The document describes using threshold-based agent models to optimize plant placement in a landscape. It proposes an agent-based algorithm where individual "plants" search the landscape for optimal locations based on their light and water requirements. A genetic algorithm approach is also mentioned. The goal is to maximize overall plant growth by finding placements where each plant meets a 70% threshold of its ideal growth conditions. Future work could include formal analysis and comparisons to determine how well the approach works at finding the optimal plant collection for a given landscape.

1. Effect of disturbances on subtle-guided
and streaker-guided swarms of bees
By Apratim Shaw

2. Hypothesis
Can robustness to disturbances shed light into the preferred
method of informed flocking in honey bees?

3. Movement of the swarm to new nest
Homeless bees form a cluster around queen
Scout bees search for new nesting site
Scout bees guide the swarm to new site
Worker bees build a new nest
The influence of queen mandibular pheromones on worker attraction to
swarm clusters … Winston et al. 1989
House hunting by honey-bee swarms … Camazine et al. 1999

4. Guiding mechanisms
Pheromone guides
Subtle guides
Streaker guides

5. Model
Reactive algorithm based model
Follower bee
Interaction force based
Threshold based
Guide bee
Subtle
Streaker
Random noise in movements
Limited Range of sensors

6. Follower bee
Herding tendency of follower
bees modeled by an
interaction force. (limited
range)
Dispersing tendency is
modeled by randomness in
the velocity
j ≠i
(
Fi = ∑ 1 − 2e
j
− 0.5 rij 2
)rˆ ,
ij rij ≤R
Damping term is included to
Fi = 0 , rij > R
slow the bees down in the
absence of external stimulus.

7. Subtle guide
Potential gradient drives
subtle guides towards the
destination.
Velocity of subtle guides is
only marginally higher than
the average velocity of
follower bees

8. Streaker guide
Streaker bees make high
speed flights through the
swarm in the direction of the
new home.
On reaching the front-end of
the swarm, the streakers
return at low speed towards
the rear. Return paths still
not known.
Model does not show the
return path of streakers, but
uses a short delay to
account for return time.

9. Threshold based followers
Followers of subtle guides are driven entirely by the interaction forces
that arises out of their herding tendency.
Followers of streaker guides are driven by a threshold based algorithm.
This allows them to latch on to the velocity of any nearby bee with a
velocity exceeding the threshold value.

10. Disturbance
Uniform disturbance
Unidirectional wind
Both types equally robust
Scattering disturbance
Eddies & turbulences
Difference in robustness

11. Experiment
Subtle Guide Streaker Guide

12. Questions
Thank you.

13. Threshold Algorithms
Stephen Heck (Computer Science)
Ask Questions!

14. Introduction - Threshold Algorithms
Threshold based agent models are a simple and elegent way of
modelling complex phenomena in biological systems.
Beyond giving insight into biological systems, this modelling
tool can be applied in a variety of applications.

15. Biological Motivation - Corpse Clustering in Ants
Several species of ants are known to cluster corpses
Messor sancta:
(a) initial state (b) 2 hours (c) 6 hours (d) 26 hours
(images from http://www.chemoton.org/ref39.html)

16. Deneubourg’s Basic Clustering Algorithm
Randomly move
Compute Perceived item Density Score
Use a threshold function to determine whether to pick up or
drop an item
Iterate

17. What is a Threshold Function?
Sigmoid Threshold Function:
s2
f (s, θ) =
s2 + θ2
Notes:
0 ≤ f ≤ 1 ⇒ f is a probability
the higher f is, the more likely the agent will perform its
function
s is the stimulus
θ is the stimulus point where an agent has a 50% chance of
becomming/staying active

18. Sigmoid Threshold Function
Sigmoid Function Plot
1
theta = 0.500000
0.9 theta = 1.000000
theta = 2.000000
0.8 theta = 4.000000
theta = 8.000000
0.7 theta = 16.000000
prob of activation
0.6
0.5
0.4
0.3
0.2
0.1
0 −3 −2 −1 0 1 2
10 10 10 10 10 10
log of stimulus

19. Basic Clustering Algorithm Details
Probability of picking up an item:
2
kp
pp =
kp + f
Probability of dropping up an item:
2
f
pp =
kd + f
Notes:
kp and kd are specified constants
f can be thought of as a density score for the item an agent is
considering picking-up/dropping

20. Threshold Function Behavior
Pick−up Threshold
1
k = 0.100000
0.8 k = 0.200000
k = 0.300000
prob of activation
0.6
0.4
0.2
0
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
f = Perceived Density Score
Drop Threshold
1
0.8
prob of activation
0.6
0.4
0.2
0
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
f = Perceived Density Score

21. Defining the Density Score
The density score can be defined many ways
Basic Algorithm Density Score is implemented as a short-term
memory: An agent keeps track of the number of items
encountered (N) during the past T timesteps
N
f =
T

22. Results - Basic Algorithm
kp = .1 kd = .3 T = 50
Number of Agents = 10
Number of items = 1000
Number of time steps = 106
Begin State t=0
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

23. Sorting - Lumer-Faieta Algorithm
Now consider clustering n sets of things with any number of
attributes
Same basic algorithm applies
Similar in concept to SOMs

24. Lumer-Faieta Algorithm
Density Score
1 d(oi , oj )
f (oi ) = 1−
neigh(oi ) α
oi ∈neigh(oi )
Notes: d(oi , oj ) is a distance function defined on some set of
attributes
α is the “descriminating factor”, it determines the level at which 2
objects become different

25. Density Score
Density score
1.5
1
Density Score
0.5
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
alpha

26. Lumer-Faieta Algorithm - Drop Threshold
Drop Threshold
pd = 2 ∗ f if f ≤ k2
pd = 1 otherwise
Notes: Conceptually this behaves the same way as all threshold
functions do.

