3.4. MULTI-OBJECTIVE MCTS FOR GVGAI 41
25
Game
Vanila
MCTS
Fast-Evo
MCTS
KB MCTS
KB Fast-Evo
MCTS
Aliens 36.72 (0.9) 38.4 (0.8) 37.56 (1.0) 54.92 (1.6)
Boulderdash 9.96 (1.0) 12.16 (1.2) 17.28 (1.7) 16.44 (1.8)
Butterfl ies 27.84 (2.8) 31.36 (3.4) 31.04 (3.4) 28.96 (2.8)
Chase 4.04 (0.6) 4.8 (0.6) 3.56 (0.7) 9.28 (0.5)
Frogs -0.88 (0.3) -1.04 (0.2) -1.2 (0.2) -0.68 (0.2)
Missile Command -1.44 (0.3) -1.44 (0.3) -1.28 (0.3) 3.24 (1.3)
Portals 0.12 (0.06) 0.28 (0.09) 0.16 (0.07) 0.28 (0.09)
Sokoban 0.16 (0.1) 0.32 (0.1) 0.7 (0.2) 0.6 (0.1)
Survive Zombies 13.28 (2.3) 14.32 (2.4) 18.56 (3.1) 21.36 (3.3)
Zelda 0.08 (0.3) 0.6 (0.3) 0.8 (0.3) 0.6 (0.3)
Overall 9.0 (0.9) 10.0 (1.0) 10.7 (1.0) 13.5 (1.2)
3.4.1 MULTI-OBJECTIVE OPTIMIZATION
optimize
˚
f
1
.Ex/; f
2
.Ex/; : : : ; f
m
.Ex/
Ex 2 m. 2/ f
i
W <
n
! < Ex D
.x
1
; x
2
; : : : ; x
n
/
T
decision vectors <
n
Z <
m
objective vectors
m
E
f .Ex/ D .f
1
.Ex/; f
2
.Ex/; : : : ; f
m
.Ex// Ex
m
Ex dominate Ey
f
i
.Ex/ f
i
. Ey/ 8i D 1; 2; : : : ; m
f
j
.Ex/ f
j
. Ey/ j
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