![> Artificial Intelligence: Bacterial Foraging < 2
A. The Chemotaxis
Foraging is done by all animals, even humans. It means to
wander in search of food or materials. Humans use all five of
their senses in order to find some good food at the local
grocery store. E coli, on the other hand, use all their
membrane receptors in order to find food. When they locate
food (amino acids, sugars…etc.), E coli will move towards the
higher concentration. Unlike ants, E coli’s locomotion have
two movements: (1) tumble movement and (2) swim
movement [4,6]. In addition to that, the bacteria will have
lesser probability for it to tumble on a food gradient because it
is in a run (a long period of swimming).
Chemotaxis is the orientation of an agent along a chemical
concentration gradient, either toward or away from stimulus.
As far as E. coli goes, they will always go towards food;
however, away from noxious areas. That noxious area could
be some type of acid, but in the case of the mine detection
problem it could be a cliff. (There were no noxious areas
created in this program due to the fact that the Sahin’s program
had none).
B. Communication
The E. coli chemotaxis signal transduction system monitors
a wide range of internal and external signals. Cells
perceive extracellular nutrients, intracellular redox potential,
pH, temperature and a spectrum of repellents using
only five membrane receptors and the phosphotransferase
system [8]. And with the receptors all around its membrane, E
coli are extremely sensitive in their environment, which in turn
allows them to have a long range sensor [4,8].
They are even able to communicate to each other. They do
this similar to broadcast system. In that, they would secrete a
chemical to attract other bacteria. And with their ability
sensitive sensors in place, it is like they are broadcasting to
each other[3]. This communication allows them to directly
communicate to each other to a point.
This type of communication is not seen in ant foraging at
all. In fact they have a more indirect approach of
communication called stigmergy. With stigmergy, pheromone
trails are placed around the food, in order to attract other ants
to come and help out [3,4]. This indirect approach is like send
an email to a professor: he will not read until he stumbles
upon it, whereas bacterial agents would just call the professor
on a phone. This indirect approach is the main reason why the
ant foraging is not as fast as bacteria.
C. Reproduction
Once a bacterium has enough nutrients, it begins to get longer.
And eventually split into two bacteria [4]. This called mitosis.
D. Elimination and Dispersion
It is possible that over time that the bacterial colony’s
environment can change. It can change due to the
consumption of nutrients in the area or just nature (water)
[4]. With that in mind, the bacteria may or may not increase
it’s chances of finding a mine. It may even worsen the
chance. This event only occurs after much reproduction has
occurred.
III. THE PROBLEM
For years, countries have been trying to answer the age ole
question: how do you find a lost mine? Countries, like the
United States, have tried using sniffer dogs to find mines;
however, this was clearly not a safe answer. But currently
metal detectors are being used. The armies do not, however,
use it in their own country; it is more typical to use this in an
unknown country. And even in that case, mines are still not
being searched thoroughly through the country. With that in
mind, a person can still walk on mine coming from the store at
any time. The likelihood is small, though. Because solving
problems using swarm intelligence is constantly expanding,
bacterial foraging was used in order to solve to problem, which
eliminates the central intelligence of driving these agents.
IV. THE BACTERIAL FORAGING ALGORITHM
The problem that needed to be solved is use bacterial foraging
techniques and compare it to that of ant foraging techniques
for the mine detection problem. The main thing in order to
make this program comparable to Dr. Sahin’s ant foraging
simulation was the following:
The equation in creating the mines was copied from
Dr. Sahin’s version in order to have some control
over it.
Each agent could tumble one unit2
.
The agents would be equally placed around the field.
The radius of nutrient around each mine had to be 3
units. (It is important to realize that outside of the
radius the numbers are so small that they can be
approximated to 0.)
The cell-to-cell attraction function was not changed
to what Dr. Passino originally had. It was kept for
the sake of arguments.
Reproduction, Elimination/Dispersal for the most part was
not truly implemented into the program. Despite the fact
that Dr. Sahin’s program created a function for his agents to
unfreeze themselves, mine did not until the advanced
version was created.
A. The Chemotaxis
Because E. coli have the ability to tumble and swim within
nutrient gradients, two separate movements had to be made.
When there is no mine, the bacteria will tumble. Each one will
tumble, searching for a mine; however, it will not go back to
past 4 moves in order to make the tumble more efficient;
however this is in the more advanced version. When a mine
has been located, they will swim based on the best nutrients—
in the advanced version, the agents will swim towards the
mine. Furthermore, in conjunction with Passino’s model of
2
Originally, the agents movement length was too random and because of
that, they would average in 100s in order to defuse the field.](https://image.slidesharecdn.com/168597b5-a459-4ce3-ba24-5b4f3a11e533-150911145901-lva1-app6892/85/Bacterial-Foraging-Applied-to-the-Mine-Detection-Problem-2-320.jpg)
![> Artificial Intelligence: Bacterial Foraging < 10
E. Conclusion of Results
Name Mean Lower
Control
Limit
Upper
Control
Limit
50 20 50 20 50 20
A 37.83 75.4 13.62 1.6 62.04 167.3
B
With
Swim
31 66.1 0 0 62.91 183.7
Without
Swim
39.1 70.4 0 1.2 78.5 139.7
C
With
Swim
30 47.2 0 0 59.9 101.1
Without
Swim
38.53 58.1 12.67 0 64.4 127.5
D
Regular 23.07 56 4.91 0 41.23 110.1
Without
Swim
31.5 67.9 0 0 75.34 161.5
Without
Scatter
23.03 85.3 0 0 47.89 180.7
Table 2: This table concludes all the charts’ means and
limits for both 50 agents and 20 agents. The agents are
looking for 10 mines in a 30x30 field.
