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"""Search (Chapters 3-4)
The way to use this code is to subclass Problem to create a class of problems,
then create problem instances and solve them with calls to the various search
functions."""
from
utils
import
(
is_in
,
argmin
,
argmax
,
argmax_random_tie
,
probability
,
weighted_sampler
,
memoize
,
print_table
,
open_data
,
Stack
,
FIFOQueue
,
PriorityQueue
,
name
,
distance
)
from
collections
import
defaultdict
import
math
import
random
import
sys
import
bisect
infinity
=
float
(
'inf'
)
# ______________________________________________________________________________
class
Problem
(
object
):
"""The abstract class for a formal problem. You should subclass
this and implement the methods actions and result, and possibly
__init__, goal_test, and path_cost. Then you will create instances
of your subclass and solve them with the various search functions."""
def
__init__
(
self
,
initial
,
goal
=
None
):
"""The constructor specifies the initial state, and possibly a goal
state, if there is a unique goal. Your subclass's constructor can add
other arguments."""
self
.
initial
=
initial
self
.
goal
=
goal
def
actions
(
self
,
state
):
"""Return the actions that can be executed in the given
state. The result would typically be a list, but if there are
many actions, consider yielding them one at a time in an
iterator, rather than building them all at once."""
raise
NotImplementedError
def
result
(
self
,
state
,
action
):
"""Return the state that results from executing the given
action in the given state. The action must be one of
self.actions(state)."""
raise
NotImplementedError
def
goal_test
(
self
,
state
):
"""Return True if the state is a goal. The default method compares the
state to self.goal or checks for state in self.goal if it is a
list, as specified in the constructor. Override this method if
checking against a single self.goal is not enough."""
if
isinstance
(
self
.
goal
,
list
):
return
is_in
(
state
,
self
.
goal
)
else
:
return
state
==
self
.
goal
def
path_cost
(
self
,
c
,
state1
,
action
,
state2
):
"""Return the cost of a solution path that arrives at state2 from
state1 via action, assuming cost c to get up to state1. If the problem
is such that the path doesn't matter, this function will only look at
state2. If the path does matter, it will consider c and maybe state1
and action. The default method costs 1 for every step in the path."""
return
c
+
1
def
value
(
self
,
state
):
"""For optimization problems, each state has a value. Hill-climbing
and related algorithms try to maximize this value."""
raise
NotImplementedError
# ______________________________________________________________________________
class
Node
:
"""A node in a search tree. Contains a pointer to the parent (the node
that this is a successor of) and to the actual state for this node. Note
that if a state is arrived at by two paths, then there are two nodes with
the same state. Also includes the action that got us to this state, and
the total path_cost (also known as g) to reach the node. Other functions
may add an f and h value; see best_first_graph_search and astar_search for
an explanation of how the f and h values are handled. You will not need to
subclass this class."""
def
__init__
(
self
,
state
,
parent
=
None
,
action
=
None
,
path_cost
=
0
):
"""Create a search tree Node, derived from a parent by an action."""
self
.
state
=
state
self
.
parent
=
parent
self
.
action
=
action
self
.
path_cost
=
path_cost
self
.
depth
=
0
if
parent
:
self
.
depth
=
parent
.
depth
+
1
def
__repr__
(
self
):
return
"<Node {}>"
.
format
(
self
.
state
)
def
__lt__
(
self
,
node
):
return
self
.
state
<
node
.
state
def
expand
(
self
,
problem
):
"""List the nodes reachable in one step from this node."""
return
[
self
.
child_node
(
problem
,
action
)
for
action
in
problem
.
actions
(
self
.
state
)]
def
child_node
(
self
,
problem
,
action
):
"""[Figure 3.10]"""
next
=
problem
.
result
(
self
.
state
,
action
)
return
Node
(
next
,
self
,
action
,
problem
.
path_cost
(
self
.
path_cost
,
self
.
state
,
action
,
next
))
def
solution
(
self
):
"""Return the sequence of actions to go from the root to this node."""
return
[
node
.
action
for
node
in
self
.
path
()[
1
:]]
def
path
(
self
):
"""Return a list of nodes forming the path from the root to this node."""
node
,
path_back
=
self
, []
while
node
:
path_back
.
append
(
node
)
node
=
node
.
parent
return
list
(
reversed
(
path_back
))
# We want for a queue of nodes in breadth_first_search or
# astar_search to have no duplicated states, so we treat nodes
# with the same state as equal. [Problem: this may not be what you
# want in other contexts.]
def
__eq__
(
self
,
other
):
return
isinstance
(
other
,
Node
)
and
self
.
state
==
other
.
state
def
__hash__
(
self
):
return
hash
(
self
.
state
)
# ______________________________________________________________________________
class
SimpleProblemSolvingAgentProgram
:
"""Abstract framework for a problem-solving agent. [Figure 3.1]"""
def
__init__
(
self
,
initial_state
=
None
):
"""State is an sbstract representation of the state
of the world, and seq is the list of actions required
to get to a particular state from the initial state(root)."""
