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ANT COLONYANT COLONYALGORITHM ANDALGORITHM AND
ITSITS
APPLICATIONSAPPLICATIONS
Submitted by,ROCKEY SUSEELAN
M.Tech(2nd SEM), E.S
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CONTENTSCONTENTS
INTRODUCTION.
BEHAVIOR REAL OF ANTS.
ACO.
APPLICATIONS.
ADVANTAGES.
DISADVANTAGES.
CONCLUSION.
REFERENCES.
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INTRODUCTIONINTRODUCTION
The Ant Colony Algorithm is based on thebehavior of real ants foraging for food.
Real ants communicate with each otherusing an aromatic essence calledpheromone, which they leave on the pathsthey traverse.
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Natural behavior of ants have inspired
scientists to mimic insect operational
methods to solve real-life complex
problems.
By observing ant behavior, scientists have
begun to understand their means of
communication.
Ant-based behavioral patterns to address
the real time problems - first proposed by
Marco Dorigo.
REAL ANT BEHAVIOR
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ANT BEHAVIOR
The more ants follow a trail, the more attractive thattrail becomes for being followed
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EXPERIMENTAL STUDY OF ANTS
The more ants follow a trail, the more attractive thattrail becomes for being followed
NEST FOOD
NEST FOOD
NEST FOOD
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Let um and lm be the number of ants thathave used the upper and lower branches.
The probability Pu(m) with which the(m+1)th ant chooses the upper branch is:
)()()()(
klku
kuP
mm
mm
hh
h
u
!
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ROUTE SELECTIONROUTE SELECTION
Ants are forced to decide whether they should
go left or right, and the choice that is made is a
random decision.
Pheromone accumulation is faster on the
shorter path.
The difference in pheromone content between
the two paths over time makes the ants choose
the shorter path.
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GOAL OF ACO HEURISTICGOAL OF ACO HEURISTIC
Artificial ants form a multi-agent system
performing the functions as observed in the
real ant system.
The ACO meta-heuristic relies on the co-operation of a
group of artificial ants to obtain a good solution to a
discrete optimization problem such as the TSP
Artificial ants are mutants of a real antsystem.
The resulting shortest route mappingdetermined by the agents can be applied tothe optimization problem.
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REAL vs. ARTIFICIAL ANTSREAL vs. ARTIFICIAL ANTS
Discrete time steps
Memory Allocation
Quality of Solution
Time of Pheromonedeposition
Distance
Estimation
REAL ANT ARTIFICIAL ANT
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ACOCHARACTERISTICS
Exploit a positive feedback mechanism.
Demonstrate a distributed computational
architecture.
Exploit a global data structure that changes
dynamically as each ant transverses the route.
Involves probabilistic transitions among states
or rather between nodes.
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FLOWCHARTOF ACO
Have allplace been
visited
Have themaximum
Iterations beenperformed
START ACO
Locate ants randomlyin places across thegrid and store the
current place
in the list
Determine probabilisticallyas to which place to visit next
Move to next place andput this place in the
list
Record the length oftour and clear the list
Determine the shortesttour till now and
update pheromone
NO
YES
STOPACO
YESNO
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KEY PARAMETERS
Trail intensity is given by value ofXij which indicates the
intensity of the pheromone on the trail segment.
Trail visibility (Heuristic factor) is Lij = 1/dij .
The relative importance of the intensity in theprobabilistic transition is E.
The importance of the visibility of the trail segment is F.
The trail persistence or evaporation rate is given as V.
Q is a constant and the amount of pheromone laid on atrail segment employed by an Ant. This amount may be
modified in various manners.
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PROBABILISTIC SELECTION
Helps determine the city to visit next while
the ant is in a tour.
Determined by variables such as the
pheromone content in an edge (i,j) at timeinstant t, heuristic function of the desirability
of adding edge, and their control parameters.
? A ? A? A ? A
)(
)(
0
)()(
)()(
iJjif
iJjiftt
tp
k
kilil
ijij
k
iji
kJl
!
FE
FE
LXLX
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ALGORITHMS3 ALGORITHMS
The ant-cycle is the approach discussed so far
Information is updated at the end of each tour as such
function of tour length
The ant-density is an approach wherein the
pheromone quantity Q is deposited once the segment
is transverse.
Pretty much a greedy approach (local information) and not
really providing relative information
The ant-quantity is an approach wherein thepheromone quantity Q/dij is deposited once the
segment is transverse.
Also a greedy approach but providing some relative
information by scaling Q by the length of the segment
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TRAVELLING SALESMANPROBLEM
OBJECTIVE:
Given a set of n cities, the Traveling
Salesman Problem requires a salesman tofind the shortest route between the given
cities and return to the starting city, while
keeping in mind that each city can be visited
only once.
