first commit

sho/basics.py

@@ -0,0 +1,70 @@
+import numpy as np
+
+def sphere(x,offset=0.5):
+    """Computes the square of a multi-dimensional vector x."""
+    f = 0
+    for i in range(len(x)):
+        f += (x[i]-offset)**2
+    return f
+
+def onemax(x):
+    """Sum the given bitstring."""
+    s = 0
+    for i in x:
+        s += i
+    return s
+
+def numerical_random(d):
+    """Draw a random multi-dimensional vector in [0,1]**d"""
+    return np.random.random(d)
+
+def bitstring_random(d):
+    """Draw a random bistring of size d, with P(1)=0.5."""
+    return [int(round(i)) for i in np.random.random(d)]
+
+def search(objective_function, dimension, iterations, generator, history=None):
+    """Search the given objective_function of the given dimension,
+    during the given number of iterations, generating random solution
+    with the given generator.
+    Returns the best value of the function and the best solution."""
+    best_val = float("inf")
+    best_sol = None
+    for i in range(iterations):
+        sol = generator(dimension)
+        val = objective_function(sol)
+        if val < best_val:
+            best_val = val
+            best_sol = sol
+        if history is not None:
+            history.append((val,sol))
+    return best_val, best_sol
+
+
+if __name__=="__main__":
+    import matplotlib.pyplot as plt
+    from mpl_toolkits.mplot3d import Axes3D
+    import plot
+
+    print("Random search over 10-OneMax")
+    print("After 10 iterations:")
+    val,sol = search(onemax, 10, 10, bitstring_random)
+    print("\t",val,sol)
+    print("After 1000 iterations:")
+    val,sol = search(onemax, 10, 1000, bitstring_random)
+    print("\t",val,sol)
+
+    print("Random search over 2-Sphere")
+    print("After 10 iterations:")
+    val,sol = search(sphere, 2, 10, numerical_random)
+    print("\t",val,sol)
+    print("After 50 iterations:")
+    history = []
+    val,sol = search(sphere, 2, 50, numerical_random, history)
+    print("\t",val,sol)
+
+    fig = plt.figure()
+    ax = fig.gca(projection='3d')
+    shape = (20,20)
+    plot.surface(ax, shape, sphere)
+    plot.path(ax, shape, history)
+    plt.show()