self
.
state
=
initial_state
self
.
seq
=
[]
def
__call__
(
self
,
percept
):
"""[Figure 3.1] Formulate a goal and problem, then
search for a sequence of actions to solve it."""
self
.
state
=
self
.
update_state
(
self
.
state
,
percept
)
if
not
self
.
seq
:
goal
=
self
.
formulate_goal
(
self
.
state
)
problem
=
self
.
formulate_problem
(
self
.
state
,
goal
)
self
.
seq
=
self
.
search
(
problem
)
if
not
self
.
seq
:
return
None
return
self
.
seq
.
pop
(
0
)
def
update_state
(
self
,
percept
):
raise
NotImplementedError
def
formulate_goal
(
self
,
state
):
raise
NotImplementedError
def
formulate_problem
(
self
,
state
,
goal
):
raise
NotImplementedError
def
search
(
self
,
problem
):
raise
NotImplementedError
# ______________________________________________________________________________
# Uninformed Search algorithms
def
tree_search
(
problem
,
frontier
):
"""Search through the successors of a problem to find a goal.
The argument frontier should be an empty queue.
Don't worry about repeated paths to a state. [Figure 3.7]"""
frontier
.
append
(
Node
(
problem
.
initial
))
while
frontier
:
node
=
frontier
.
pop
()
if
problem
.
goal_test
(
node
.
state
):
return
node
frontier
.
extend
(
node
.
expand
(
problem
))
return
None
def
graph_search
(
problem
,
frontier
):
"""Search through the successors of a problem to find a goal.
The argument frontier should be an empty queue.
If two paths reach a state, only use the first one. [Figure 3.7]"""
frontier
.
append
(
Node
(
problem
.
initial
))
explored
=
set
()
while
frontier
:
node
=
frontier
.
pop
()
if
problem
.
goal_test
(
node
.
state
):
return
node
explored
.
add
(
node
.
state
)
frontier
.
extend
(
child
for
child
in
node
.
expand
(
problem
)
if
child
.
state
not
in
explored
and
child
not
in
frontier
)
return
None
def
breadth_first_tree_search
(
problem
):
"""Search the shallowest nodes in the search tree first."""
return
tree_search
(
problem
,
FIFOQueue
())
def
depth_first_tree_search
(
problem
):
"""Search the deepest nodes in the search tree first."""
return
tree_search
(
problem
,
Stack
())
def
depth_first_graph_search
(
problem
):
"""Search the deepest nodes in the search tree first."""
return
graph_search
(
problem
,
Stack
())
def
breadth_first_search
(
problem
):
"""[Figure 3.11]"""
node
=
Node
(
problem
.
initial
)
if
problem
.
goal_test
(
node
.
state
):
return
node
frontier
=
FIFOQueue
()
frontier
.
append
(
node
)
explored
=
set
()
while
frontier
:
node
=
frontier
.
pop
()
explored
.
add
(
node
.
state
)
for
child
in
node
.
expand
(
problem
):
if
child
.
state
not
in
explored
and
child
not
in
frontier
:
if
problem
.
goal_test
(
child
.
state
):
return
child
frontier
.
append
(
child
)
return
None
def
best_first_graph_search
(
problem
,
f
):
"""Search the nodes with the lowest f scores first.
You specify the function f(node) that you want to minimize; for example,
if f is a heuristic estimate to the goal, then we have greedy best
first search; if f is node.depth then we have breadth-first search.
There is a subtlety: the line "f = memoize(f, 'f')" means that the f
values will be cached on the nodes as they are computed. So after doing
a best first search you can examine the f values of the path returned."""
f
=
memoize
(
f
,
'f'
)
node
=
Node
(
problem
.
initial
)
if
problem
.
goal_test
(
node
.
state
):
return
node
frontier
=
PriorityQueue
(
min
,
f
)
frontier
.
append
(
node
)
explored
=
set
()
while
frontier
:
node
=
frontier
.
pop
()
if
problem
.
goal_test
(
node
.
state
):
return
node
explored
.
add
(
node
.
state
)
for
child
in
node
.
expand
(
problem
):
if
child
.
state
not
in
explored
and
child
not
in
frontier
:
frontier
.
append
(
child
)
elif
child
in
frontier
:
incumbent
=
frontier
[
child
]
if
f
(
child
)
<
f
(
incumbent
):
del
frontier
[
incumbent
]
frontier
.
append
(
child
)
return
None
def
uniform_cost_search
(
problem
):
"""[Figure 3.14]"""
return
best_first_graph_search
(
problem
,
lambda
node
:
node
.
path_cost
)
def
depth_limited_search
(
problem
,
limit
=
50
):
"""[Figure 3.17]"""
def
recursive_dls
(
node
,
problem
,
limit
):
if
problem
.
goal_test
(
node
.
state
):
return
node
elif
limit
==
0
:
return
'cutoff'
else
:
cutoff_occurred
=
False
for
child
in
node
.