Name Mean Lower
Control
Limit
Upper
Control
Limit
P-
Value
A 197.1 81 313.2 0.101
B
With
Swim
125.3 16 234.6 0.485
Without
Swim
126.5 86.9 166.1 0.175
C
With
Swim
103.8 0 217 0.101
Without
Swim
116.4 0 280.7 0.265
D
Regular 154.7 0 396.1 0.258
Without
Swim
122 27.4 216.6 0.362
Without
Scatter
88.6 0 206.5 0.175
Table 3: This table concludes all the charts’ means and
limits. It displays when the programs are at their
breaking points i.e. 10 agents and 10 mines in a 30x30 field.
From studying Table 2, it can be concluded that normally
bacterial foraging is faster than ant foraging. Now yes, in the
many charts before that, there were at times that the data was
out of control, meaning a data point was above or below the
limits. And because of the averages should be lower; however,
even when the data was changed (taking out the best and worse
cases) the averages were not greatly affected by it.
Furthermore, this data (both ants and bacteria) needed to be
re-tested at times when the data was way out of control. For
example, in ant foraging the number of steps can easily get as
high as 800, while bacteria can get as high as 500. That data
had to be taken out because of two reasons: (1) Rarely did it
happen; (2) The data was beyond out of control.
In the basic version, the agents just tumble and swim. When
a mine has been located, they will swim to that location. A
reason why this was the basic version was because the agents
did not move efficiently enough. They sometimes was would
move to the lower left corner of the field. And on top of that,
if a lot of them end up in the same spot and a mine has been
located, a few them would leave and swim to the mine. A
possible reason for this was the repulsion force between the
agents. Rarely would the agents just get stuck because of this.
Although, it ran better than the ant foraging, the advanced
version was needed in order to stop the agents from doing that.
The reason that the advanced version was made was due to
the fact that the agents moved inefficiently in the basic version.
Again, in the basic version, the agents that are about seven
steps away from the mine would always move to the left. The
reason was simply because the agent would take the first
minimum that it calculated and go there. The advanced
version fixed that by allowing the agent to find all of its
minimums first, and choose the one that would lead it to other
mines. In doing so, the swarming aspect of the agents was
discovered. In addition to fixing that error, the reproduction
function was turned back on3
; however, it has not been
optimized to its truest potential.
Now as far as the experiment without the cell-to-cell
attraction was only tested for the sake of argument. It says that
normally without the cell-to-cell attraction force, the agents
move much quicker—they run longer because the other
bacteria are not holding them back. However, the problem
with this version is the fact that agents are wasting steps. All
of the agents move towards one mine, even if they have to
move from one corner to another corner of the field. On top of
that, E. coli do have an attraction force between each other.
So this experiment, though helpful in future work, can be
scrapped out.
The dispersal and elimination event never occurred in the
program because when it was turned back on, the agents were
moving better.
When the program was at its breaking point i.e. 10 agents
with 10 mines, bacterial foraging came through. Despite Dr.
Sahin’s unfrozen method with the ants, the bacteria normally
3
The reason why it was turned off in the first place was because the agents
needed to find mines without all the extra communication. But basically, in
the end, it was for simple bragging rights. When it is programmed correctly,
the agents will take even less steps, especially when they get frozen.[1]](https://image.slidesharecdn.com/168597b5-a459-4ce3-ba24-5b4f3a11e533-150911145901-lva1-app6892/85/Bacterial-Foraging-Applied-to-the-Mine-Detection-Problem-10-320.jpg)
![> Artificial Intelligence: Bacterial Foraging < 11
attracted each other in order to avoid that. However, both
foragers, ants and bacteria, did go way out of control a lot; and
therefore, the data did have to be re-tested.
VI. FUTURE WORK
There are certain areas in the program that can be optimized
and made more efficient. For one thing, E. coli cannot
reproduce when there is no food gradient. With that, the
reproduction can be optimized in order to effectively, halt
freezing. But in the truest form, reproduction should have
these qualities:
The agent reproduces once it has gathered enough
nutrients and a certain amount of steps has passed.
Reproduction only occurs after a certain amount of
steps has occurred and a mine has been found.
Reproduction should not occur without nutrients.
The idle agents will move to the same location as
the “mother” agent and copy the mother’s
attributes.
If there are no idle agents, the weaker agents will
go there.
Then the mother cannot reproduce until it reaches
the next level of nutrients.
Another area to be optimized would be the
dispersal/elimination process of E. coli. Once the bacteria
have allowed a lot of reproduction to occur and there are still
mines to be the found, certain bacterium will be eliminated and
dispersed.
It should be noted that no bacterium will appear in a new
location when either reproduction or elimination and dispersal
has occurred. Rather, the bacteria will move one step at a time
to the new location. In doing so, the searching of the
bacterium will be optimized.
What might further optimize this search algorithm would be
to allow bacteria that are far away from an active mine should
just keep searching for other mines in the area. However, this
would take away some of its swarming attributes.
VII. CONCLUSION
Although this search algorithm is not optimized, in its most
advanced version, it can be deduced that bacterial foraging is
better than ant foraging. It is not the fact that bacterial
foraging can swim; but rather, it is the simple fact that E. coli
use a more direct approach as far as communication:
broadcasting. And because they have sensors all around their
body, they can sense the nutrients from the mines much better
than ants.
Because bacterial foraging has proven itself to be a better
search algorithm against ant foraging, it should be better any
different problem. The reason for this statement is because of
it’s broadcast-like communication, bacterial foraging is a
better swarm optimization than ants. And because of
bacteria’s ability to run, ants will no longer be able to compete
against bacteria, especially when it is optimized.
