Rocky 09-08-11-Ant Colony

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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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Rocky 09-08-11-Ant Colony

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