def beam_search(problem, beam_width=1, graph=True):
"""
A variant of breadth-first search where all nodes in the fringe
are expanded, but the resulting new fringe is limited to have length
beam_width, where the nodes with the worst value are dropped. The default
beam width is 1, which yields greedy best-first search (i.e., hill
climbing).
There are different ways to implement beam search, namely best-first
beam search and breadth-first beam search. According to:
Wilt, C. M., Thayer, J. T., & Ruml, W. (2010). A comparison of
greedy search algorithms. In Third Annual Symposium on Combinatorial
Search.
breadth-first beam search almost always performs better. They find that
allowing the search to re-expand duplicate nodes if they have a lower cost
improves search performance. Thus, our implementation is a breadth-first
beam search that re-expand duplicate nodes with lower cost.
:param problem: The problem to solve.
:type problem: :class:`Problem`
:param beam_width: The size of the beam (defaults to 1).
:type beam_width: int
:param graph_search: whether to use graph or tree search.
:type graph_search: boolean
"""
closed = {}
fringe = PriorityQueue(node_value=problem.node_value)
fringe.push(problem.initial)
closed[problem.initial] = problem.initial.cost()
while len(fringe) > 0:
parents = []
while len(fringe) > 0 and len(parents) < beam_width:
parent = fringe.pop()
if problem.goal_test(parent, problem.goal):
yield SolutionNode(parent, problem.goal)
parents.append(parent)
fringe.clear()
for node in parents:
for s in problem.successors(node):
if not graph:
fringe.push(s)
elif s not in closed or s.cost() < closed[s]:
fringe.push(s)
closed[s] = s.cost()
def beam_search(problem, beam_width=1, graph_search=True):
"""
A variant of breadth-first search where all nodes in the fringe
are expanded, but the resulting new fringe is limited to have length
beam_width, where the nodes with the worst value are dropped. The default
beam width is 1, which yields greedy best-first search (i.e., hill climbing).
There are different ways to implement beam search, namely best-first
beam search and breadth-first beam search. According to:
Wilt, C. M., Thayer, J. T., & Ruml, W. (2010). A comparison of
greedy search algorithms. In Third Annual Symposium on Combinatorial
Search.
breadth-first beam search almost always performs better. They find that
allowing the search to re-expand duplicate nodes if they have a lower cost
improves search performance. Thus, our implementation is a breadth-first
beam search that re-expand duplicate nodes with lower cost.
:param problem: The problem to solve.
:type problem: :class:`Problem`
:param beam_width: The size of the beam (defaults to 1).
:type beam_width: int
:param graph_search: whether to use graph or tree search.
:type graph_search: boolean
"""
closed = {}
fringe = PriorityQueue(node_value=problem.node_value)
fringe.push(problem.initial)
closed[problem.initial] = problem.initial.cost()
while len(fringe) > 0:
parents = []
while len(fringe) > 0 and len(parents) < beam_width:
parent = fringe.pop()
if problem.goal_test(parent):
yield parent
parents.append(parent)
fringe.clear()
for node in parents:
for s in problem.successors(node):
if not graph_search:
fringe.push(s)
elif s not in closed or s.cost() < closed[s]:
fringe.push(s)
closed[s] = s.cost()
def local_beam_search(problem, beam_width=1, max_sideways=0,
graph_search=True, cost_limit=float('-inf')):
"""
A variant of :func:`py_search.informed_search.beam_search` that can be
applied to local search problems. When the beam width of 1 this approach
yields behavior similar to :func:`hill_climbing`.
:param problem: The problem to solve.
:type problem: :class:`py_search.base.Problem`
:param beam_width: The size of the search beam.
:type beam_width: int
:param max_sideways: Specifies the max number of contiguous sideways moves.
:type max_sideways: int
:param graph_search: Whether to use graph search (no duplicates) or tree
search (duplicates)
:type graph_search: Boolean
"""
b = None
bv = float('inf')
sideways_moves = 0
fringe = PriorityQueue(node_value=problem.node_value)
fringe.push(problem.initial)
while len(fringe) < beam_width:
fringe.push(problem.random_node())
if graph_search:
closed = set()
closed.add(problem.initial)
while len(fringe) > 0 and sideways_moves <= max_sideways:
pv = fringe.peek_value()
if pv > bv:
yield b
if pv == bv:
sideways_moves += 1
else:
sideways_moves = 0
parents = []
while len(fringe) > 0 and len(parents) < beam_width:
parent = fringe.pop()
parents.append(parent)
fringe.clear()
b = parents[0]
bv = pv
for node in parents:
for s in problem.successors(node):
added = True
if not graph_search:
fringe.push(s)
elif s not in closed:
fringe.push(s)
closed.add(s)
else:
added = False
if added and fringe.peek_value() <= cost_limit:
yield fringe.peek()
yield b
def local_beam_search(problem, beam_width=1, max_sideways=0, graph=True):
"""
A variant of :func:`py_search.informed_search.beam_search` that can be
applied to local search problems. When the beam width of 1 this approach
yields behavior similar to :func:`hill_climbing`.
The problem.goal_test function can be used to terminate search early if a
good enough solution has been found. If goal_test(node) return True, then
search is immediately terminated and the node is returned.
:param problem: The problem to solve.
:type problem: :class:`py_search.base.Problem`
:param beam_width: The size of the search beam.
:type beam_width: int
:param max_sideways: Specifies the max number of contiguous sideways moves.
:type max_sideways: int
:param graph: Whether to use graph search (no duplicates) or tree
search (duplicates)
:type graph: Boolean
"""
b = None
bv = float('inf')
sideways_moves = 0
fringe = PriorityQueue(node_value=problem.node_value)
fringe.push(problem.initial)
while len(fringe) < beam_width:
fringe.push(problem.random_node())
if graph:
closed = set()
closed.add(problem.initial)
while len(fringe) > 0 and sideways_moves <= max_sideways:
pv = fringe.peek_value()
if bv < pv:
yield SolutionNode(b, problem.goal)
if pv == bv:
sideways_moves += 1
else:
sideways_moves = 0
parents = []
while len(fringe) > 0 and len(parents) < beam_width:
parent = fringe.pop()
parents.append(parent)
fringe.clear()
b = parents[0]
bv = pv
for node in parents:
if problem.goal_test(node, problem.goal):
yield SolutionNode(node, problem.goal)
for s in problem.successors(node):
if not graph:
fringe.push(s)
elif s not in closed:
fringe.push(s)
closed.add(s)
yield SolutionNode(b, problem.goal)