VIII. ACKNOWLEDGEMENT
This research could have not been made possible without Dr.
Passino’s previous work on bacteria foraging. Furthermore,
Dr. Sahin needs to be thanked for his suggestions on
optimizing the program and his overall guidance.
IX. REFERENCES
[1] A Swarm Intelligence based approach to the Mine
Detection Problem, Vignesh Kumar and Dr. Ferat Sahin
[2] Ant colony optimization based swarms: implementation for
the mine detection application, Munirajan, V.K.; Sahin, F.;
Cole, E.
[3] An Introduction to Swarm Intelligence Issues; Gianni Di
Caro
[4] Biomimicry of bacterial foraging for distributed
optimization and control, Kevin M. Passino
[5] A tutorial introduction to Swarm; Marcus Daniels, Alex
Lancaster, Benedikt Stefansson
[6] Receptor clustering and signal processing in E. coli
chemotaxis, Victor Sourjik
[7] Cell Motility, Chemosensing, and Chemotaxis,
http://www.cfdrc.com/bizareas/biomedlife/comp_med/che
motaxis.
[8] Bacteria chemotaxis: The five sensors of a bacterium,
Thorsten W. Grebe and Jeff Stock](https://image.slidesharecdn.com/168597b5-a459-4ce3-ba24-5b4f3a11e533-150911145901-lva1-app6892/85/Bacterial-Foraging-Applied-to-the-Mine-Detection-Problem-11-320.jpg)
Bacterial Foraging Applied to the Mine Detection Problem
- 1. > Artificial Intelligence: Bacterial Foraging < 1 Abstract—This paper focuses on a comparison between bacterial foraging and ant foraging for the mine detection problem. The problem with mines is simple: no one knows where they are around the world; and because of that, people fear that they might walk right on top of one. In the mine detection problem, the agents (E. coli) must effectively and optimally move to a mine in order to defuse it. And in the end, the agents must verify whether the given field is cleared of mines in least amount of time. Obviously, the bacterial colony system is studied in order to solve the mine detection problem. It is then tested and advanced in order to make it comparable to ant foraging. Index Terms—Bacterial Foraging, E. coli, swarm intelligence, chemotaxis. I. INTRODUCTION With Mines placed all over the world, scientists have always been interested in solving this problem with natural heuristics. Natural heuristics is simply an educational method in which learning takes place through discoveries that result from investigations (randomly generated hypotheses) by the agent. In this case, foraging techniques have been used in order to solve this complex problem; however, it still has no perfect solution. In Dr. Sahin’s ant foraging, it was discovered that freezing can occur. He solved that simple error; however, he then found a new error with ant foraging. They do not work in teams like bacterial foraging. Although ants are considered to be a very strong group as far as foraging techniques, the program shows that the ants have a hard time working by themselves. As far as bacterial foraging goes, they work both collectively and individually. Four bacterial agents can clear a mine field simply by natural selection—the one who gets the most food has a much better chance of living as compared the bacterium that did not eat as much. It should be obvious that the bacteria will constantly be reproducing themselves in order Manuscript received May 25, 2006. This work was supported in part by the Electrical Engineering Department at Rochester Institute of Technology. James Harris is with the Electrical Engineering Department at Rochester Institute of Technology, Rochester, NY 14623 USA. to get all four of them into one mine gradient. The main difference between the ant and the bacteria is simply the fact that bacteria have better communication than ants. But despite that, many scientists do not believe that bacterial foraging can measure up to ant foraging, though. II. BACTERIAL COLONIES Bacterial colonies are the least studied foraging technique amongst AI scientists. It is due to the fact that they feel that because ant foraging has the most of the characteristics of swarm intelligence: No centralized control Allocation of computing resources to a swarm or just a bunch of simple units Agents interact in a relatively simple and localized way Some useful global behavior can be attained First of all, E. coli are social, meaning this: they will secrete an attractant chemical to call their colonial mates to share food; however, unlike ants, they do not see each other as food1 . They would actually attract each other in order to swarm the food gradient together. Ants can do the same thing after leaving much pheromones and waiting. Bacteria do not have to wait because they tend to work in groups anyways—it can be seen under a microscope. When they do reproduce there are two ways: mitosis and sex. Mitosis is the splitting of the cells on the spot. With mitosis, the new bacterium is assumed to have the same attributes as the parent in order to not only gain better results but also to keep the real world application in mind. As far as “sex,” two bacteria will just cross a few chromosomes and then undergo mitosis. But this was not incorporated into the program because of the simple knowledge that genetic algorithms is not the best method in order to solve these types of problems. Bacteria move in profuse manners. They can be motivated by chemicals, light, oxygen, and others; however, the chemical was the one studied. It is called chemotaxis. 1 This is assuming that the DNA for penicillin is not present either. If it were, and the E. coli got crossed with it is possible that the penicillin can kill off the E. coli. Bacterial Foraging Applied to the Mine Detection Problem (May 2006) James Harris, EEEC, Rochester Institute of Technology
- 2. > Artificial Intelligence: Bacterial Foraging < 2 A. The Chemotaxis Foraging is done by all animals, even humans. It means to wander in search of food or materials. Humans use all five of their senses in order to find some good food at the local grocery store. E coli, on the other hand, use all their membrane receptors in order to find food. When they locate food (amino acids, sugars…etc.), E coli will move towards the higher concentration. Unlike ants, E coli’s locomotion have two movements: (1) tumble movement and (2) swim movement [4,6]. In addition to that, the bacteria will have lesser probability for it to tumble on a food gradient because it is in a run (a long period of swimming). Chemotaxis is the orientation of an agent along a chemical concentration gradient, either toward or away from stimulus. As far as E. coli goes, they will always go towards food; however, away from noxious areas. That noxious area could be some type of acid, but in the case of the mine detection problem it could be a cliff. (There were no noxious areas created in this program due to the fact that the Sahin’s program had none). B. Communication The E. coli chemotaxis signal transduction system monitors a wide range of internal and external signals. Cells perceive extracellular nutrients, intracellular redox potential, pH, temperature and a spectrum of repellents using only five membrane receptors and the phosphotransferase system [8]. And with the receptors all around its membrane, E coli are extremely sensitive in their environment, which in turn allows them to have a long range sensor [4,8]. They are even able to communicate to each other. They do this similar to broadcast system. In that, they would secrete a chemical to attract other bacteria. And with their ability sensitive