expand
(
problem
):
result
=
recursive_dls
(
child
,
problem
,
limit
-
1
)
if
result
==
'cutoff'
:
cutoff_occurred
=
True
elif
result
is
not
None
:
return
result
return
'cutoff'
if
cutoff_occurred
else
None
# Body of depth_limited_search:
return
recursive_dls
(
Node
(
problem
.
initial
),
problem
,
limit
)
def
iterative_deepening_search
(
problem
):
"""[Figure 3.18]"""
for
depth
in
range
(
sys
.
maxsize
):
result
=
depth_limited_search
(
problem
,
depth
)
if
result
!=
'cutoff'
:
return
result
# ______________________________________________________________________________
# Bidirectional Search
# Pseudocode from https://webdocs.cs.ualberta.ca/%7Eholte/Publications/MM-AAAI2016.pdf
def
bidirectional_search
(
problem
):
e
=
problem
.
find_min_edge
()
gF
,
gB
=
{
problem
.
initial
:
0
}, {
problem
.
goal
:
0
}
openF
,
openB
=
[
problem
.
initial
], [
problem
.
goal
]
closedF
,
closedB
=
[], []
U
=
infinity
def
extend
(
U
,
open_dir
,
open_other
,
g_dir
,
g_other
,
closed_dir
):
"""Extend search in given direction"""
n
=
find_key
(
C
,
open_dir
,
g_dir
)
open_dir
.
remove
(
n
)
closed_dir
.
append
(
n
)
for
c
in
problem
.
actions
(
n
):
if
c
in
open_dir
or
c
in
closed_dir
:
if
g_dir
[
c
]
<=
problem
.
path_cost
(
g_dir
[
n
],
n
,
None
,
c
):
continue
open_dir
.
remove
(
c
)
g_dir
[
c
]
=
problem
.
path_cost
(
g_dir
[
n
],
n
,
None
,
c
)
open_dir
.
append
(
c
)
if
c
in
open_other
:
U
=
min
(
U
,
g_dir
[
c
]
+
g_other
[
c
])
return
U
,
open_dir
,
closed_dir
,
g_dir
def
find_min
(
open_dir
,
g
):
"""Finds minimum priority, g and f values in open_dir"""
m
,
m_f
=
infinity
,
infinity
for
n
in
open_dir
:
f
=
g
[
n
]
+
problem
.
h
(
n
)
pr
=
max
(
f
,
2
*
g
[
n
])
m
=
min
(
m
,
pr
)
m_f
=
min
(
m_f
,
f
)
return
m
,
m_f
,
min
(
g
.
values
())
def
find_key
(
pr_min
,
open_dir
,
g
):
"""Finds key in open_dir with value equal to pr_min
and minimum g value."""
m
=
infinity
state
=
-
1
for
n
in
open_dir
:
pr
=
max
(
g
[
n
]
+
problem
.
h
(
n
),
2
*
g
[
n
])
if
pr
==
pr_min
:
if
g
[
n
]
<
m
:
m
=
g
[
n
]
state
=
n
return
state
while
openF
and
openB
:
pr_min_f
,
f_min_f
,
g_min_f
=
find_min
(
openF
,
gF
)
pr_min_b
,
f_min_b
,
g_min_b
=
find_min
(
openB
,
gB
)
C
=
min
(
pr_min_f
,
pr_min_b
)
if
U
<=
max
(
C
,
f_min_f
,
f_min_b
,
g_min_f
+
g_min_b
+
e
):
return
U
if
C
==
pr_min_f
:
# Extend forward
U
,
openF
,
closedF
,
gF
=
extend
(
U
,
openF
,
openB
,
gF
,
gB
,
closedF
)
else
:
# Extend backward
U
,
openB
,
closedB
,
gB
=
extend
(
U
,
openB
,
openF
,
gB
,
gF
,
closedB
)
return
infinity
# ______________________________________________________________________________
# Informed (Heuristic) Search
greedy_best_first_graph_search
=
best_first_graph_search
# Greedy best-first search is accomplished by specifying f(n) = h(n).
def
astar_search
(
problem
,
h
=
None
):
"""A* search is best-first graph search with f(n) = g(n)+h(n).
You need to specify the h function when you call astar_search, or
else in your Problem subclass."""
h
=
memoize
(
h
or
problem
.
h
,
'h'
)
return
best_first_graph_search
(
problem
,
lambda
n
:
n
.
path_cost
+
h
(
n
))
# ______________________________________________________________________________
# Other search algorithms
def
recursive_best_first_search
(
problem
,
h
=
None
):
"""[Figure 3.26]"""
h
=
memoize
(
h
or
problem
.
h
,
'h'
)
def
RBFS
(
problem
,
node
,
flimit
):
if
problem
.
goal_test
(
node
.
state
):
return
node
,
0
# (The second value is immaterial)
successors
=
node
.
expand
(
problem
)
if
len
(
successors
)
==
0
:
return
None
,
infinity
for
s
in
successors
:
s
.
f
=
max
(
s
.
