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An Overview of Swarm Intelligence and Ant Colony Optimization Heuristics

A thesis report submitted in partial fulfillment of the requirements for the degree of Bachelor of Technology in

Computer Science By

Shubham Sethi Roll No.: 0804510056

& Chitra Zangid

Roll No.:0804513008

Under the guidance of Mr. Bipin Kumar Tripathi

& Mrs. Vandana Dixit Kaushik

Department of Computer Science and Engineering HBTI, Kanpur

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Harcourt Butler Technological Institute Kanpur Kanpur -208002, Uttar Pradesh

Certificate This is to certify that the work in this Thesis Report entitled “An Overview of

Swarm Intelligence and Ant Colony Optimization Heuristics” submitted

by Shubham Sethi (0804510056) and Chitra Zangid (0804513008) has been

carried out under my supervision in partial fulfillment of the requirements for

the degree of Bachelor of Technology in Computer Science during session

2011-2012 in the Department of Computer Science and Engineering,

Harcourt Butler Technological Institute, and this work has not been submitted

elsewhere.

Place: HBTI Kanpur Mr Bipin Kumar Tripathi Date : 22, November,2011 (Associate Professor)

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Acknowledgements No thesis is created entirely by an individual, many people have helped to

create this thesis and each of their contribution has been valuable. My deepest

gratitude goes to my thesis supervisor, Mr.Bipin Kumar Tripathi, Assoc.

Prof., Department of CSE, for his guidance, support, motivation and

encouragement through out the period this work was carried out. His readiness

for consultation at all times, his educative comments, his concern and assistance

even with practical things have been invaluable.

I am grateful to Mr Narendra Kohli, Assistant Prof. and Head, Dept. of CSE

for his excellent support during my work. I would also like to thank all

professors and lecturers, and members of the department of Computer Science

and Engineering for their generous help in various ways for the completion of

this thesis. A vote of thanks to my fellow students for their friendly co-

operation.

Shubham Sethi 0804510056 Chitra Zangid 0804513008

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Abstract We describe an artificial ant colony capable of solving the traveling salesman

problem (TSP). Ants of the artificial colony are able to generate successively

shorter feasible tours by using information accumulated in the form of a

pheromone trail deposited on the edges of the TSP graph. Computer simulations

demonstrate that the artificial ant colony is capable of generating good solutions

to both symmetric and asymmetric instances of the TSP. The method is an

example, like simulated annealing, neural networks, and evolutionary

computation, of the successful use of a natural metaphor to design an

optimization algorithm. colony optimization (ACO) is a recent family member

of the meta-heuristic algorithms and can be used to solve complex optimization

problems with few modifications by adding problem-dependent heuristics. ACO

is a biological inspiration simulating the ability of real ant colony of finding the

shortest path between the nest and food source. It is one of the successful

applications of swarm intelligence which is the field of artificial intelligence

that study the intelligent behavior of groups rather than of individuals such as

the behavior of natural system of social insects like ants, bees, wasps, and

termites. Swarm intelligence uses stigmergy which is a form of indirect

communication through the environment.

The class of complex optimization problems called combinatorial optimization

problems are ound in many areas of research and development. Traveling

Salesman Problem (TSP), Quadratic Assignment Problem (QAP), Vehicle

Routing Problem (VRP), Graph Coloring Problem (GCP), Sequential Ordering

Problem (SOP), Job Scheduling Problem (JSP) and Network Routing Problem

(NRP) are some examples of these problems. Combinatorial optimization

problems arise when the task is to find the best out of many possible solutions

to a given problem, provided that a clear notion of solution quality exists.

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1. Introduction

Ant Colony Optimization (ACO) is a paradigm for designing metaheuristic

algorithms for combinatorial optimization problems. The first algorithm which

can be classified within this framework was presented in 1991 [21, 13] and,

since then, many diverse variants of the basic principle have been reported in

the literature.

The essential trait of ACO algorithms is the combination of a priori information

about the structure of a promising solution with a posteriori information about

the structure of previously obtained good solutions.

