Write in Python (Artificial Intelligence on Local Search)

# TODO: Hill-climbing search algorithm: a loop that continually moves in the direction of increasing value.

# It terminates when it reaches a peak where no neighbor has a higher value.

# objective function: function to be maximized

# initial_state: initial (x, y) vector

# step_size: numerical interval by which to change the current (x,y) state to generate a new neighboring state

# print_iters: set to True to print out the current value at each iteration

# returns: best [x, y] solution found

def hill_climbing(objective_function, initial_state = np.array([0, 0]), step_size = 0.01, print_iters=True):

# set the starting point of the search algorithm

current_state = initial_state

# loop until a peak is found

i = 0

while True:

# Step 1: create a list of neighboring states to the current state

# Step 2: calculate the objective function at each of the neighboring states

# Step 3: determine the highest-valued neighboring state

# Step 4: compare the highest value among neighboring states to the current value

# if the latter is higher, we have found a peak -> return the current state

# if the former is higher, assign current state to be the best neighbor state

current_value = objective_function(current_state)

if print_iters:

print('iteration: {}, current_state: {}, current_value: {}'.format(i, current_state, current_value))

i += 1

break