=0.5)
+        ax.add_patch(circle)
+        ax.text(center[0], center[1], str(i), ha='center', va='center')
+    
+    plt.title(f"Circle Packing (n={len(centers)}, sum={sum(radii):.6f})")
+    plt.show()
+
+if __name__ == "__main__":
+    centers, radii, sum_radii = run_packing()
+    print(f"Sum of radii: {sum_radii}")
+    # AlphaEvolve improved this to 2.635
+    
+    # Uncomment to visualize:
+    # visualize(centers, radii)

examples/circle_packing/best_program_info.json

@@ -0,0 +1,16 @@
+{
+  "id": "f6cbff44-9b16-4e6c-af58-b10b6625621a",
+  "generation": 10,
+  "iteration": 0,
+  "timestamp": 1747709506.546607,
+  "parent_id": "b7f51a09-7ba5-4cdb-bc15-9c431ec8885f",
+  "metrics": {
+    "validity": 1.0,
+    "sum_radii": 2.634292402141039,
+    "target_ratio": 0.9997314619131079,
+    "combined_score": 0.9997314619131079,
+    "eval_time": 0.6134955883026123
+  },
+  "language": "python",
+  "saved_at": 1748016967.553278
+}