Metaheuristic algorithms are algorithms which, in order to escape from local

optima, drive some basic heuristic: either a constructive heuristic starting from a

null solution and adding elements to build a good complete one, or a local

search heuristic starting from a complete solution and iteratively modifying

some of its elements in order to achieve a better one. The metaheuristic part

permits the low level heuristic to obtain solutions better than those it could have

achieved alone, even if iterated. Usually, the controlling mechanism is achieved

either by constraining or by randomizing the set of local neighbor solutions to

consider in local search (as is the case of simulated annealing or tabu search ),

or by combining elements taken by different solutions (as is the case of

evolution strategies and genetic or bionomic algorithms). The characteristic of

ACO algorithms is their explicit use of elements of previous solutions. In fact,

they drive a constructive low-level solution, as GRASP does, but including it in

a population framework and randomizing the construction in a Monte Carlo

way. A Monte Carlo combination of different solution elements is suggested

also by Genetic Algorithms , but in the case of ACO the probability distribution

is explicitly defined by previously obtained solution components. The particular

way of defining components and associated probabilities is problem specific,

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and can be designed in different ways, facing a trade-off between the specificity

of the information used for the conditioning and the number of solutions which

need to be constructed before effectively biasing the probability distribution to

favor the emergence of good solutions. Different applications have favored

either the use of conditioning at the level of decision variables, thus requiring a

huge number of iterations before getting a precise distribution, or the

computational efficiency, thus using very coarse conditioning information. The

chapter is structured as follows. Section 2 describes the common elements of

the heuristics following the ACO paradigm and outlines some of the variants

proposed. Section 3 presents the application of ACO algorithms to a number of

different combinatorial optimization problems and it ends with a wider

overview of the problem attacked by means of ACO up to now. Section 4

outlines the most significant theoretical results so far published about

convergence properties of ACO variants.

2. Swarm Intelligence:

2.1Meaning Of Swarn:

A large no. of insects or small organism, specially when in motion. Swarm

Intelligence (SI) is the property of a system whereby the collective behaviors of

(unsophisticated) agents interacting locally with their environment cause

coherent functional global patterns to emerge.

SI provides a basis with which it is possible to explore collective (or distributed)

problem solving without centralized control or the provision of a global

model.Leverage the power of complex adaptive systems to solve difficult non-

linear stochastic problems

2.2 Characteristics of a swarm:

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• Distributed, no central control or data source.

• Limited communication. No (explicit) model of the environment.

• Perception of environment (sensing).

• Ability to react to environment changes.

• Social interactions (locally shared knowledge) provides the basis for

unguided problem solving.

• Achieving a collective performance which could not normally be

achieved by an individual acting alone.

3. Ants in nature

Individual ants are behaviourally very unsophisticated insects. They have a very

limited memory and exhibit individual behaviour that appears to have a large

random component. Acting as a collective however, ants manage to perform a

variety of complicated tasks with great reliability and consistency.

These behaviours emerge from the interactions between large numbers of

individual ants and their environment. In many cases, the principle of

stigmergyis used. Stigmergy is a form of indirect communication through the

environment. Like other insects, ants typically produce specific actions in

response to specific local environmental stimuli, rather than as part of the

execution of some central plan. If an ant's action changes the local environment

in a way that affects one of these specific stimuli, this will influence the

subsequent actions of ants at that location. The environmental change may take

either of two distinct forms. In the first, the physical characteristics may be

changed as a result of carrying out some task-related action, such as digging a

hole, or adding a ball of mud to a growing structure. The subsequent perception

of the changed environment may cause the next ant to enlarge the hole, or

deposit its ball of mud on top of the previous ball. In this type of stigmergy, the

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cumulative effects of these local task-related changes can guide the growth of a

complex structure.

This type of influence has been called sematectonic (Wilson, 1975). In the

second form, the environment is changed by depositing something which makes

no direct contribution to the task, but is used solely to influence subsequent

behaviour which is task related. This sign-based stigmergy has been highly

developed by ants and other exclusively social insects, which use a variety of

highly specific volatile hormones, or pheromones, to provide a sophisticated

signaling system.

