44 3. PLANNING IN GVGAI
0.02
0.02
0.120.04 0.04
0.04 0.04
0.12
0.280.120.02 0.020.12
2 .0; 1/
O
2
D 1 p
i;j
i j
O
2
3.4.3 EXPERIMENTAL WORK
C D
p
2 50
10
10 100
5 500
O
1
O
1
˛ C O
2
ˇ ˛ D ˇ D 0:5
3.4. MULTI-OBJECTIVE MCTS FOR GVGAI 45
O
1
O
2
O
1
O
2
O
1
˛ C O
2
ˇ ˛ D ˇ D 0:5
P
Aliens Frogs Missile Command Portals Zelda
Victories Percentage
Algorithm
Victories
1.0
0.8
0.6
0.4
0.2
0.0
Aliens Boulderdash Butterflies Chase Frogs Portals Sokoban ZeldaSurvive
Zombies
Missile
Command
Aliens
46 3. PLANNING IN GVGAI
Sample MCTS
Weighted Sum
MCTS
Mixed Strategy
MCTS
MO-MCTS
% Victories 32.24 (0.67) 29.80 (0.66) 30.51 (0.66) 42.38 (0.70)
100% 50
40
99;80% .0:20/
Frogs
86:40% .1:53/
Survive
Zombies
Survive Zombies
10
7 10
3
50%
3.4. MULTI-OBJECTIVE MCTS FOR GVGAI 47
p < 0:05
Game
Algorithm Victories (%)
τ (Victory)
Scores
τ (Score)
G1
A: Sample MCTS
B: Weighted Sum MCTS
C: Mixed Strategy MCTS
D: MO-MCTS
78.00 (1.85)
64:00 (2:15)
67:00 (2:10)
99.80 (0.20)
Ø
Ø
54.60 (0.39)
53.91 (0.40)
54.44 (0.40)
60.17 (0.50)
B
Ø
Ø
G2
A: Sample MCTS
B: Weighted Sum MCTS
C: Mixed Strategy MCTS
D: MO-MCTS
0.25 (0.25)
0.00 (0.00)
0.32 (0.32)
0.40 (0.28)
Ø
Ø
Ø
Ø
6.83 (0.23)
7.26 (0.26)
6.76 (0.25)
7.53 (0.21)
Ø
Ø
Ø
Ø
G3
A: Sample MCTS
B: Weighted Sum MCTS
C: Mixed Strategy MCTS
D: MO-MCTS
98.20 (0.59)
95.00 (0.97)
98.00 (0.63)
91.40 (1.25)
D
Ø
28.88 (0.62)
28.84 (0.64)
30.02 (0.66)
32.11 (0.72)
Ø
Ø
Ø
G4
A: Sample MCTS
B: Weighted Sum MCTS
C: Mixed Strategy MCTS
D: MO-MCTS
3.20 (0.79)
0.00 (0.00)
0.00 (0.00)
1.80 (0.59)
Ø
Ø
2.47 (0.09)
1.07 (0.06)
1.37 (0.06)
2.49 (0.09)
Ø
B
G5
A: Sample MCTS
B: Weighted Sum MCTS
C: Mixed Strategy MCTS
D: MO-MCTS
13.60 (1.53)
11.28 (1.47)
11.20 (1.41)
86.40 (1.53)`
Ø
Ø
Ø
-1.36 (0.05)
-1.41 (0.05)
-1.39 (0.05)
0.75 (0.03)
Ø
Ø
Ø
G6
A: Sample MCTS
B: Weighted Sum MCTS
C: Mixed Strategy MCTS
D: MO-MCTS
36.00 (2.15)
40.80 (2.20)
38.00 (2.17)
55.60 (2.22)
Ø
Ø
Ø
0.68 (0.17)
0.86 (0.19)
0.67 (0.17)
3.47 (0.21)
Ø
Ø
Ø
G7
A: Sample MCTS
B: Weighted Sum MCTS
C: Mixed Strategy MCTS
D: MO-MCTS
15.80 (1.63)
16.40 (1.66)
14.20 (1.56)
41.60 (2.20)
Ø
Ø
Ø
0.16 (0.02)
0.16 (0.02)
0.14 (0.02)
0.42 (0.02)
Ø
Ø
Ø
G8
A: Sample MCTS
B: Weighted Sum MCTS
C: Mixed Strategy MCTS
D: MO-MCTS
24.60 (1.93)
16.80 (1.67)
15.60 (1.62)
15.60 (1.62)
Ø
Ø
Ø
1.28 (0.04)
0.81 (0.04)
0.96 (0.03)
1.09 (0.04)
Ø
B
G9
A: Sample MCTS
B: Weighted Sum MCTS
C: Mixed Strategy MCTS
D: MO-MCTS
41.00 (2.20)
38.00 (2.17)
42.20 (2.21)
22.20 (1.86)
D
D
D
Ø
33.72 (1.31)
29.92 (1.14)
32.54 (1.23)
37.68 (1.21)
B
Ø
Ø
G10
A: Sample MCTS
B: Weighted Sum MCTS
C: Mixed Strategy MCTS
D: MO-MCTS
5.40 (1.01)
4.20 (0.90)
7.20 (1.16)
9.00 (1.28)
Ø
Ø
B
2.26 (0.12)
2.41 (0.13)
2.17 (0.12)
3.69 (0.14)
Ø
Ø
Ø
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