sensors in place, it is like they are broadcasting to each other[3]. This communication allows them to directly communicate to each other to a point. This type of communication is not seen in ant foraging at all. In fact they have a more indirect approach of communication called stigmergy. With stigmergy, pheromone trails are placed around the food, in order to attract other ants to come and help out [3,4]. This indirect approach is like send an email to a professor: he will not read until he stumbles upon it, whereas bacterial agents would just call the professor on a phone. This indirect approach is the main reason why the ant foraging is not as fast as bacteria. C. Reproduction Once a bacterium has enough nutrients, it begins to get longer. And eventually split into two bacteria [4]. This called mitosis. D. Elimination and Dispersion It is possible that over time that the bacterial colony’s environment can change. It can change due to the consumption of nutrients in the area or just nature (water) [4]. With that in mind, the bacteria may or may not increase it’s chances of finding a mine. It may even worsen the chance. This event only occurs after much reproduction has occurred. III. THE PROBLEM For years, countries have been trying to answer the age ole question: how do you find a lost mine? Countries, like the United States, have tried using sniffer dogs to find mines; however, this was clearly not a safe answer. But currently metal detectors are being used. The armies do not, however, use it in their own country; it is more typical to use this in an unknown country. And even in that case, mines are still not being searched thoroughly through the country. With that in mind, a person can still walk on mine coming from the store at any time. The likelihood is small, though. Because solving problems using swarm intelligence is constantly expanding, bacterial foraging was used in order to solve to problem, which eliminates the central intelligence of driving these agents. IV. THE BACTERIAL FORAGING ALGORITHM The problem that needed to be solved is use bacterial foraging techniques and compare it to that of ant foraging techniques for the mine detection problem. The main thing in order to make this program comparable to Dr. Sahin’s ant foraging simulation was the following: The equation in creating the mines was copied from Dr. Sahin’s version in order to have some control over it. Each agent could tumble one unit2 . The agents would be equally placed around the field. The radius of nutrient around each mine had to be 3 units. (It is important to realize that outside of the radius the numbers are so small that they can be approximated to 0.) The cell-to-cell attraction function was not changed to what Dr. Passino originally had. It was kept for the sake of arguments. Reproduction, Elimination/Dispersal for the most part was not truly implemented into the program. Despite the fact that Dr. Sahin’s program created a function for his agents to unfreeze themselves, mine did not until the advanced version was created. A. The Chemotaxis Because E. coli have the ability to tumble and swim within nutrient gradients, two separate movements had to be made. When there is no mine, the bacteria will tumble. Each one will tumble, searching for a mine; however, it will not go back to past 4 moves in order to make the tumble more efficient; however this is in the more advanced version. When a mine has been located, they will swim based on the best nutrients— in the advanced version, the agents will swim towards the mine. Furthermore, in conjunction with Passino’s model of 2 Originally, the agents movement length was too random and because of that, they would average in 100s in order to defuse the field.
- 3. > Artificial Intelligence: Bacterial Foraging < 3 bacterial foraging, one chemotactic step can be be at most 4 units. However, it was also tested with and without the swimming aspect of bacterial foraging. B. Cohesion-Repulsion Function Confused with the nutrient function, at first this function was used to help locate where the mine would be located. Rather, the purpose of this function is movement—this was mainly used in the searching aspect of the chemotaxis. Whenever, there was no mine detected, they needed to attract each other and at the same time repel each other in order to better locate the mines. Furthermore, this function did help keep the bacterium away from each other. This was done by simply by keeping the the ‘dr’ value at 0.2 units while the ‘da’ was held at 0.1. Again, the reason for these numbers was because it mimicked Passino’s variables. Calculations ))()(( 22 * yxwa edaJa Equation 1: This is the equation of the attractant force ))()(( 22 * yxwr edrJr Equation 2: This is the equation of the repellent force JrJaJar Equation 3: The total force that each bacterium pulls on each other. x=1 y=2 Cohesion-repulsion function for two cells 0 5 10 15 20 25 0 5 10 15 20 25 Figure 1: This is the contour graph of Equation 3, representing the cohesion-repulsion of two cells. Symbol Quantity Ja Diffusible Attractant Force da Amplification factor coefficient wa Attractant secretion coefficient Jr Diffusible Repellent Force dr Amplification factor coefficient wr Chemical cohesion signal coefficient X Data point Y Data point Table 1: Table of Symbols used C. Nutrient Function The nutrient function was created from the Gaussian probability function. The coefficient of -10 was used in order to allow the bacteria to attract and repell each other. Originally, when it was at -1000, the bacteria’s cell-to-cell attraction force had very little affect if any. Furthermore, the function turns on and off, which is determined by the arrays ‘ShowMine’ and ‘DeactivatedMines.’ Initially, ShowMine was filled with zeros, while DeactivatedMines was filled with ones—they were both equal in length and the same length as the number of mines. Furthermore, when a mine was located, it’s respective key value in the ShowMine array would change to a 1, but it would not disappear until four bacteria would come to help deactivate it. When it is deactivated, the mine’s respective value in the DeactivatedMines array would become 0. So in to conclude this function is variable based on what mines have been located and what mines have been deactivated. D. Reproduction and Elimination/Dispersion This piece of the function was not incorporated into the function for the purpose of bragging rights. Despite the bragging rights when it was finally implemented into the program, the weak bacteria would simply move, step by step, to its new location rather than just appearing there. The reproduction, which is the upcoming version, will reproduce like this: The agent reproduces once it has gathered enough nutrients and a certain amount of steps has passed. Reproduction only occurs after a certain amount of steps has occurred and a mine has been found. Reproduction should not occur without nutrients. The idle agents will move to the same location as the “mother” agent and copy the mother’s attributes. If there are no idle agents, the weaker agents will go there. Then the mother cannot reproduce until it reaches the next level of nutrients. The dispersion aspect, which is in the upcoming newer version, would allow a better searching aspect to the program, in theory. Therefore the dispersion may or may not give better results, depending if it takes the agents that long to safeguard the field.