path_cost
+
h
(
s
),
node
.
f
)
while
True
:
# Order by lowest f value
successors
.
sort
(
key
=
lambda
x
:
x
.
f
)
best
=
successors
[
0
]
if
best
.
f
>
flimit
:
return
None
,
best
.
f
if
len
(
successors
)
>
1
:
alternative
=
successors
[
1
].
f
else
:
alternative
=
infinity
result
,
best
.
f
=
RBFS
(
problem
,
best
,
min
(
flimit
,
alternative
))
if
result
is
not
None
:
return
result
,
best
.
f
node
=
Node
(
problem
.
initial
)
node
.
f
=
h
(
node
)
result
,
bestf
=
RBFS
(
problem
,
node
,
infinity
)
return
result
def
hill_climbing
(
problem
):
"""From the initial node, keep choosing the neighbor with highest value,
stopping when no neighbor is better. [Figure 4.2]"""
current
=
Node
(
problem
.
initial
)
while
True
:
neighbors
=
current
.
expand
(
problem
)
if
not
neighbors
:
break
neighbor
=
argmax_random_tie
(
neighbors
,
key
=
lambda
node
:
problem
.
value
(
node
.
state
))
if
problem
.
value
(
neighbor
.
state
)
<=
problem
.
value
(
current
.
state
):
break
current
=
neighbor
return
current
.
state
def
exp_schedule
(
k
=
20
,
lam
=
0.005
,
limit
=
100
):
"""One possible schedule function for simulated annealing"""
return
lambda
t
: (
k
*
math
.
exp
(
-
lam
*
t
)
if
t
<
limit
else
0
)
def
simulated_annealing
(
problem
,
schedule
=
exp_schedule
()):
"""[Figure 4.5] CAUTION: This differs from the pseudocode as it
returns a state instead of a Node."""
current
=
Node
(
problem
.
initial
)
for
t
in
range
(
sys
.
maxsize
):
T
=
schedule
(
t
)
if
T
==
0
:
return
current
.
state
neighbors
=
current
.
expand
(
problem
)
if
not
neighbors
:
return
current
.
state
next
=
random
.
choice
(
neighbors
)
delta_e
=
problem
.
value
(
next
.
state
)
-
problem
.
value
(
current
.
state
)
if
delta_e
>
0
or
probability
(
math
.
exp
(
delta_e
/
T
)):
current
=
next
def
and_or_graph_search
(
problem
):
"""[Figure 4.11]Used when the environment is nondeterministic and completely observable.
Contains OR nodes where the agent is free to choose any action.
After every action there is an AND node which contains all possible states
the agent may reach due to stochastic nature of environment.
The agent must be able to handle all possible states of the AND node (as it
may end up in any of them).
Returns a conditional plan to reach goal state,
or failure if the former is not possible."""
# functions used by and_or_search
def
or_search
(
state
,
problem
,
path
):
"""returns a plan as a list of actions"""
if
problem
.
goal_test
(
state
):
return
[]
if
state
in
path
:
return
None
for
action
in
problem
.
actions
(
state
):
plan
=
and_search
(
problem
.
result
(
state
,
action
),
problem
,
path
+
[
state
, ])
if
plan
is
not
None
:
return
[
action
,
plan
]
def
and_search
(
states
,
problem
,
path
):
"""Returns plan in form of dictionary where we take action plan[s] if we reach state s."""
plan
=
{}
for
s
in
states
:
plan
[
s
]
=
or_search
(
s
,
problem
,
path
)
if
plan
[
s
]
is
None
:
return
None
return
plan
# body of and or search
return
or_search
(
problem
.
initial
,
problem
, [])
class
PeakFindingProblem
(
Problem
):
"""Problem of finding the highest peak in a limited grid"""
def
__init__
(
self
,
initial
,
grid
):
"""The grid is a 2 dimensional array/list whose state is specified by tuple of indices"""
Problem
.
__init__
(
self
,
initial
)
self
.
grid
=
grid
self
.
n
=
len
(
grid
)
assert
self
.
n
>
0
self
.
m
=
len
(
grid
[
0
])
assert
self
.
m
>
0
def
actions
(
self
,
state
):
"""Allows movement in only 4 directions"""
# TODO: Add flag to allow diagonal motion
allowed_actions
=
[]
if
state
[
0
]
>
0
:
allowed_actions
.
append
(
'N'
)
if
state
[
0
]
<
self
.
n
-
1
:
allowed_actions
.
append
(
'S'
)
if
state
[
1
]
>
0
:
allowed_actions
.
append
(
'W'
)
if
state
[
1
]
<
self
.
m
-
1
:
allowed_actions
.
append
(
'E'
)
return
allowed_actions
def
result
(
self
,
state
,
action
):
"""Moves in the direction specified by action"""
x
,
y
=
state
x
=
x
+
(
1
if
action
==
'S'
else
(
-
1
if
action
==
'N'
else
0
))
y
=
y
+
(
1
if
action
==
'E'
else
(
-
1
if
action
==
'W'
else
0
))
return
(
x
,
y
)
def
value
(
self
,
state
):
"""Value of a state is the value it is the index to"""
x
,
y
=
state
assert
0
<=
x
<
self
.
