Add Hill Climbing algorithm in HillClimp.py

HillClimp.py

@@ -0,0 +1,30 @@
+import numpy as np
+
+# Define the objective function (for example: maximize f(x) = -x^2 + 5)
+def objective(x):
+    return -x[0] ** 2 + 5
+
+# Generate neighboring solutions
+def generate_neighbors(x, step_size=0.1):
+    return [np.array([x[0] + step_size]), np.array([x[0] - step_size])]
+
+# Hill Climbing Algorithm
+def hill_climbing(objective, initial, n_iterations=100, step_size=0.1):
+    current = np.array([initial])
+    current_eval = objective(current)
+    for i in range(n_iterations):
+        neighbors = generate_neighbors(current, step_size)
+        neighbor_evals = [objective(n) for n in neighbors]
+        best_idx = np.argmax(neighbor_evals)
+        if neighbor_evals[best_idx] > current_eval:
+            current = neighbors[best_idx]
+            current_eval = neighbor_evals[best_idx]
+            print(f"Step {i+1}: x = {current[0]:.4f}, f(x) = {current_eval:.4f}")
+        else:
+            print("No better neighbors found. Algorithm converged.")
+            break
+    return current, current_eval
+
+# Example usage
+final_position, final_value = hill_climbing(objective, initial=2.0)
+print("Best solution:", final_position, "Optimal value:", final_value)