- 4. > Artificial Intelligence: Bacterial Foraging < 4 V. RESULTS A. Ant Foraging Results (A) Observation IndividualValue 28252219161310741 200 150 100 50 0 _ X=82.8 UC L=167.3 LC L=-1.6 Observation MovingRange 28252219161310741 160 120 80 40 0 __ MR=31.8 UC L=103.8 LC L=0 1 1 1 I-MR Chart of Ant Figure 2: This is the control chart, representing 20 ants searching for 10 mines in a 30x30 field. The data point shown that was out of control; however, when removed did not improve the average significantly. Observation IndividualValue 28252219161310741 60 50 40 30 20 _ X=37.83 UC L=62.04 LC L=13.62 Observation MovingRange 28252219161310741 30 20 10 0 __ MR=9.10 UC L=29.74 LC L=0 I-MR Chart of Ant Figure 3: This is the control chart, representing 50 ants searching for 10 mines in a 30x30 field. Ant Percent 5004003002001000-100 99 95 90 80 70 60 50 40 30 20 10 5 1 Mean 197.1 StDev 77.48 N 10 AD 0.574 P-Value 0.101 Probability Plot of Ant Normal - 95% CI Figure 4: This is the probability chart, representing 10 ants searching for 10 mines in a 30x30 field. Observation IndividualValue 10987654321 400 300 200 100 _ X=197.1 UC L=313.2 LC L=81.0 Observation MovingRange 10987654321 200 150 100 50 0 __ MR=43.7 UC L=142.7 LC L=0 1 1 I-MR Chart of Ant Figure 5: This is the control chart, representing 10 ants searching for 10 mines in a 30x30 field. B. Basic Bacteria Foraging Results (B) Observation IndividualValue 30272421181512963 150 100 50 0 -50 _ X=66.1 UC L=183.7 LC L=-51.6 Observation MovingRange 30272421181512963 160 120 80 40 0 __ MR=44.2 UC L=144.5 LC L=0 I-MR Chart of 20 Normal Bacteria Figure 6: This is the control chart, representing 20 bacterial agents searching for 10 mines in a 30x30 field. This is just the basic version. Observation IndividualValue 30272421181512963 160 120 80 40 0 _ X=70.4 UC L=139.7 LC L=1.2 Observation MovingRange 30272421181512963 80 60 40 20 0 __ MR=26.03 UC L=85.06 LC L=0 I-MR Chart of 20 Bacteria w/o Swimming Figure 7: This is the control chart, representing 20 bacterial agents searching for 10 mines in a 30x30 field. This is just the basic version without swimming.
- 5. > Artificial Intelligence: Bacterial Foraging < 5 Observation IndividualValue 30272421181512963 80 60 40 20 0 _ X=31 UC L=62.91 LC L=-0.91 Observation MovingRange 30272421181512963 48 36 24 12 0 __ MR=12 UC L=39.21 LC L=0 1 1 1 I-MR Chart of 50 Normal Bacteria Figure 8: This is the control chart, representing 50 bacterial agents searching for 10 mines in a 30x30 field. This is just the basic version. Observation IndividualValue 30272421181512963 100 75 50 25 0 _ X=39.1 UC L=78.5 LC L=-0.2 Observation MovingRange 30272421181512963 80 60 40 20 0 __ MR=14.79 UC L=48.33 LC L=0 1 11 I-MR Chart of 50 Bacteria w/o Swimming Figure 9: This is the control chart, representing 50 bacterial agents searching for 10 mines in a 30x30 field. This is just the basic version, but without swimming. 10 Normal Bacteria Percent 3002001000-100 99 95 90 80 70 60 50 40 30 20 10 5 1 Mean 0.485 125.3 StDev 50.61 N 10 AD 0.314 P-Value Probability Plot of 10 Normal Bacteria Normal - 95% CI Figure 10: This is the probability chart, representing 10 bacterial agents searching for 10 mines in a 30x30 field. This is just the basic version. 10 Bacteria w/o Swimming Percent 2001751501251007550 99 95 90 80 70 60 50 40 30 20 10 5 1 Mean 0.175 126.5 StDev 19.52 N 10 AD 0.484 P-Value Probability Plot of 10 Bacteria w/o Swimming Normal - 95% CI Figure 11: This is the probability chart, representing 10 bacterial agents searching for 10 mines in a 30x30 field. This is just the basic version without swimming. Observation IndividualValue 10987654321 200 150 100 50 0 _ X=125.3 UC L=234.6 LC L=16.0 Observation MovingRange 10987654321 150 100 50 0 __ MR=41.1 UC L=134.3 LC L=0 I-MR Chart of 10 Normal Bacteria Figure 12: This is the control chart, representing 10 bacterial agents searching for 10 mines in a 30x30 field. This is just the basic version. Observation IndividualValue 10987654321 160 140 120 100 _ X=126.5 UC L=166.10 LC L=86.90 Observation MovingRange 10987654321 48 36 24 12 0 __ MR=14.89 UC L=48.65 LC L=0 I-MR Chart of 10 Bacteria w/o Swimming Figure 13: This is the control chart, representing 10 bacterial agents searching for 10 mines in a 30x30 field. This is just the basic version without the swimming
