Abstract: Meta heuristic() 2 while (termination criterion not satisfied)

Abstract:

This paper will present an overview of ant
algorithms that is algorithms for colony optimization that took insight which
was observed from ant colonies .We are going to discuss about the findings on
real ants and Ant Colony Optimization (ACO) algorithm is applied to wide range
of problems like Travelling Salesman , Job-Shop Scheduling ,Vehicle Routing.

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 Introduction:

Ant Colony Optimization is a probabilistic technique which is used for
searching optimal path in the graph based on behaviour of ants seeking a path
between their colony and source of food. It is a Meta-heuristic optimization.
It was first proposed by Marco Dorigo in 1992 as a multi-agent approach to
difficult combinatorial optimization problems such as Travelling salesman
problem (TSP), Quadratic assignment problem (QAP).

The ACO metaheuristic consists of group of
artificial ants with the characteristics to search good solutions to discrete
optimization problem. An Ant algorithm was inspired by the observation of real
ant colonies, Ants are social insects (i.e.) insects that lives in colonies and
whose behavior is directed more to the survival of the colony as a whole than
to that of a single individual component of the colony. An important and
interesting behavior of ant colonies is that their behavior and in particular,
how ants can find the shortest paths between food sources and their nest.

While walking from food sources to the
nest and vice versa, ants deposit on the ground a substance called pheromone,
forming in this way a pheromone trail. Ants can smell these this chemical and
when choosing their way tend to choose, in probability paths marked by them and
allows them to travel from food source to their colonies. Other ants from the
colony follow their nestmates to follow their paths to the food source. This is
how shortest path is emerged for their food hunting.

 The
?rst ants to arrive at the food source are those that took the two shortest
branches, so that, when these ants start their return trip, more pheromone is
present on the short branch than on the long branch, stimulating successive
ants to choose the short branch. 

Ant
Optimization Algorithms:

           
Ant Colony Optimization Algorithm:

1 procedure ACO Meta heuristic()

2 while (termination criterion not
satisfied)

3 schedule activities

4 ants generation and activity();

5 pheromone evaporation();

6 daemon actions(); foptionalg

7 end schedule activities

 8
end while

9 end procedure

10 procedure ants generation and
activity()

11 while (available resources)

12 schedule the creation of a new ant();

13 new active ant();

14 end while

15 end procedure

16 procedure new active ant() fant
lifecycleg

17 initialize ant();

18 M = update ant memory();

19 while (current state 6= target state)

20 A = read local ant-routing table();

21 P = compute transition probabilities(A;
M; problem constraints);

22 next state = apply ant decision
policy(P; problem constraints);

23 move to next state(next state);

24 if (online step-by-step pheromone
update)

25 deposit pheromone on the visited arc();

26 update ant-routing table();

27 end if

28 M = update internal state();

29 end while

30 if (online delayed pheromone update)

31 evaluate solution();

32 deposit pheromone on all visited
arcs();

 33
update ant-routing table();

34 end if

35 die();

36 end procedure

 

Ant
System(AS):

First ACO
algorithm to be proposed (1992) Pheromone values are updated by all the ants
that have completed the tour.

                                        ?ij ?
(1 ? ?) · ?ij + Pm k=1 ?? k ij

 where ? is the evaporation rate m is the
number of ants ?? k ij is pheromone quantity laid on edge (i, j) by the k th
ant ?? k i,j = ( 1/Lk if ant k travels on edge i, j 0 otherwise where Lk is the
tour length of the k th ant.

 

 

Ant System Algorithm:

                              1: for each colony do

                             2:
for each ant do

            
                3: generate route  

                             4: evaluate route

                             5:
evaporate pheromone in trails

                             6:
deposit pheromone on trails

                             7: end for

                             8: end for

Ant Colony System(ACS):

First major
improvement over Ant System Differences with Ant System:

1 Decision
Rule – Pseudorandom proportional rule

2 Local
Pheromone Update

3 Best only
offline Pheromone Update

Ants in ACS
use the pseudorandom proportional rule Probability for an ant to move from city
i to city j depends on a random variable q uniformly distributed over 0, 1,
and a parameter q0. If q ? q0, then, among the feasible components, the
component that maximizes the product ?il? ? il is chosen, otherwise the same
equation as in Ant System is used. This rule favours exploitation of pheromone
information

Diversifying
component against exploitation: local pheromone update. The local pheromone
update is performed by all ants after each step. Each ant applies it only to
the last edge traversed: ?ij = (1 ? ?) · ?ij + ? · ?0 where ? ? (0, 1 is the
pheromone decay coefficient ?0 is the initial value of the pheromone

Best only
offline pheromone update after construction Offline pheromone update equation
?ij ? (1 ? ?) · ?ij + ? · ?? best ij where ? best ij = ( 1/Lbest if best ant k
travels on edge i, j 0 otherwise Lbest can be set to the length of the best
tour found in the current iteration or the best solution found since the start
of the algorithm.

Ant Colony System Algorithm:

                                           1:
for each colony do

                                           2:
for each ant do

                                           3:
generate route

                                           4:
evaluate route

5: evaporate pheromone in all trails (? rate)

                                           6:
deposit pheromone on all trails

                                           7:
end for

              
8: evaporate pheromone in best global route (?2 rate)

                                           9:
deposit pheromone on best global route

                                          10:
end for

Max-Min Ant System (MMAS):

Developed
by St¨utzle and Hoos (1996), as another variation for the TSP, the MMAS
algorithm shows di?erences in the steps of pheromone deposition and
evaporation, that occur only after the i-th ant for each colony stablish its
trail.

Differences
with Ant System: 1 Best only offline Pheromone Update 2 Min and Max values of
the pheromone are explicitly limited ?ij is constrained between ?min and ?max
(explicitly set by algorithm designer). After pheromone update, ?ij is set to
?max if ?ij > ?max and to ?min if ?ij

x

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