42 3. PLANNING IN GVGAI
Ex Ey Ex dominates Ey
partial ordering
Ex Ey Ey Ex indifferent
non-dominated set
P Pareto-set
P P Pareto-front
H V P H V .P /
P H V .P /
3.4.2 MULTI-OBJECTIVE MCTS
m r r back-
propagation
R P
Algorithm 3.3
Input: node
Input: r
Input: dominated r node
procedure node; r; dominated D false
node:Visits D node:Visits C 1
node:R D node:R C r
if dominated then
if node:P r then
dominated D true
else
P
node:P D node:P [ r
end if
end if
Update.node:parent; r; dominated/
3.4. MULTI-OBJECTIVE MCTS FOR GVGAI 43
P
r not r P
P r r P
P H V .P /
Q.s; a/
a
D argmax
a2A.s/
(
HV.P / C C
s
ln N.s/
N.s; a/
)
:
P
Heuristics for GVGAI
Score (Objective O
1
)
10
6
10
6
Level Exploration (Objective O
2
)
pheromone
p
ij
2 Œ0; 1 i j
p
ij
p
ij
p
i;j
D
df
C .1
df
/
dc
p
i;j
;
df
2 .0; 1/
dc
2 .0; 1/
df
D 0:4
dc
D 0:99
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