Abstract: of an ant colony optimization method. From

Abstract:

         In this paper
we will be presenting about an overview and evolution of ant algorithms which
was observed from ant colonies. The types of ant algorithms like Ant System,
Ant colony System, Max-Min Ant System are disclosed and they are interpreted
through the flow chart. Comparative study is done between ant algorithms and it
is implemented in Travelling Salesman Problem, the better suited algorithm is
derived.

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Introduction:

    

Ant Colony Optimization:

Evolution:

 

Ant System Algorithm(AS):

    Ant system was
originally the term used to refer to a range of ant based algorithm where the
specific algorithm implementation was referred to as ant cycle. The so called
Ant Cycle Algorithm is canonically referred to as Ant System. The ant algorithm
is the baseline for ant colony optimization method. The first ACO algorithm was
proposed in the year 1992.The ant system algorithm is inspired by the foraging
behaviour of ants especially the pheromone communication between ants and
regarding a good path between the colony and the food resource in the
environment. This mechanism is called stigmergy.

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 Colony System Algorithm:

Ant Colony System algorithm is an example of an ant colony
optimization method. From the field of Swarm intelligence,Meta heuristic and
computational intelligence. Ant colony system is an extension to the ant system
algorithm and it is related to other ant colony optimization.

                                 ?ij ? (1 ? ?) x ?ij + ? x ? ?ij

    where 

 

s?ij represents the
pheromone for the component (graph edge) (i,j), 

? is the decay
factor,

 and ? ?ij  is
the maximizing solution cost for the best solution found so far if the
component ij is used in the
globally best known solution, otherwise it is 0.

MAX MIN ANT
SYSTEM:

      Max min ant system is  to combine an improved exploitation of the
best solutions found during the search with an effective mechanism for avoiding
early search stagnation. max min ant which has been specifically developed to
meet these requirements differ in three accepts in AS.

i). This ant may be the one which found the best solution in
the current iteration (iteration-best ant) or the one which found the best
solution from the beginning of the trial (global-best ant).

ii)To avoid stagnation of the search the range of possible
pheromone trails on each solution component is limited to an interval (?min  ?max + ).

iii) we initialize the pheromone trails to ?max, achieving
in this way a higher exploration of solutions at the start of the algorithm.
The algorithm constructs a solution by adding solution components in the list
of components that specify partial solutions, until an entire solution is
constructed. The probability of selecting solution component c(i) is given in
(1). Index i denotes a solution construction step, ?c(i) is the trail value
associated with component c(i), and ?c(i) is the heuristic value associated
with c(i). In step i, a component is selected from Li , a set of components.
Parameters ? and ? are used to maintain balance between trails and heuristic
values.

 

                                     pc(i)      

After the population of solutions is constructed the best
solution is found and trails are updated. The update process includes trail
evaporation (2) for all trails, and trail reinforcement (3) for all components
included in the iteration or global best solution.

                                                           
?c (j)=(1-P). ?c(j)

 

 

Abstract:

         In this paper
we will be presenting about an overview and evolution of ant algorithms which
was observed from ant colonies. The types of ant algorithms like Ant System,
Ant colony System, Max-Min Ant System are disclosed and they are interpreted
through the flow chart. Comparative study is done between ant algorithms and it
is implemented in Travelling Salesman Problem, the better suited algorithm is
derived.

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For You For Only $13.90/page!


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Introduction:

    

Ant Colony Optimization:

Evolution:

 

Ant System Algorithm(AS):

    Ant system was
originally the term used to refer to a range of ant based algorithm where the
specific algorithm implementation was referred to as ant cycle. The so called
Ant Cycle Algorithm is canonically referred to as Ant System. The ant algorithm
is the baseline for ant colony optimization method. The first ACO algorithm was
proposed in the year 1992.The ant system algorithm is inspired by the foraging
behaviour of ants especially the pheromone communication between ants and
regarding a good path between the colony and the food resource in the
environment. This mechanism is called stigmergy.

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 Colony System Algorithm:

Ant Colony System algorithm is an example of an ant colony
optimization method. From the field of Swarm intelligence,Meta heuristic and
computational intelligence. Ant colony system is an extension to the ant system
algorithm and it is related to other ant colony optimization.

                                 ?ij ? (1 ? ?) x ?ij + ? x ? ?ij

    where 

 

s?ij represents the
pheromone for the component (graph edge) (i,j), 

? is the decay
factor,

 and ? ?ij  is
the maximizing solution cost for the best solution found so far if the
component ij is used in the
globally best known solution, otherwise it is 0.

MAX MIN ANT
SYSTEM:

      Max min ant system is  to combine an improved exploitation of the
best solutions found during the search with an effective mechanism for avoiding
early search stagnation. max min ant which has been specifically developed to
meet these requirements differ in three accepts in AS.

i). This ant may be the one which found the best solution in
the current iteration (iteration-best ant) or the one which found the best
solution from the beginning of the trial (global-best ant).

ii)To avoid stagnation of the search the range of possible
pheromone trails on each solution component is limited to an interval (?min  ?max + ).

iii) we initialize the pheromone trails to ?max, achieving
in this way a higher exploration of solutions at the start of the algorithm.
The algorithm constructs a solution by adding solution components in the list
of components that specify partial solutions, until an entire solution is
constructed. The probability of selecting solution component c(i) is given in
(1). Index i denotes a solution construction step, ?c(i) is the trail value
associated with component c(i), and ?c(i) is the heuristic value associated
with c(i). In step i, a component is selected from Li , a set of components.
Parameters ? and ? are used to maintain balance between trails and heuristic
values.

 

                                     pc(i)      

After the population of solutions is constructed the best
solution is found and trails are updated. The update process includes trail
evaporation (2) for all trails, and trail reinforcement (3) for all components
included in the iteration or global best solution.

                                                           
?c (j)=(1-P). ?c(j)

 

 

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