Introduction

Movement of ants depends upon the

amount of pheromone available on the edges of the graph. The probability pit of

transition of those virtual ant from node I to t using the formula given below

We Will Write a Custom Essay about Introduction i ((T ^?)*( N^ ß))/(sum((T ^?)*( N^**For You For Only $13.90/page!**

order now

Pit=( ?i?+?iß)/?( ?Ni?+ ?Niß)

Where ?i indicate the

attractiveness of transition in the past and ?i denote the transition

attractiveness of the ants.

Ni- set the nodes connected to the

point i.

?, ß- are the parameters.

ACO algorithm

Step 1: Start.

Step 2: Init the pheromones for all

the connection between cities.

Step 3: Consider 20 (may be more

than that) ants.

Step 4. For each ant do

Step

4.a) Start the ant from an random city.

Step

4.b) Choose the next city using probability equation based on the pheromone

strength and distance to the next city.

Probability can be measure as probability for the path k to i

((T ^?)*( N^ ß))/(sum((T ^?)*( N^ ß))for

all the points not yet in the path.

Where T is 1/dij

D(I,j)=sqtr((xi-xj)2 +(yi=yj)2)

N is the amount of pheromone and

alpha and beta are the two parameters.

Step

4.c) Visit all the city once and construct a path.

Step

4,d) Combine all the pheromones from all the path and update it as

1/dij=Initial pheromone from k to

i=(1-rho)*(pheromone from k to i)+(sum of pheromone from k to I from most

recent wave)

Where rho is the decay constant.

Step

4.e) do the same step from (4.a) to (4.e) until there is no change to get the

best path and time.

Step 5. Implement the updation and

check for the best solution.

Step 6. End.

Initial Values

i)

Iteration is set to 100 with population default

value 20.

ii)

For each path initial pheromone as 1.0( It may

varies and outcome are observed)

iii)

Rate of evaporation( initial value 0.1) that is

rho.( It varies according to the length of path, availability of number of

ants)

iv)

Values of alpha and beta (may vary and thus

result effects) Initial value alpha=1.0 and beta=2.0 and Pheromone

deposit factor(Q)

– 1