n
assert
0
<=
y
<
self
.
m
return
self
.
grid
[
x
][
y
]
class
OnlineDFSAgent
:
"""[Figure 4.21] The abstract class for an OnlineDFSAgent. Override
update_state method to convert percept to state. While initializing
the subclass a problem needs to be provided which is an instance of
a subclass of the Problem class."""
def
__init__
(
self
,
problem
):
self
.
problem
=
problem
self
.
s
=
None
self
.
a
=
None
self
.
untried
=
defaultdict
(
list
)
self
.
unbacktracked
=
defaultdict
(
list
)
self
.
result
=
{}
def
__call__
(
self
,
percept
):
s1
=
self
.
update_state
(
percept
)
if
self
.
problem
.
goal_test
(
s1
):
self
.
a
=
None
else
:
if
s1
not
in
self
.
untried
.
keys
():
self
.
untried
[
s1
]
=
self
.
problem
.
actions
(
s1
)
if
self
.
s
is
not
None
:
if
s1
!=
self
.
result
[(
self
.
s
,
self
.
a
)]:
self
.
result
[(
self
.
s
,
self
.
a
)]
=
s1
self
.
unbacktracked
[
s1
].
insert
(
0
,
self
.
s
)
if
len
(
self
.
untried
[
s1
])
==
0
:
if
len
(
self
.
unbacktracked
[
s1
])
==
0
:
self
.
a
=
None
else
:
# else a <- an action b such that result[s', b] = POP(unbacktracked[s'])
unbacktracked_pop
=
self
.
unbacktracked
[
s1
].
pop
(
0
)
for
(
s
,
b
)
in
self
.
result
.
keys
():
if
self
.
result
[(
s
,
b
)]
==
unbacktracked_pop
:
self
.
a
=
b
break
else
:
self
.
a
=
self
.
untried
[
s1
].
pop
(
0
)
self
.
s
=
s1
return
self
.
a
def
update_state
(
self
,
percept
):
"""To be overridden in most cases. The default case
assumes the percept to be of type state."""
return
percept
# ______________________________________________________________________________
class
OnlineSearchProblem
(
Problem
):
"""
A problem which is solved by an agent executing
actions, rather than by just computation.
Carried in a deterministic and a fully observable environment."""
def
__init__
(
self
,
initial
,
goal
,
graph
):
self
.
initial
=
initial
self
.
goal
=
goal
self
.
graph
=
graph
def
actions
(
self
,
state
):
return
self
.
graph
.
dict
[
state
].
keys
()
def
output
(
self
,
state
,
action
):
return
self
.
graph
.
dict
[
state
][
action
]
def
h
(
self
,
state
):
"""Returns least possible cost to reach a goal for the given state."""
return
self
.
graph
.
least_costs
[
state
]
def
c
(
self
,
s
,
a
,
s1
):
"""Returns a cost estimate for an agent to move from state 's' to state 's1'."""
return
1
def
update_state
(
self
,
percept
):
raise
NotImplementedError
def
goal_test
(
self
,
state
):
if
state
==
self
.
goal
:
return
True
return
False
class
LRTAStarAgent
:
""" [Figure 4.24]
Abstract class for LRTA*-Agent. A problem needs to be
provided which is an instanace of a subclass of Problem Class.
Takes a OnlineSearchProblem [Figure 4.23] as a problem.
"""
def
__init__
(
self
,
problem
):
self
.
problem
=
problem
# self.result = {} # no need as we are using problem.result
self
.
H
=
{}
self
.
s
=
None
self
.
a
=
None
def
__call__
(
self
,
s1
):
# as of now s1 is a state rather than a percept
if
self
.
problem
.
goal_test
(
s1
):
self
.
a
=
None
return
self
.
a
else
:
if
s1
not
in
self
.
H
:
self
.
H
[
s1
]
=
self
.
problem
.
h
(
s1
)
if
self
.
s
is
not
None
:
# self.result[(self.s, self.a)] = s1 # no need as we are using problem.output
# minimum cost for action b in problem.actions(s)
self
.
H
[
self
.
s
]
=
min
(
self
.
LRTA_cost
(
self
.
s
,
b
,
self
.
problem
.
output
(
self
.
s
,
b
),
self
.
H
)
for
b
in
self
.
problem
.
actions
(
self
.
s
))
# an action b in problem.actions(s1) that minimizes costs
self
.
a
=
argmin
(
self
.
problem
.
actions
(
s1
),
key
=
lambda
b
:
self
.
LRTA_cost
(
s1
,
b
,
self
.
problem
.
output
(
s1
,
b
),
self
.