4. Basic principles of trail laying

Depending on the species, ants may lay pheromone trails when travelling from

the nest to food, or from food to the nest, or when travelling in either direction.

They also follow these trails with a fidelity which is a function of the trail

strength, among other variables. Ants drop pheromones as they walk by

stopping briefly and touching their gaster, which carries the pheromone

secreting gland, on the ground. The strength of the trail they lay is a function of

the rate at which they make deposits, and the amount per deposit. Since

pheromones evaporate and diffuse away, the strength of the trail when it is

encountered by another ant is a function of the original strength, and the time

since the trail was laid. Most trails consist of several superimposed trails from

many different ants, which may have been laid at different times; it is the

composite trail strength which is sensed by the ants

5. Pheromone

In the natural world, ants (initially) wander randomly, and upon finding food

return to their colony while laying down pheromone trails. If other ants find

such a path, they are likely not to keep travelling at random, but to instead

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follow the trail, returning and reinforcing it if they eventually find food (see Ant

communication).

Over time, however, the pheromone trail starts to evaporate, thus reducing its

attractive strength. The more time it takes for an ant to travel down the path and

back again, the more time the pheromones have to evaporate. A short path, by

comparison, gets marched over more frequently, and thus the pheromone

density becomes higher on shorter paths than longer ones. Pheromone

evaporation also has the advantage of avoiding the convergence to a locally

optimal solution. If there were no evaporation at all, the paths chosen by the

first ants would tend to be excessively attractive to the following ones. In that

case, the exploration of the solution space would be constrained.

Thus, when one ant finds a good (i.e., short) path from the colony to a food

source, other ants are more likely to follow that path, and positive feedback

eventually leads all the ants following a single path. The idea of the ant colony

algorithm is to mimic this behavior with "simulated ants" walking around the

graph representing the problem to solve.

The original idea comes from observing the exploitation of food resources

among ants, in which ants’ individually limited cognitive abilities have

collectively been able to find the shortest path between a food source and the

nest.

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The first ant finds the food source (F), via any way (a), then returns to the nest

(N),leaving behind a trail pheromone .

Ants indiscriminately follow four possible ways, but the strengthening of the

runway makes it more attractive as the shortest route. Ants take the shortest

route, long portions of other ways lose their trail pheromones.

The basic philosophy of the algorithm involves the movement of a colony of

ants through the different states of the problem influenced by two local decision

policies, viz., trails and attractiveness. Thereby, each such ant incrementally

constructs a solution to the problem. When an ant completes a solution, or

during the construction phase, the ant evaluates the solution and modifies the

trail value on the components used in its solution. This pheromone information

will direct the search of the future ants. Furthermore, the algorithm also includes

two more mechanisms, viz., trail evaporation and daemon actions. Trail

evaporation reduces all trail values over time thereby avoiding any possibilities

of getting stuck in local optima. The daemon actions are used to bias the search

process from a non-local perspective.

6. Ant Colony Optimization

ACO is a class of algorithms, whose first member, called Ant System, was

initially proposed by Colorni, Dorigo and Maniezzo [13, 21, 18]. The main

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underlying idea, loosely inspired by the behavior of real ants, is that of a parallel

search over several constructive computational threads based on local problem

data and on a dynamic memory structure containing information on the quality

of previously obtained result. The collective behavior emerging from the

interaction of the different search threads has proved effective in solving

combinatorial optimization (CO) problems.

Following , we use the following notation. A combinatorial optimization

problem is a problem defined over a set C = c1, ... , cn of basic components. A

subset S of components represents a solution of the problem; F Í 2C is the

subset of feasible solutions, thus a solution S is feasible if and only if S Î F. A

cost function z is defined over the solution domain, z : 2C à R, the objective

being to find a minimum cost feasible solution S*, i.e., to find S*: S* Î F and

z(S*) £ z(S), "SÎF.