- 6. > Artificial Intelligence: Bacterial Foraging < 6 C. Advanced Bacteria Foraging Results (C) Observation IndividualValue 30272421181512963 100 75 50 25 0 _ X=47.2 UC L=101.1 LC L=-6.7 Observation MovingRange 30272421181512963 60 45 30 15 0 __ MR=20.28 UC L=66.25 LC L=0 I-MR Chart of 20 Advanced Bacteria Figure 14: This is the control chart, representing 50 bacterial agents searching for 10 mines in a 30x30 field. This is a more advanced version. Observation IndividualValue 30272421181512963 120 90 60 30 0 _ X=58.1 UC L=127.5 LC L=-11.3 Observation MovingRange 30272421181512963 80 60 40 20 0 __ MR=26.10 UC L=85.29 LC L=0 I-MR Chart of 20 Advanced Bacteria w/o Swim Figure 15: This is the control chart, representing 20 bacterial agents searching for 10 mines in a 30x30 field. This is a more advanced version without the swimming. Observation IndividualValue 30272421181512963 60 45 30 15 0 _ X=30 UC L=59.90 LC L=0.10 Observation MovingRange 30272421181512963 40 30 20 10 0 __ MR=11.24 UC L=36.73 LC L=0 I-MR Chart of 50 Advanced Bacteria Figure 16: This is the control chart, representing 50 bacterial agents searching for 10 mines in a 30x30 field. This is a more advanced version Observation IndividualValue 30272421181512963 60 40 20 _ X=38.53 UC L=64.40 LC L=12.67 Observation MovingRange 30272421181512963 30 20 10 0 __ MR=9.72 UC L=31.77 LC L=0 1 I-MR Chart of 50 Advanced Bacteria w/o Swim Figure 17: This is the control chart, representing 50 bacterial agents searching for 10 mines in a 30x30 field. This is a more advanced version without the swimming. 10 Advanced Bacteria Percent 200150100500 99 95 90 80 70 60 50 40 30 20 10 5 1 Mean 0.101 103.8 StDev 30.85 N 10 AD 0.574 P-Value Probability Plot of 10 Advanced Bacteria Normal - 95% CI Figure 18: This is the probability chart, representing 10 bacterial agents searching for 10 mines in a 30x30 field. This is a more advanced version. 10 Advanced Bacteria w/o Swim Percent 3002001000-100 99 95 90 80 70 60 50 40 30 20 10 5 1 Mean 0.265 116.4 StDev 48.47 N 10 AD 0.417 P-Value Probability Plot of 10 Advanced Bacteria w/o Swim Normal - 95% CI Figure 19: This is the probability chart, representing 10 bacterial agents searching for 10 mines in a 30x30 field. This is a more advanced version without the swimming.
- 7. > Artificial Intelligence: Bacterial Foraging < 7 Observation IndividualValue 10987654321 200 150 100 50 0 _ X=103.8 UC L=217.0 LC L=-9.4 Observation MovingRange 10987654321 150 100 50 0 __ MR=42.6 UC L=139.0 LC L=0 I-MR Chart of 10 Advanced Bacteria Figure 20: This is the control chart, representing 10 bacterial agents searching for 10 mines in a 30x30 field. This is a more advanced version. Observation IndividualValue 10987654321 300 200 100 0 _ X=116.4 UC L=280.7 LC L=-47.9 Observation MovingRange 10987654321 200 150 100 50 0 __ MR=61.8 UC L=201.8 LC L=0 I-MR Chart of 10 Advanced Bacteria w/o Swim Figure 21: This is the control chart, representing 10 bacterial agents searching for 10 mines in a 30x30 field. This is a more advanced version without the swimming. D. Bacteria without Attraction Results (D) Observation IndividualValue 28252219161310741 150 100 50 0 -50 _ X=56.0 UC L=145.6 LC L=-33.6 Observation MovingRange 28252219161310741 100 75 50 25 0 __ MR=33.7 UC L=110.1 LC L=0 I-MR Chart of Normal Bacterial Figure 22: This is the control chart, representing 20 bacterial agents searching for 10 mines in a 30x30 field. This version has no cell-to-cell attraction. Observation IndividualValue 28252219161310741 200 150 100 50 0 _ X=67.9 UC L=161.5 LC L=-25.6 Observation MovingRange 28252219161310741 160 120 80 40 0 __ MR=35.2 UC L=114.9 LC L=0 1 1 1 I-MR Chart of Bacteria without Swimming Figure 23: This is the control chart, representing 