H
))
self
.
s
=
s1
return
self
.
a
def
LRTA_cost
(
self
,
s
,
a
,
s1
,
H
):
"""Returns cost to move from state 's' to state 's1' plus
estimated cost to get to goal from s1."""
print
(
s
,
a
,
s1
)
if
s1
is
None
:
return
self
.
problem
.
h
(
s
)
else
:
# sometimes we need to get H[s1] which we haven't yet added to H
# to replace this try, except: we can initialize H with values from problem.h
try
:
return
self
.
problem
.
c
(
s
,
a
,
s1
)
+
self
.
H
[
s1
]
except
:
return
self
.
problem
.
c
(
s
,
a
,
s1
)
+
self
.
problem
.
h
(
s1
)
# ______________________________________________________________________________
# Genetic Algorithm
def
genetic_search
(
problem
,
fitness_fn
,
ngen
=
1000
,
pmut
=
0.1
,
n
=
20
):
"""Call genetic_algorithm on the appropriate parts of a problem.
This requires the problem to have states that can mate and mutate,
plus a value method that scores states."""
# NOTE: This is not tested and might not work.
# TODO: Use this function to make Problems work with genetic_algorithm.
s
=
problem
.
initial_state
states
=
[
problem
.
result
(
s
,
a
)
for
a
in
problem
.
actions
(
s
)]
random
.
shuffle
(
states
)
return
genetic_algorithm
(
states
[:
n
],
problem
.
value
,
ngen
,
pmut
)
def
genetic_algorithm
(
population
,
fitness_fn
,
gene_pool
=
[
0
,
1
],
f_thres
=
None
,
ngen
=
1000
,
pmut
=
0.1
):
# noqa
"""[Figure 4.8]"""
for
i
in
range
(
ngen
):
new_population
=
[]
random_selection
=
selection_chances
(
fitness_fn
,
population
)
for
j
in
range
(
len
(
population
)):
x
=
random_selection
()
y
=
random_selection
()
child
=
reproduce
(
x
,
y
)
if
random
.
uniform
(
0
,
1
)
<
pmut
:
child
=
mutate
(
child
,
gene_pool
)
new_population
.
append
(
child
)
population
=
new_population
if
f_thres
:
fittest_individual
=
argmax
(
population
,
key
=
fitness_fn
)
if
fitness_fn
(
fittest_individual
)
>=
f_thres
:
return
fittest_individual
return
argmax
(
population
,
key
=
fitness_fn
)
def
init_population
(
pop_number
,
gene_pool
,
state_length
):
"""Initializes population for genetic algorithm
pop_number : Number of individuals in population
gene_pool : List of possible values for individuals
state_length: The length of each individual"""
g
=
len
(
gene_pool
)
population
=
[]
for
i
in
range
(
pop_number
):
new_individual
=
[
gene_pool
[
random
.
randrange
(
0
,
g
)]
for
j
in
range
(
state_length
)]
population
.
append
(
new_individual
)
return
population
def
selection_chances
(
fitness_fn
,
population
):
fitnesses
=
map
(
fitness_fn
,
population
)
return
weighted_sampler
(
population
,
fitnesses
)
def
reproduce
(
x
,
y
):
n
=
len
(
x
)
c
=
random
.
randrange
(
1
,
n
)
return
x
[:
c
]
+
y
[
c
:]
def
mutate
(
x
,
gene_pool
):
n
=
len
(
x
)
g
=
len
(
gene_pool
)
c
=
random
.
randrange
(
0
,
n
)
r
=
random
.
randrange
(
0
,
g
)
new_gene
=
gene_pool
[
r
]
return
x
[:
c
]
+
[
new_gene
]
+
x
[
c
+
1
:]
# _____________________________________________________________________________
# The remainder of this file implements examples for the search algorithms.
# ______________________________________________________________________________
# Graphs and Graph Problems
class
Graph
:
"""A graph connects nodes (verticies) by edges (links). Each edge can also
have a length associated with it. The constructor call is something like:
g = Graph({'A': {'B': 1, 'C': 2})
this makes a graph with 3 nodes, A, B, and C, with an edge of length 1 from
A to B, and an edge of length 2 from A to C. You can also do:
g = Graph({'A': {'B': 1, 'C': 2}, directed=False)
This makes an undirected graph, so inverse links are also added. The graph
stays undirected; if you add more links with g.connect('B', 'C', 3), then
inverse link is also added. You can use g.nodes() to get a list of nodes,
g.get('A') to get a dict of links out of A, and g.get('A', 'B') to get the
length of the link from A to B. 'Lengths' can actually be any object at
all, and nodes can be any hashable object."""
def
__init__
(
self
,
dict
=
None
,
directed
=
True
):
self
.
dict
=
dict
or
{}
self
.
directed
=
directed
if
not
directed
:
self
.
make_undirected
()
def
make_undirected
(
self
):
"""Make a digraph into an undirected graph by adding symmetric edges."""
for
a
in
list
(
self
.
dict
.
keys
()):
for
(
b
,
dist
)
in
self
.
dict
[
a
].
items
():
self
.
connect1
(
b
,
a
,
dist
)
def
connect
(
self
,
A
,
B
,
distance
=
1
):
"""Add a link from A and B of given distance, and also add the inverse
link if the graph is undirected."""
self
.
connect1
(
A
,
B
,
distance
)
if
not
self
.
directed
:
self
.
connect1
(
B
,
A
,
distance
)
def
connect1
(
self
,
A
,
B
,
distance
):
"""Add a link from A to B of given distance, in one direction only."""
self
.
dict
.
setdefault
(
A
, {})[
B
]
=
distance
def
get
(
self
,
a
,
b
=
None
):
"""Return a link distance or a dict of {node: distance} entries.