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TRAVELLING SALESMAN PROBLEM
Ant Cycle Algorithm
Step 1:
pheromone traces have equal values for every edge.
place ants in graphs nodes.
Step 2: locate start-up node (city) of every ant on first
position in list.
Step 3:
repeat, for every ant, until list is full move ant from current node to a neighbour node,
chosen with probability
depending on traces value and on weight of edgebetween the two nodes -/
put chosen node in ants list
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Step 4: For each ant,
compute tour length described by the ant. modify the optimal value found (in case of a better
value).
add pheromone on tours edges, depending of thislength.
Step 5:
increment number of iterations.
Step 6:
if (maximum iterations number is not reached) and
there is no stagnation behaviour)
then
empty listsgo to step 2
else
print best solution found
end algorithm
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TSP APPLICATIONS
Lots of practical applications
Manufacturing routing such as movement of
parts along manufacturing floor or the amountof solder on circuit board.
Network design such as determining the
amount of cabling required
Two main types
Symmetric
Asymmetric
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SYMMETRICAL FPGA PLACEMENT
The Field Programmable Gate Array (FPGA)
has gained rapid commercial acceptance as
of its low cost and fast prototyping.
But the area efficiency and performance are
still their drawbacks. So it is necessary to
apply efficient algorithms to handle FPGA
placement for obtaining good area efficiency
and performance.
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FPGA
All FPGAs are composed of three fundamental
components: logic blocks, I/O blocks and
programmable routing resource.
A circuit is implemented by programming each of
logic blocks to implement a small portion of the logic
required by the circuit.
Each of the I/O blocks acts as either an input pad or
an output pad. The programmable routing resource is
configured to make all necessary connections among
different logic blocks. Since routing resources may
occupy 70-90% of the chip area, a good placement
and routing algorithm is very important to overall
FPGA design.
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FPGA ARCHITECTURE
Each routing channel is assumed to have a fixed
number of channel tracks.
Each wire segment spans the distance of one
CLB. Two IOBs fit in the space of each CLB along
the periphery of the FPGA.
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ACO PLACEMENT
FPGA placement is a process which assigns the
blocks in the net list of circuit into CLBs in FPGA
chip.
In the process, the position of the blocks can bechooses to move so that the cost function is
minimized gradually. At the end of placement,
we can get an optimal result.
The most important component of using ACO
algorithm in placement is the management of
pheromone trails.
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According to ACO, we can select the CLBs as the
pheromone trail loader. We set an initial value of
pheromone for each CLB. The value of pheromone
trail will update with the process of placement going
on
The pheromone trail according to the following
formula:
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In the above formula, ij represents the phremone
value of assign Blockj into CLBi. And represents
evaporation coefficient in ACO algorithm.
In the process of placement, if CLBi is selected by the
Blockj in the current placement, we will update the
pheromone trail of CLBi.
We will compute the value of ij according to the
following formula:
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In the above relation, cur_cost is the cost value of
current placement, Q is user-defined parameter.
Since other CLBs except CLBi
are not selected in
this placement, we only decrease the pheromone trail
for them. That is to say, ij is equal to zero for
these CLBs in this placement.
The probability for these CLBs in the next iteration is
large and other CLBs are almost ignored. It will make
the proposed algorithm a local search algorithm.
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In order to avoid the situation, we introduce a new
technique named Max-Min Ant System(MMAS).In this system,
a max value and a min value will be given for pheromone trail.
In first formula
min and
max represent the min value andmax value of pheromone trial in the stage of placement.
In the routing stage, the channel width is decided by the
max width of channels. So if we consider the overlapping
among the bounding boxes in the stage of placement, thechannel width of all channels will be decreased. Then the
routing congestion will also be reduced in the stage of routing.
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The probability of assign Blocki to CLBj
depends on the combination of pheromone
trail and attractiveness. We can compute it
according to the following formula:
where tabuk is the tabu list of ant k, while parameters andspecify the impact of trail and attractiveness, respectively.
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ADVANTAGES
Parallel Computation Mechanism.
The Positive Feedback in ACO accounts for rapid
discovery of good solutions.
ACO employs Distributed computation, which
avoids premature convergence.
Easy Combination With Other Methods.
Good Robustness.
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DISADVANTAGES
These algorithms have slower convergence thanother Heuristics.
They performed poorly for TSP problems larger
than 75 cities.
Long-time Searching.
There is no centralized processor to guide the
Ant System towards good solutions.
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CONCLUSION
As a structure-based algorithm essentially for solving thediscrete domain optimization problems, ant colony
algorithm has many merits, but at the same time it also
has shortcomings including a long searching time and the
local optimum.
Because of its promising characters such as strong
robustness powerful searching ability and easy
combination with other intelligent algorithms, it provides
wide range of application.
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ReferencesReferences
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ReferencesReferences
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ReferencesReferences
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ReferencesReferences
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ReferencesReferences