20 bacterial agents searching for 10 mines in a 30x30 field. This version has no cell-to-cell attraction and no swimming. Observation IndividualValue 28252219161310741 200 150 100 50 0 _ X=85.3 UC L=180.7 LC L=-10.0 Observation MovingRange 28252219161310741 100 75 50 25 0 __ MR=35.9 UC L=117.2 LC L=0 I-MR Chart of Bacteria w/o Optimized Search Figure 24: This is the control chart, representing 20 bacterial agents searching for 10 mines in a 30x30 field. This version has no cell-to-cell attraction and no scatter function. Observation IndividualValue 28252219161310741 40 30 20 10 0 _ X=23.07 UC L=41.23 LC L=4.91 Observation MovingRange 28252219161310741 30 20 10 0 __ MR=6.83 UC L=22.31 LC L=0 1 1 1 I-MR Chart of Normal Bacterial Figure 25: This is the control chart, representing 50 bacterial agents searching for 10 mines in a 30x30 field. This version has no cell-to-cell attraction
- 8. > Artificial Intelligence: Bacterial Foraging < 8 Observation IndividualValue 28252219161310741 80 60 40 20 0 _ X=31.5 UC L=75.34 LC L=-12.34 Observation MovingRange 28252219161310741 60 45 30 15 0 __ MR=16.48 UC L=53.85 LC L=0 I-MR Chart of Bacteria without Swimming Figure 26: This is the control chart, representing 50 bacterial agents searching for 10 mines in a 30x30 field. This version has no cell-to-cell attraction and no swimming. Observation IndividualValue 28252219161310741 48 36 24 12 0 _ X=23.03 UC L=47.89 LC L=-1.82 Observation MovingRange 28252219161310741 40 30 20 10 0 __ MR=9.34 UC L=30.53 LC L=0 1 11 I-MR Chart of Bacteria w/o Optimized Search Figure 27: This is the control chart, representing 50 bacterial agents searching for 10 mines in a 30x30 field. This version has no cell-to-cell attraction and no scatter function. Normal Bacterial Percent 5004003002001000-100-200 99 95 90 80 70 60 50 40 30 20 10 5 1 Mean 154.7 StDev 85.94 N 10 AD 0.421 P-Value 0.258 Probability Plot of Normal Bacterial Normal - 95% CI Figure 28: This is the probability chart, representing 10 bacterial agents searching for 10 mines in a 30x30 field. This version has no cell-to-cell attraction Bacteria without Swimming Percent 300250200150100500 99 95 90 80 70 60 50 40 30 20 10 5 1 Mean 122 StDev 40.29 N 10 AD 0.365 P-Value 0.362 Probability Plot of Bacteria without Swimming Normal - 95% CI Figure 29: This is the probability chart, representing 10 bacterial agents searching for 10 mines in a 30x30 field. This version has no cell-to-cell attraction and no swimming. Bacteria w/o Optimized Search Percent 200150100500 99 95 90 80 70 60 50 40 30 20 10 5 1 Mean 88.6 StDev 34.58 N 10 AD 0.483 P-Value 0.175 Probability Plot of Bacteria w/o Optimized Search Normal - 95% CI Figure 30: This is the probability chart, representing 10 bacterial agents searching for 10 mines in a 30x30 field. This version has no cell-to-cell attraction and no scatter function Observation IndividualValue 10987654321 450 300 150 0 _ X=154.7 UC L=396.1 LC L=-86.7 Observation MovingRange 10987654321 300 200 100 0 __ MR=90.8 UC L=296.6 LC L=0 I-MR Chart of Normal Bacterial Figure 31: This is the control chart, representing 10 bacterial agents searching for 10 mines in a 30x30 field. This version has no cell-to-cell attraction.
- 9. > Artificial Intelligence: Bacterial Foraging < 9 Observation IndividualValue 10987654321 200 150 100 50 0 _ X=122 UC L=216.6 LC L=27.4 Observation MovingRange 10987654321 100 75 50 25 0 __ MR=35.6 UC L=116.2 LC L=0 I-MR Chart of Bacteria without Swimming Figure 32: This is the control chart, representing 10 bacterial agents searching for 10 mines in a 30x30 field. This version has no cell-to-cell attraction and no swimming. Observation IndividualValue 10987654321 200 150 100 50 0 _ X=88.6 UC L=206.5 LC L=-29.3 Observation MovingRange 10987654321 160 120 80 40 0 __ MR=44.3 UC L=144.8 LC L=0 I-MR Chart of Bacteria w/o Optimized Search Figure 33: This is the control chart, representing 10 bacterial agents searching for 10 mines in a 30x30 field. This version has no cell-to-cell attraction and no scatter function.
