slime mold network design - carnegie mellon school of computer …02317/slides/lec_13.pdf · 2016....
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Algorithms in Nature
Slime mold network design
Physarum polycephalum
1cm
Physarum polycephalum
Discrete Form
2N
jN
iN
1N
ijM
Start point
Goal 1N2N
iN )(tip Pressure
ijM ijL
)(tijD
)(tijQ Flux
Length
Conductivity
Modeling of the flux
)( jiij
ijij pp
LD
Q −=
iN )(tip Pressure
ijM ijL
)(tijD
)(tijQ Flux
Length
Conductivity
)(tip Electric Pressure
)( tij
ij
DL
Electric Resistance
)(tijQ Electric Current
Modeling of the tube growth
ijij rDijQDdtd
−= || r :degenerate rate
(constant)
time
rijQ ||
ijD)(tijD
T shape vessel
The tube at dead end disappears
Ring shape vessel
Only shortest tube remains
)( 212
112 LL ≠
Stable equilibrium point Unstable equilibrium point
Ring shape vessel
Both tubes remain
)( 212
112 LL =
Stable equilibrium point Unstable equilibrium point
Solving Maze
Apply for road navigation system
START
GOAL
Using constraints for limiting search space
food
food
Ex 2. Shortest path on Weighted graph
ijij DrijQDdtd
)(|| x−=
=13
)(xr
Slime Mold: Rules for Biologically Inspired
Adaptive Network Design
Tero et al. Science 2010
Network design
• At each iteration select two random points • One acts as a food source, the other as the sink • Compute flux between them based on all other points / tubes in the graph
1. We can reproduce the adaptive network of the true slime mold.
2. “Physarum Solver” can find the shortest path.
Summary
1. What about multiple food sources?
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