Given this, the functioning of an ACO algorithm can be summarized as follows.

A set of computational concurrent and asynchronous agents (a colony of ants)

moves through states of the problem corresponding to partial solutions of the

problem to solve. They move by applying a stochastic local decision policy

based on two parameters, called trails and attractiveness. By moving, each ant

incrementally constructs a solution to the problem. When an ant completes a

solution, or during the construction phase, the ant evaluates the solution and

modifies the trail value on the components used in its solution. This pheromone

information will direct the search of the future ants.

Furthermore, an ACO algorithm includes two more mechanisms : trail

evaporation and, optionally, daemon actions. Trail evaporation decreases all

trail values over time, in order to avoid unlimited accumulation of trails over

some component. Daemon actions can be used to implement centralized actions

which cannot be performed by single ants, such as the invocation of a local

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optimization procedure, or the update of global information to be used to decide

whether to bias the search process from a non-local perspective.

6.1Improvements to algo

Here are some of most popular variations of ACO Algorithms

• Elitist ant system: The global best solution deposits pheromone on every

iteration along with all the other ants.

• Max-Min ant system (MMAS): Added Maximum and Minimum

pheromone amounts [τmax,τmin] Only global best or iteration best tour

deposited pheromone. All edges are initialized to τmax and reinitialized

to τmax when nearing stagnation.

• Ant Colony System:It has been presented above.

• Rank-based ant system (ASrank):All solutions are ranked according to

their length. The amount of pheromone deposited is then weighted for

each solution, such that solutions with shorter paths deposit more

pheromone than the solutions with longer paths.

• Continuous orthogonal ant colony (COAC): The pheromone deposit

mechanism of COAC is to enable ants to search for solutions

collaboratively and effectively. By using an orthogonal design method,

ants in the feasible domain can explore their chosen regions rapidly and

efficiently, with enhanced global search capability and accuracy.

• The orthogonal design method and the adaptive radius adjustment method

can also be extended to other optimization algorithms for delivering

wider advantages in solving practical problems.

7. Double Bridge Experiment

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In a series of experiments on a colony of ants with a choice between two

unequal length paths leading to a source of food, biologists have observed that

ants tended to use the shortest route.

follows:

An ant (called "blitz") runs more or less at random around the colony

discovers a food source, it returns more or less directly to the nest, leaving in its

path a trail of pheromone.

These pheromones are attractive, nearby ants will be inclined to follow, more or

less directly, the track.Returning to the colony, these

route.

If there are two routes to reach the same food source then, in a given amount of

time, the shorter one will be traveled b

The short route will be increasingly enhanced, and therefore become more

attractive.The long route will eventually disappear

volatile. Eventually, all the ants have determined and therefore "chosen" the

shortest route.Ants use the environment as a

exchange information indirectly by depositing pheromones, all detailing the

In a series of experiments on a colony of ants with a choice between two

unequal length paths leading to a source of food, biologists have observed that

ants tended to use the shortest route. A model explaining this behavio

blitz") runs more or less at random around the colony

discovers a food source, it returns more or less directly to the nest, leaving in its

.

These pheromones are attractive, nearby ants will be inclined to follow, more or

Returning to the colony, these ants will strengthen the

If there are two routes to reach the same food source then, in a given amount of

time, the shorter one will be traveled by more ants than the long route.

e will be increasingly enhanced, and therefore become more

The long route will eventually disappear because pheromones are

Eventually, all the ants have determined and therefore "chosen" the

shortest route.Ants use the environment as a medium of communication. They

exchange information indirectly by depositing pheromones, all detailing the

In a series of experiments on a colony of ants with a choice between two

unequal length paths leading to a source of food, biologists have observed that

A model explaining this behavior is as

blitz") runs more or less at random around the colony. If it

discovers a food source, it returns more or less directly to the nest, leaving in its

These pheromones are attractive, nearby ants will be inclined to follow, more or

ants will strengthen the

If there are two routes to reach the same food source then, in a given amount of

y more ants than the long route.

