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Solving the shortest path problem by Physarum Solver - Modeling of the Adaptive Network of True Slime Mold

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Title: Solving the shortest path problem by Physarum Solver - Modeling of the Adaptive Network of True Slime Mold


1
Solving the shortest path problem by Physarum
Solver - Modeling of the Adaptive Network of True
Slime Mold
Hokkaido Univ. Atsushi Tero Hiroshima Univ.
Ryo Kobayashi Hokkaido Univ. Toshiyuki Nakagaki
2
Physarum polycephalum
1cm
3
Physarum polycephalum
4
Solving maze
5
Discrete Form
6
Discrete Form
7
Discrete Form
Pressure
Length
Conductivity
Flux
8
Modeling of the flux of the sol
Pressure
Length
Conductivity
Flux
9
Kirchhoff law
10
Electric sources
11
Modeling of the tube growth
degenerate rate (constant)
12
Model equations
Flux of sol
Tube growth
13
T shape vessel
The tube at dead end disappears
14
Ring shape vessel
Only shortest tube remains
15
Ring shape vessel
Both tubes remain
16
Solving Maze
17
Solving Maze
????
???
18
Solving Maze
????
???
19
Apply for road navigation system
START
GOAL
20
Summary
  1. We can reproduce the adaptive network of the true
    slime mold.
  2. Physarum Solver can find the shortest path.

Current Work
  1. Simulation with many food sources

21
Thats all. Thank you very much!!
22
Apply for road navigation system
START
GOAL
23
Ex 2. Shortest path on Weighted graph
food
24
Ex 2. Shortest path on Weighted graph
25
Ex 2. Shortest path on Weighted graph
26
Solving Maze
Does physarum have enough intelligence to solve
the maze?
START
GOAL
27
Shortest Path From Seattle to Houston
28
Ex. 3 Path choice
vessel
Physarum
food
29
Model Equation
Model of Tube Growth
30
Both tubes remain
Simulation Result
31
Almost all tube remain
??????????
32
Simulation Result
33
One tube remains (chose by initial condition )
Simulation Result
34
One tube remains (chose by initial condition )
??????????
35
Simulation Result
Model of Tube Growth
36
Model Equation
37
Simulation Result with each
Flux
38
Both tubes remain
Simulation Result
39
Application
40
Application
41
Thank you for your attention!!
42
Modeling of the flux of the sol
Poiseuille Flow
43
Ex 2. Shortest path on Weighted graph
44
One tube remains
Simulation Result
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