solving the shortest path problem by physarum solver - modeling of the adaptive network of true...
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Physarum polycephalum
1cm
Physarum polycephalum
Solving maze
Discrete Form
2N
jN
iN
1N
ijM
Discrete Form
1ijM
iN jN
2ijM
Discrete Form
2N
jN
iN
1N
ijM
Start point
Goal
1N
2N
iN )(tip Pressure
ijM ijL
)(tijD
)(tijQ Flux
Length
Conductivity
Modeling of the flux of the sol
)( jiij
ijij pp
L
DQ
iN )(tip Pressure
ijM ijL
)(tijD
)(tijQ Flux
Length
Conductivity
)(tip Electric Pressure
)( tij
ij
D
LElectric Resistance
)(tijQ Electric Current
Kirchhoff law
jN
2,1j0 iij Q
1N
0I
FS2N
0IFS
Electric sources
0
0
0 2
0 1
I Q
I Q
ii
ii
Modeling of the tube growth
ijij rDijQD
dt
d || r :degenerate rate
(constant)
time
rijQ ||
ijD )(tijD
Model equations
Flux of sol Tube growth
ijij rDijQD
dt
d ||
2,1j
0
0
0 2
0 1
I Q
I Q
ii
ii
0 iij Q)( ji
ij
ijij pp
L
DQ
T shape vessel
The tube at dead end disappears
Ring shape vessel
Only shortest tube remains
)( 212
112 LL
Stable equilibrium pointUnstable equilibrium point
Ring shape vessel
Both tubes remain
)( 212
112 LL
Stable equilibrium pointUnstable equilibrium point
Solving Maze
Solving Maze
スタート
ゴール
Solving Maze
スタート
ゴール
Apply for road navigation system
START
GOAL
1. We can reproduce the adaptive network of the true slime mold.
2. “Physarum Solver” can find the shortest path.
Summary
1. Simulation with many food sources
Current Work
That’s all. Thank you very much!!
Apply for road navigation system
START
GOAL
Ex 2. Shortest path on Weighted graph
food
food
Ex 2. Shortest path on Weighted graph
nyflexibilit
region
：：
nyflexibilit
region
：：
Ex 2. Shortest path on Weighted graph
ijij DrijQD
dt
d)(|| x
1
3)(xr
Solving Maze
START
GOAL
Does physarum have enough intelligence to solve the maze?
Shortest Path From Seattle to Houston
Ex. 3 Path choice
food
vessel
Physarum
Model Equation
ijijij rDQDdt
d
Model of Tube Growth
One(Short)
Both
180180
1
1
10
)1(
Both tubes remain
Stable equilibrium pointUnstable equilibrium point
Simulation Result
)1(
Almost all tube remain
数値シミュレーション
)1( Simulation Result
One tube remains (chose by initial condition )
Simulation Result )1(
Stable equilibrium pointUnstable equilibrium point
One tube remains (chose by initial condition )
数値シミュレーション )1(
Simulation Result
One(initial condition)
One(Short)
Both
Both
180180
1
1
10
ijijij rDQDdt
d
Model of Tube Growth
Model Equation
Q
jiD
1
1
ijij rDQ
QD
dt
d
1||
||
01||
||
ijrDQ
Q
)3(
Simulation Result with each 0I
Flux
Number of the tube
Both tubes remain
)0.3(1||
||0
IrDQ
QD
dt
dij
ij
ijij
Simulation Result
Application
Application
Thank you for your attention!!
a2 Q
Modeling of the flux of the sol
FluxPoiseuille Flow
ij
jiijij L
ppaQ
)(
8
4
8
4ij
ij
aD )( ji
ij
ijij pp
L
DQ
Ex 2. Shortest path on Weighted graph
ijjiij
ij LrppL
D)(x
partlower
partupperr
3/11
3/23)(x
ijji
ij
ij LppL
Dr ˆˆ)(
x
ijijij DrQDdt
d)(x
)0.2(1||
||0
IrDQ
QD
dt
dij
ij
ijij
One tube remains
Simulation Result
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