27. Drop Threshold
Drop Threshold
1.5
k = 0.100000
k = 0.200000
k = 0.400000
1
prob of activation
0.5
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
f = Perceived Density Score

28. Applications
Trash collection/organization
No more raking leaves!
High-dimensional data exploration
Any problem where you want to gather items that are
dispersed over some physical region.

29. Caveats
106 iterations
No gaurantee on the number of clusters that will be formed

30. Improvements
Different types of agents, fast moving/less descriminative
agents and slower/more discriminative agents
Directed movement through Pheromones/memory - agents
remember the last m items it picked-up and move towards the
most similar location
Agents that have not performed an action in a while start
destroying clusters - helps avoid locally optimal solutions

31. Summary
Threshold algorithms are cool
Questions?

32. A story about plants and putting
them in their place(s)
Some approaches to combinatorial optimization
By Rhonda Hoenigman
Multi-robot Systems
Final Presentation

33. Problem Statement

Original Question: Given a landscape with
light and water conditions available, and
plant types (different light and water
requirements, and sizes)

How many plants and of what type can
the landscape support?

34. Complexity

Really hard problem

Modified question: Find best places for fixed
collection of plants.

Problem is exponential (if landscape discretized).
− i.e. We have 5 plants and 60 spots where
the plants could go. What are the best
spots?
− Problem has complexity of 605

Collection is not fixed, so problem is harder than
exponential.

35. Algorithms

Agent-based model
− Me
− Find best locations for fixed collection
− Use solution to modify collection and add
more plants

Genetic algorithm
− Patrick

36. Motivation and relevance to robot
systems

Harvest Automation

Maximize growth and get robots to do the
work

37. Setting up the problem
• Plant Model – how plants grow
• Optimization criteria
• Algorithm to optimize
• Evaluate the results

38. Plant Model

Reasonable representation for how plants
grow – not too much detail

Limiting model to light and water
requirements

3 categories of light requirements
− Shade, partial sun, and full sun

2 categories of water requirements
− Low and high

39. Light requirements
Adapted from: Harvey, G.W. Photosynthetic performance of isolated leaf cells from sun and shade plants, Carnegie Inst. Washington Yearbook, (79), 161-164.

40. Water Requirements
Adapted from: Van Gardingen, P.R. and Grace, J. Plants and Wind, Advances in Botanical Research, (18), 192-254.

41. Landscape Representation

Conditions effecting plants

Discrete cells, 1ft x 1ft

Each cell has values for morning light,
afternoon light, and water available.

42. Plant-landscape Interaction

Plant occupies one cell

Plants influence their surroundings by
generating shade and using water
– Shading reduces light by 30 percent

Influence based on plant size
– Interaction if plant is larger than 1ft.

43. Optimization - Growth Score

Objective function

Maximize growth score for each plant,
individually

Growth score is percent of ideal.
– If plants are at light saturation point, and
enough water is available, growth =
– Growth limited by not enough light, or not
enough water

70 percent is good enough

44. Agent-based algorithm
• Generate random collection of plants
– Randomly selected light and water
requirements, sizes, and x,y locations.
• Find best places on the landscape for that
fixed collection
– From starting locations, move plants
around until growth score is above 0.70.
– Change initial x,y locations and restart
– Limit number of new locations that a plant
can try out before stopping.
• Limiting moves ensures algorithm will stop

45. Searching for plant collection
• Based on agent-based algorithm for fixed
collection.
• Discard plants that don't find a suitable location
– Growth score below 0.70
• Generate new plant probabilistically based on
what survived on previous iteration
• Continue adding plants until average number of
plants on landscape is not changing more than
some threshold.

46. Experiment
• Created a 6x10 grid (landscape) with arbitrary
light and water conditions.
• 5 plants – selected to match conditions on
landscape
– Test that algorithm works
– Multiple samples of 5 plants
• 5 plants – selected randomly
• Landscape designed to be water-restrictive
– Water available should limit growth for
some plants

47. Results
• 5 plants – one large full sun, low water,
and 4 shade, low water of various sizes
– All plants found suitable locations
• Random trials
– High water plants survived half the time

48. Results – fixed collection
• How well did algorithm place the fixed
collection
• Present examples of how it did over x
trials for y number of plants
• To do: validate against exhaustive search.
• Also, no analysis of difficulty for any given
collection

49. Results – emerging collection
• Start: 5 plants, one large full sun, 4
shade, all low water
• Multiple trials from random starting
collection.
– Algorithm did converge
– Number of plants did increase from
starting collection of five.

51. Future Work
Formal analysis of results – compare to
exhaustive search for a few examples
No comparison to landscape maximum.
Not sure this worked very well at finding the
collection.