- 10. > Artificial Intelligence: Bacterial Foraging < 10 E. Conclusion of Results Name Mean Lower Control Limit Upper Control Limit 50 20 50 20 50 20 A 37.83 75.4 13.62 1.6 62.04 167.3 B With Swim 31 66.1 0 0 62.91 183.7 Without Swim 39.1 70.4 0 1.2 78.5 139.7 C With Swim 30 47.2 0 0 59.9 101.1 Without Swim 38.53 58.1 12.67 0 64.4 127.5 D Regular 23.07 56 4.91 0 41.23 110.1 Without Swim 31.5 67.9 0 0 75.34 161.5 Without Scatter 23.03 85.3 0 0 47.89 180.7 Table 2: This table concludes all the charts’ means and limits for both 50 agents and 20 agents. The agents are looking for 10 mines in a 30x30 field. Name Mean Lower Control Limit Upper Control Limit P- Value A 197.1 81 313.2 0.101 B With Swim 125.3 16 234.6 0.485 Without Swim 126.5 86.9 166.1 0.175 C With Swim 103.8 0 217 0.101 Without Swim 116.4 0 280.7 0.265 D Regular 154.7 0 396.1 0.258 Without Swim 122 27.4 216.6 0.362 Without Scatter 88.6 0 206.5 0.175 Table 3: This table concludes all the charts’ means and limits. It displays when the programs are at their breaking points i.e. 10 agents and 10 mines in a 30x30 field. From studying Table 2, it can be concluded that normally bacterial foraging is faster than ant foraging. Now yes, in the many charts before that, there were at times that the data was out of control, meaning a data point was above or below the limits. And because of the averages should be lower; however, even when the data was changed (taking out the best and worse cases) the averages were not greatly affected by it. Furthermore, this data (both ants and bacteria) needed to be re-tested at times when the data was way out of control. For example, in ant foraging the number of steps can easily get as high as 800, while bacteria can get as high as 500. That data had to be taken out because of two reasons: (1) Rarely did it happen; (2) The data was beyond out of control. In the basic version, the agents just tumble and swim. When a mine has been located, they will swim to that location. A reason why this was the basic version was because the agents did not move efficiently enough. They sometimes was would move to the lower left corner of the field. And on top of that, if a lot of them end up in the same spot and a mine has been located, a few them would leave and swim to the mine. A possible reason for this was the repulsion force between the agents. Rarely would the agents just get stuck because of this. Although, it ran better than the ant foraging, the advanced version was needed in order to stop the agents from doing that. The reason that the advanced version was made was due to the fact that the agents moved inefficiently in the basic version. Again, in the basic version, the agents that are about seven steps away from the mine would always move to the left. The reason was simply because the agent would take the first minimum that it calculated and go there. The advanced version fixed that by allowing the agent to find all of its minimums first, and choose the one that would lead it to other mines. In doing so, the swarming aspect of the agents was discovered. In addition to fixing that error, the reproduction function was turned back on3 ; however, it has not been optimized to its truest potential. Now as far as the experiment without the cell-to-cell attraction was only tested for the sake of argument. It says that normally without the cell-to-cell attraction force, the agents move much quicker—they run longer because the other bacteria are not holding them back. However, the problem with this version is the fact that agents are wasting steps. All of the agents move towards one mine, even if they have to move from one corner to another corner of the field. On top of that, E. coli do have an attraction force between each other. So this experiment, though helpful in future work, can be scrapped out. The dispersal and elimination event never occurred in the program because when it was turned back on, the agents were moving better. When the program was at its breaking point i.e. 10 agents with 10 mines, bacterial foraging came through. Despite Dr. Sahin’s unfrozen method with the ants, the bacteria normally 3 The reason why it was turned off in the first place was because the agents needed to find mines without all the extra communication. But basically, in the end, it was for simple bragging rights. When it is programmed correctly, the agents will take even less steps, especially when they get frozen.[1]
- 11. > Artificial Intelligence: Bacterial Foraging < 11 attracted each other in order to avoid that. However, both foragers, ants and bacteria, did go way out of control a lot; and therefore, the data did have to be re-tested. VI. FUTURE WORK There are certain areas in the program that can be optimized and made more efficient. For one thing, E. coli cannot reproduce when there is no food gradient. With that, the reproduction can be optimized in order to effectively, halt freezing. But in the truest form, reproduction should have these qualities: The agent reproduces once it has gathered enough nutrients and a certain amount of steps has passed. Reproduction only occurs after a certain amount of steps has occurred and a mine has been found. Reproduction should not occur without nutrients. The idle agents will move to the same location as the “mother” agent and copy the mother’s attributes. If there are no idle agents, the weaker agents will go there. Then the mother cannot reproduce until it reaches the next level of nutrients. Another area to be optimized would be the dispersal/elimination process of E. coli. Once the bacteria have allowed a lot of reproduction to occur and there are still mines to be the found, certain bacterium will be eliminated and dispersed. It should be noted that no bacterium will appear in a new location when either reproduction or elimination and dispersal has occurred. Rather, the bacteria will move one step at a time to the new location. In doing so, the searching of the bacterium will be optimized. What might further optimize this search algorithm would be to allow bacteria that are far away from an active mine should just keep searching for other mines in the area. However, this would take away some of its swarming attributes. VII. CONCLUSION Although this search algorithm is not optimized, in its most advanced version, it can be deduced that bacterial foraging is better than ant foraging. It is not the fact that bacterial foraging can swim; but rather, it is the simple fact that E. coli use a more direct approach as far as communication: broadcasting. And because they have sensors all around their body, they can sense the nutrients from the mines much better than ants. Because bacterial foraging has proven itself to be a better search algorithm against ant foraging, it should be better any different problem. The reason for this statement is because of it’s broadcast-like communication, bacterial foraging is a better swarm optimization than ants. And because of bacteria’s ability to run, ants will no longer be able to compete against bacteria, especially when it is optimized. VIII. ACKNOWLEDGEMENT This research could have not been made possible without Dr. Passino’s previous work on bacteria foraging. Furthermore, Dr. Sahin needs to be thanked for his suggestions on optimizing the program and his overall guidance. IX. REFERENCES [1] A Swarm Intelligence based approach to the Mine Detection Problem, Vignesh Kumar and Dr. Ferat Sahin [2] Ant colony optimization based swarms: implementation for the mine detection application, Munirajan, V.K.; Sahin, F.; Cole, E. [3] An Introduction to Swarm Intelligence Issues; Gianni Di Caro [4] Biomimicry of bacterial foraging for distributed optimization and control, Kevin M. Passino [5] A tutorial introduction to Swarm; Marcus Daniels, Alex Lancaster, Benedikt Stefansson [6] Receptor clustering and signal processing in E. coli chemotaxis, Victor Sourjik [7] Cell Motility, Chemosensing, and Chemotaxis, http://www.cfdrc.com/bizareas/biomedlife/comp_med/che motaxis. [8] Bacteria chemotaxis: The five sensors of a bacterium, Thorsten W. Grebe and Jeff Stock