.get(a,b) returns the distance or None;
.get(a) returns a dict of {node: distance} entries, possibly {}."""
links
=
self
.
dict
.
setdefault
(
a
, {})
if
b
is
None
:
return
links
else
:
return
links
.
get
(
b
)
def
nodes
(
self
):
"""Return a list of nodes in the graph."""
return
list
(
self
.
dict
.
keys
())
def
UndirectedGraph
(
dict
=
None
):
"""Build a Graph where every edge (including future ones) goes both ways."""
return
Graph
(
dict
=
dict
,
directed
=
False
)
def
RandomGraph
(
nodes
=
list
(
range
(
10
)),
min_links
=
2
,
width
=
400
,
height
=
300
,
curvature
=
lambda
:
random
.
uniform
(
1.1
,
1.5
)):
"""Construct a random graph, with the specified nodes, and random links.
The nodes are laid out randomly on a (width x height) rectangle.
Then each node is connected to the min_links nearest neighbors.
Because inverse links are added, some nodes will have more connections.
The distance between nodes is the hypotenuse times curvature(),
where curvature() defaults to a random number between 1.1 and 1.5."""
g
=
UndirectedGraph
()
g
.
locations
=
{}
# Build the cities
for
node
in
nodes
:
g
.
locations
[
node
]
=
(
random
.
randrange
(
width
),
random
.
randrange
(
height
))
# Build roads from each city to at least min_links nearest neighbors.
for
i
in
range
(
min_links
):
for
node
in
nodes
:
if
len
(
g
.
get
(
node
))
<
min_links
:
here
=
g
.
locations
[
node
]
def
distance_to_node
(
n
):
if
n
is
node
or
g
.
get
(
node
,
n
):
return
infinity
return
distance
(
g
.
locations
[
n
],
here
)
neighbor
=
argmin
(
nodes
,
key
=
distance_to_node
)
d
=
distance
(
g
.
locations
[
neighbor
],
here
)
*
curvature
()
g
.
connect
(
node
,
neighbor
,
int
(
d
))
return
g
""" [Figure 3.2]
Simplified road map of Romania
"""
romania_map
=
UndirectedGraph
(
dict
(
Arad
=
dict
(
Zerind
=
75
,
Sibiu
=
140
,
Timisoara
=
118
),
Bucharest
=
dict
(
Urziceni
=
85
,
Pitesti
=
101
,
Giurgiu
=
90
,
Fagaras
=
211
),
Craiova
=
dict
(
Drobeta
=
120
,
Rimnicu
=
146
,
Pitesti
=
138
),
Drobeta
=
dict
(
Mehadia
=
75
),
Eforie
=
dict
(
Hirsova
=
86
),
Fagaras
=
dict
(
Sibiu
=
99
),
Hirsova
=
dict
(
Urziceni
=
98
),
Iasi
=
dict
(
Vaslui
=
92
,
Neamt
=
87
),
Lugoj
=
dict
(
Timisoara
=
111
,
Mehadia
=
70
),
Oradea
=
dict
(
Zerind
=
71
,
Sibiu
=
151
),
Pitesti
=
dict
(
Rimnicu
=
97
),
Rimnicu
=
dict
(
Sibiu
=
80
),
Urziceni
=
dict
(
Vaslui
=
142
)))
romania_map
.