e will be increasingly enhanced, and therefore become more

because pheromones are

Eventually, all the ants have determined and therefore "chosen" the

medium of communication. They

exchange information indirectly by depositing pheromones, all detailing the

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status of their "work". The information exchanged has a local scope, only an ant

located where the pheromones were left has a notion of them. This system is

called "Stigmergy" and occurs in many social animal societies (it has been

studied in the case of the construction of pillars in the nests of termites). The

mechanism to solve a problem too complex to be addressed by single ants is a

good example of a self-organized system. This system is based on positive

feedback (the deposit of pheromone attracts other ants that will strengthen it

themselves) and negative (dissipation of the route by evaporation prevents the

system from thrashing). Theoretically, if the quantity of pheromone remained

the same over time on all edges, no route would be chosen. However, because

of feedback, a slight variation on an edge will be amplified and thus allow the

choice of an edge. The algorithm will move from an unstable state in which no

edge is stronger than another, to a stable state where the route is composed of

the strongest edges.

8. Applications

Ant colony optimization algorithms have been applied to many combinatorial

optimization problems, ranging from quadratic assignment to protein folding or

routing vehicles and a lot of derived methods have been adapted to dynamic

problems in real variables, stochastic problems, multi-targets and parallel

implementations. It has also been used to produce near-optimal solutions to the

travelling salesman problem. They have an advantage over simulated annealing

and genetic algorithm approaches of similar problems when the graph may

change dynamically; the ant colony algorithm can be run continuously and

adapt to changes in real time. This is of interest in network routing and urban

transportation systems.

As a very good example, ant colony optimization algorithms have been used to

produce near-optimal solutions to the travelling salesman problem. The first

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ACO algorithm was called the Ant system and it was aimed to solve the

travelling salesman problem, in which the goal is to find the shortest round-trip

to link a series of cities.

8.1 Scheduling problem

• Job-shop scheduling problem (JSP)

• Open-shop scheduling problem (OSP)

• Permutation flow shop problem (PFSP)

• Single machine total tardiness problem (SMTTP)

• Single machine total weighted tardiness problem (SMTWTP)

• Resource-constrained project scheduling problem (RCPSP)

• Group-shop scheduling problem (GSP)

• Single-machine total tardiness problem with sequence dependent setup

times (SMTTPDST)

• Multistage Flowshop Scheduling Problem (MFSP) with sequence

dependent setup/changeover times

8.2 Vehicle routing problem

• Capacitated vehicle routing problem (CVRP)

• Multi-depot vehicle routing problem (MDVRP)

• Period vehicle routing problem (PVRP)

• Split delivery vehicle routing problem (SDVRP)

• Stochastic vehicle routing problem (SVRP)

• Vehicle routing problem with pick-up and delivery (VRPPD)

• Vehicle routing problem with time windows (VRPTW)

• Time Dependent Vehicle Routing Problem with Time Windows

(TDVRPTW)

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8.3 Assignment problem

• Quadratic assignment problem (QAP)

• Generalized assignment problem (GAP)

• Frequency assignment problem (FAP)

• Redundancy allocation problem (RAP)

8.4 Set problem

• Set covering problem(SCP)

• Set partition problem (SPP)

• Weight constrained graph tree partition problem (WCGTPP)

• Arc-weighted l-cardinality tree problem (AWlCTP)

• Multiple knapsack problem (MKP)

• Maximum independent set problem (MIS)[46]

8.5 Others

• Classification

• Connection-oriented network routing.

• Connectionless network routing.

• Data mining.

• Discounted cash flows in project scheduling

• Distributed Information Retrieval.Grid Workflow Scheduling Problem.

• Image processing.

• Intelligent testing system.

• System identification.

• Protein Folding.

• Power Electronic Circuit Design.

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9.Travelling Salesman problem

The traveling salesman problem (TSP) is the problem of finding a shortest

closed tour which visits all the cities in a given set. In this article we will restrict

attention to TSPs in which cities are on a plane and a path (edge) exists between

each pair of cities (i.e., the TSP graph is completely connected).

