Simply Logical Ð Chapter 6 p.117-8
search_bstf([Goal|Rest],Goal):goal(Goal).
search_bstf([Current|Rest],Goal):children(Current,Children),
add_bstf(Children,Rest,NewAgenda),
search_bstf(NewAgenda,Goal).
% add_bstf(A,B,C) <- C contains the elements of A and B
%
(B and C sorted according to eval/2)
add_bstf([],Agenda,Agenda).
add_bstf([Child|Children],OldAgenda,NewAgenda):add_one(Child,OldAgenda,TmpAgenda),
add_bstf(Children,TmpAgenda,NewAgenda).
% add_one(S,A,B) <- B is A with S inserted acc. to eval/2
add_one(Child,OldAgenda,NewAgenda):eval(Child,Value),
add_one(Value,Child,OldAgenda,NewAgenda).
Best-first search
© Peter Flach, 2000
Simply Logical Ð Chapter 6 p.120
© Peter Flach, 2000
% tiles_a(A,M,V0,V) <- goal position can be reached from
%
one of the positions on A with last
%
move M (best-first strategy)
tiles_a([v(V,LastMove)|Rest],LastMove,Visited,Visited):goal(LastMove).
tiles_a([v(V,LastMove)|Rest],Goal,Visited0,Visited):show_move(LastMove,V),
setof0(v(Value,NextMove),
( move(LastMove,NextMove),
eval(NextMove,Value) ),
Children),
% Children sorted on Value
merge(Children,Rest,NewAgenda),
% best-first
tiles_a(NewAgenda,Goal,[LastMove|Visited0],Visited).
Solving a puzzle
Simply Logical Ð Chapter 6 p.123
© Peter Flach, 2000
outOfPlace
bLeftOfw
➂ ➁ ➀
➀ ➁ ➂
➃ ➂ ➁
➁ ➂ ➃
0
9
0
12
0
18
1
9
1
10
1
15
2
8
3
9
3
13
4
7
4
7
4
11
5
7
6
7
6
8
6
6
8
4
7
7
8
4
9
4
8
7
9
4
11
3
9
6
10
3
12
2
10
6
12
2
14
0
12
2
13
1
13
2
15
0
15
0
Comparing heuristics
Simply Logical Ð Chapter 6 p.124
© Peter Flach, 2000
☞ An A algorithm is a best-first search algorithm that aims at
minimising the total cost along a path from start to goal.
f(n) = g(n) + h(n)
estimate of total
cost along path
through n
A algorithm
actual cost to
reach n
estimate of cost
to reach goal
from n
Simply Logical Ð Chapter 6 p.125
© Peter Flach, 2000
☞ A heuristic is (globally) optimistic or admissible if the
estimated cost of reaching a goal is always less than
the actual cost.
h(n) ² h*(n)
estimate of cost
to reach goal
from n
actual (unknown)
cost to reach goal
from n
☞ A heuristic is monotonic (locally optimistic) if the
estimated cost of reaching any node is always less
than the actual cost.
h(n1)Ð h(n2)² h*(n1)Ðh*(n2)
Global and local optimism
Simply Logical Ð Chapter 6 p.126
© Peter Flach, 2000
start 3
1
p
0
q
r
s
2
[start-3]
1
goal
start
3
start 3
1
p
r
0
p
1
r
0
2
goal
q
1
0
q
r
2
1
goal
goal
start 3
p
1
p
0
q
r
2
q
s
1
goal
goal
start 3
q
goal
1
1
p
0
q
r
2
s
goal
2
[s-3,s-4]
1
start 3
p
2
[r-3,s-4]
s
1
start 3
s
Non-monotonic heuristic
p
2
[q-2,r-3]
goal
1
[p-2,r-3]
1
start 3
r
0
r
goal
s
1
q
s
q
goal
0
start 3
r
0
p
1
p
1
1
2
2
1
start 3
s
s
r
goal
r
0
q
start 3
s
1
0
s
p
q
p
1
r
0
1
2
q
s
1
start 3
1
2
[goal-3,s-4]
Simply Logical Ð Chapter 6 p.127
© Peter Flach, 2000
search_beam(Agenda,Goal):search_beam(1,Agenda,[],Goal).
search_beam(D,[],NextLayer,Goal):D1 is D+1,
search_beam(D1,NextLayer,[],Goal).
search_beam(D,[Goal|Rest],NextLayer,Goal):goal(Goal).
search_beam(D,[Current|Rest],NextLayer,Goal):children(Current,Children),
add_beam(D,Children,NextLayer,NewNextLayer),
search_beam(D,Rest,NewNextLayer,Goal).
☞ Here, the number of children to be added to the beam is
made dependent on the depth D of the node
✓ in order to keep depth as a ÔglobalÕ variable, search is layer-by-layer
Beam search
Simply Logical Ð Chapter 6 p.128
© Peter Flach, 2000
search_hc(Goal,Goal):goal(Goal).
search_hc(Current,Goal):children(Current,Children),
select_best(Children,Best),
search_hc(Best,Goal).
% hill_climbing as a variant of best-first search
search_hc([Goal
|_],Goal
Goal):):search_hc([Goal|_],
goal(Goal
).
goal(Goal).
search_hc([Current
|_],Goal):search_hc([Current|_],Goal):children(Current
,Children),
children(Current,
Children),
add_bstf(Children
,[],NewAgenda
NewAgenda),
),
add_bstf(Children,[],
search_hc(NewAgenda
,Goal).
search_hc(NewAgenda,Goal).
Hill-climbing