locations
=
dict
(
Arad
=
(
91
,
492
),
Bucharest
=
(
400
,
327
),
Craiova
=
(
253
,
288
),
Drobeta
=
(
165
,
299
),
Eforie
=
(
562
,
293
),
Fagaras
=
(
305
,
449
),
Giurgiu
=
(
375
,
270
),
Hirsova
=
(
534
,
350
),
Iasi
=
(
473
,
506
),
Lugoj
=
(
165
,
379
),
Mehadia
=
(
168
,
339
),
Neamt
=
(
406
,
537
),
Oradea
=
(
131
,
571
),
Pitesti
=
(
320
,
368
),
Rimnicu
=
(
233
,
410
),
Sibiu
=
(
207
,
457
),
Timisoara
=
(
94
,
410
),
Urziceni
=
(
456
,
350
),
Vaslui
=
(
509
,
444
),
Zerind
=
(
108
,
531
))
""" [Figure 4.9]
Eight possible states of the vacumm world
Each state is represented as
* "State of the left room" "State of the right room" "Room in which the agent
is present"
1 - DDL Dirty Dirty Left
2 - DDR Dirty Dirty Right
3 - DCL Dirty Clean Left
4 - DCR Dirty Clean Right
5 - CDL Clean Dirty Left
6 - CDR Clean Dirty Right
7 - CCL Clean Clean Left
8 - CCR Clean Clean Right
"""
vacumm_world
=
Graph
(
dict
(
State_1
=
dict
(
Suck
=
[
'State_7'
,
'State_5'
],
Right
=
[
'State_2'
]),
State_2
=
dict
(
Suck
=
[
'State_8'
,
'State_4'
],
Left
=
[
'State_2'
]),
State_3
=
dict
(
Suck
=
[
'State_7'
],
Right
=
[
'State_4'
]),
State_4
=
dict
(
Suck
=
[
'State_4'
,
'State_2'
],
Left
=
[
'State_3'
]),
State_5
=
dict
(
Suck
=
[
'State_5'
,
'State_1'
],
Right
=
[
'State_6'
]),
State_6
=
dict
(
Suck
=
[
'State_8'
],
Left
=
[
'State_5'
]),
State_7
=
dict
(
Suck
=
[
'State_7'
,
'State_3'
],
Right
=
[
'State_8'
]),
State_8
=
dict
(
Suck
=
[
'State_8'
,
'State_6'
],
Left
=
[
'State_7'
])
))
""" [Figure 4.23]
One-dimensional state space Graph
"""
one_dim_state_space
=
Graph
(
dict
(
State_1
=
dict
(
Right
=
'State_2'
),
State_2
=
dict
(
Right
=
'State_3'
,
Left
=
'State_1'
),
State_3
=
dict
(
Right
=
'State_4'
,
Left
=
'State_2'
),
State_4
=
dict
(
Right
=
'State_5'
,
Left
=
'State_3'
),
State_5
=
dict
(
Right
=
'State_6'
,
Left
=
'State_4'
),
State_6
=
dict
(
Left
=
'State_5'
)
))
one_dim_state_space
.
least_costs
=
dict
(
State_1
=
8
,
State_2
=
9
,
State_3
=
2
,
State_4
=
2
,
State_5
=
4
,
State_6
=
3
)
""" [Figure 6.1]
Principal states and territories of Australia
"""
australia_map
=
UndirectedGraph
(
dict
(
T
=
dict
(),
SA
=
dict
(
WA
=
1
,
NT
=
1
,
Q
=
1
,
NSW
=
1
,
V
=
1
),
NT
=
dict
(
WA
=
1
,
Q
=
1
),
NSW
=
dict
(
Q
=
1
,
V
=
1
)))
australia_map
.
locations
=
dict
(
WA
=
(
120
,
24
),
NT
=
(
135
,
20
),
SA
=
(
135
,
30
),
Q
=
(
145
,
20
),
NSW
=
(
145
,
32
),
T
=
(
145
,
42
),
V
=
(
145
,
37
))
class
GraphProblem
(
Problem
):
"""The problem of searching a graph from one node to another."""
def
__init__
(
self
,
initial
,
goal
,
graph
):
Problem
.
__init__
(
self
,
initial
,
goal
)
self
.
graph
=
graph
def
actions
(
self
,
A
):
"""The actions at a graph node are just its neighbors."""
return
list
(
self
.
graph
.
get
(
A
).
keys
())
def
result
(
self
,
state
,
action
):
"""The result of going to a neighbor is just that neighbor."""
return
action
def
path_cost
(
self
,
cost_so_far
,
A
,
action
,
B
):
return
cost_so_far
+
(
self
.
graph
.
get
(
A
,
B
)
or
infinity
)
def
find_min_edge
(
self
):
"""Find minimum value of edges."""
m
=
infinity
for
d
in
self
.
graph
.
dict
.
values
():
local_min
=
min
(
d
.
values
())
m
=
min
(
m
,
local_min
)
return
m
def
h
(
self
,
node
):
"""h function is straight-line distance from a node's state to goal."""
locs
=
getattr
(
self
.
graph
,
'locations'
,
None
)
if
locs
:
if
type
(
node
)
is
str
:
return
int
(
distance
(
locs
[
node
],
locs
[
self
.
goal
]))
return
int
(
distance
(
locs
[
node
.
state
],
locs
[
self
.
goal
]))
else
:
return
infinity
class
GraphProblemStochastic
(
GraphProblem
):
"""
A version of GraphProblem where an action can lead to
nondeterministic output i.e. multiple possible states.
Define the graph as dict(A = dict(Action = [[<Result 1>, <Result 2>, ...], <cost>], ...), ...)
A the dictionary format is different, make sure the graph is created as a directed graph.
"""
def
result
(
self
,
state
,
action
):
return
self
.
graph
.
get
(
state
,
action
)
def
path_cost
(
self
):
raise
NotImplementedError
# ______________________________________________________________________________
class
NQueensProblem
(
Problem
):
"""The problem of placing N queens on an NxN board with none attacking
View remainder of file in raw view
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