9.1 Artificial ants

In this work an artificial ant is an agent which moves from city to city on a TSP

graph. It chooses the city to move to using a probabilistic function both of trail

accumulated on edges and of a heuristic value, which was chosen here to be a

function of the edges length. Artificial ants probabilistically prefer cities that are

connected by edges with a lot of pheromone trail and which are close-by.

Initially, m artificial ants are placed on randomly selected cities. At each time

step they move to new cities and modify the pheromone trail on the edges used

–this is termed local trail updating. When all the ants have completed a tour the

ant that made the shortest tour modifies the edges belonging to its tour –termed

global trail updating– by adding an amount of pheromone trail that is inversely

proportional to the tour length.

These are three ideas from natural ant behavior that we have transferred to our

artificial ant colony: (i) the preference for paths with a high pheromone level,

(ii) the higher rate of growth of the amount of pheromone on shorter paths, and

(iii) the trail mediated communication among ants. Artificial ants were also

given a few capabilities which do not have a natural counterpart, but which have

been observed to be well suited to the TSP application: artificial ants can

determine how far away cities are, and they are endowed with a working

memory Mk used to memorize cities already visited (the working memory is

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emptied at the beginning of each new tour, and is updated after each time step

by adding the new visited city).

There are many different ways to translate the above principles into a

computational system apt to solve the TSP. In our ant colony system (ACS) an

artificial ant k in city r chooses the city s to move to among those which do not

belong to its working memory Mk by applying the following probabilistic

formula:

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Local updating is intended to avoid a very strong edge being chosen by all the

ants: Everytime an edge is chosen by an ant its amount of pheromone is

changed by applying the local trail updating formula: τ (r,s)←(1−α )⋅τ (r,s) +α ⋅τ

0, where τ 0 is a parameter. Local trail updating is also motivated by trail

evaporation in real ants.

Interestingly, we can interpret the ant colony as a reinforcement learning

system, in which reinforcements modify the strength (i.e., pheromone trail) of

connections between cities. In fact, the above formulas (1) and (2) dictate that

an ant can either, with probability q0, exploit the experience accumulated by the

ant colony in the form of pheromone trail (pheromone trail will tend to grow on

those edges which belong to short tours, making them more desirable), or, with

probability (1-q0), apply a biased exploration (exploration is biased towards

short and high trail edges) of new paths by choosing the city to move to

randomly, with a probability distribution that is a function of both the

accumulated pheromone trail, the heuristic function, and the working memory

Mk.

It is interesting to note that ACS employs a novel type of exploration strategy.

First, there is the stochastic component S of formula (1): here the exploration of

new paths is biased towards short and high trail edges. (Formula (1), which we

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call pseudo-random-proportional action choice rule, is strongly reminiscent of

the pseudo-random action choice rule often used in reinforcement learning; see

for example Q-learning (Watkins and Dayan, 1992)). Second, local trail

updating tends to encourage exploration since each path taken has its

pheromone value reduced by the local updating formula.

10. Load Balancing Problem

10.1 Ant-Based Control (ABC) for network management

How could this trail laying and following behaviour be applied to something

like a telecommunications network? And can we overcome the blocking

problem and the shortcut problem? This section describes how we implemented

an artificial ant population on the network model.

We replaced the routing tables in the network nodes by tables of probabilities,

which we will call ‘pheromone tables’, as the pheromone strengths are

represented by these probabilities. Every node has a pheromone table for every

possible destination in the network, and each table has an entry for every

neighbour. For example, a node with four neighbours in a 30-node network has

29 pheromone tables with four entries each. One could say that an n-node

network uses n different kinds of pheromones. The entries in the tables are the

probabilities which influence the ants’ selection of the next node on the way to

their destination node.

The method used to update the probabilities is quite simple: when an ant arrives

at a node, the entry in the pheromone table corresponding to the node from

which the ant has just come is increased according to the formula:

Increase the probability of the visited link by:

ρρρρ

∆+∆+

=1old

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Decrease the probability of the others by :

where

Since the new values sum to 1, they can again be interpreted as probabilities.

Note that a probability can be reduced only by the operation of normalization

following an increase in another cell in the table; since the reduction is achieved

by multiplying by a factor less than one, the probability can approach zero if the

other cell or cells are increased many times, but will never reach it. For a given

value of Dp the absolute and relative increase in probability is much greater for

initially small probabilities than for those which are larger. This has the effect of

weighting information from ants coming from nodes which are not on the

currently referred route, a feature which may assist in the rapid solution of the

shortcut problem.

10.2 Ageing and delaying ants

A primary requirement of this work was to find some simple methods of

encouraging the ants to find routes which are relatively short, yet which avoid

nodes which are heavily congested. Two methods are used. The first is to make

Dp, the value used to change the pheromone tables, reduce progressively with

the age of the ant. When the ant moves at one node per time step, the age of the

ant corresponds to the path length it has traced; this biases the system to respond

more strongly to those ants which have moved along shorter trails. The second

method, which depends on the first, is to delay ants at nodes that are congested

with calls to a degree which increases with the degree of congestion. This delay

has two complementary effects:

ρρρ∆+

=1

old

=∆

agef

1ρ

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• It temporarily reduces the flow rate of ants from the congested node to its

neighbours, thereby preventing those ants from affecting the pheromone

tables which are routing ants to the congested node, and allowing the

probabilities for alternative choices to increase rapidly.

• Since the ants are older than they otherwise would have been when they

finally reach the neighbouring nodes, they have less effect on the

pheromone tables.

10.3 How calls are routed

Having explained how ants ‘choose’ their routes through the network, let us

consider the calls. Calls operate independently of the ants. To determine the

route for a call from a particular node to a destination, the largest probability in

the pheromone table for this destination is looked up. The neighbour node

corresponding to this probability will be the next node on the route to this

destination. The route is valid if the destination is reached, and the call is then

placed on the network, unless one of the nodes on the route is congested; in that

case the call fails to be placed on the network.

In this way, calls and ants dynamically interact with each other. Newly arriving

calls influence the load on nodes, which will influence the ants by means of the

delay mechanism. Ants influence the routes represented by the pheromone

tables, which in their turn determine the routing of new calls. One needs to

realise that the pheromone table by which an individual ant is influenced, is a

different table than the pheromone table that will be updated by this ant. The

load on the network at any given time influences which calls can subsequently

be placed on the network and which calls will fail; which of course determines

the load at a later stage. Relationship between calls, node utilisation, pheromone

tables and ants. An arrow indicates the direction of influence.

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Relationship between calls, node utilisation, pheromone tables and ants. An

arrow indicates the direction of influence.

11. Conclusions

Ant Colony Optimization has been and continues to be a fruitful paradigm for

designing effective combinatorial optimization solution algorithms. After more

tha ten years of studies, both its application effectiveness and its theoretical

groundings have been demonstrated, making ACO one of the most successful

paradigm in the metaheuristic area.

This overview tries to propose the reader both introductory elements and

pointers to recent results, obtained in the different directions pursued by current

research on ACO.

No doubt new results will both improve those outlined here and widen the area

of applicability of the ACO paradigm.

12. References

[1] B. Barán, M Almirón, E. Chaparro. ‘Ant Distributed System for Solving the Traveling Salesman Problem’. pp. 779-789. Vol. 215 th Informatic Latinoamerican Conference-CLEI,. Paraguay (1999). [2] S. Bak, J. Cobb, E. Leiss. ‘Load Balancing Routing via Randomization’. pp. 999-1010. Vol. 215 th Informatic Latino american Conference-CLEI. Paraguay (1999). [3] M. Dorigo, V. Maniezzo, A. Colorni. ‘The Ant System: Optimization by a colony of cooperating agents’. pp. 1-13. Vol. 26-Part B. IEEE Transactions

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