parallel implementation of ant colony optimization on traveling salesman problem

PARALLEL IMPLEMENTATION OF ANT COLONY OPTIMIZATION ON TRAVELING SALESMAN PROBLEM

Yogesh sharma IIT2009175

Ankur mangal IIT2009176

Under the supervision of Dr.K.P.Singh

TRAVELING SALESMAN PROBLEM (TSP)

Traveling salesman problem :- A salesman must visit n cities, passing through each city only once, beginning from one of them which is considered as his base,and returning to it.

The cost of the transportation among the cities is given.

The program of the journey is requested , that is the order of visiting the cities in such a way that the cost is the minimum.

TRAVELING SALESMAN PROBLEM

Traveling salesman problem is NP-complete. This means that to obtain optimal route we have to through all possible routes and Number of routes increase exponentially.

TRAVELING SALESMAN PROBLEM

Number of possible routes with 50 cities is (50-2)! , which is

12,413,915,592,536,072,670,862,289,047,373,375,038,521,486,354,677,760,000,000,000.

So for large instance compute optimal solution is impossible.

Instead of finding exact solution optimization tachniques compute solution that is close to the optimal solution.

Ant colony optimization is a metaheuristic to compute a solution close to optimal solution.

ANT COLONY OPTIMIZATION ( ACO )

Ant colony optimization algorithm is a metaheuristic that can be used to define heuristic function applicable to wide set of different problems.

ACO is inspired by behaviour of real ants. Key concept of ACO based on communication

among ants based on the use of chemical produce by ants called as pheromone.

Ants use pheromone trail to making path on ground.

ANT COLONY OPTIMIZATION ( ACO )

ANT COLONY OPTIMIZATION ( ACO )

Algorithm:- Procedure ACOMetaheuristic

Set parameters, initialize pheromone trails

While( termination condition not met ) Do

Construct SolutionUpdate pheromone daemon Action

endend

ANT COLONY OPTIMIZATION ( ACO )

Construct solution :- Construct solution manage a colony of ants that visit adjacent states of consider problem (i.e. Traveling salesman problem ) construction graph Gc( v , e ).

They move by a local decision policy make use of pheromone trail and heuristic information.

Initially , ant are out on randimely chosen paths.

At each construction step , ant k apply problalistic choice to decide which state to visit next.

ANT COLONY ALGORITHM ( ACO ) Probability for kth ant to move from state i to state j is

given by

xy is amount of pheromone for transition from x to y.

xy is heuristic information. is parameter to control influence of pheromone.

is parameter to control influence of heuristic value.

ANT COLONY OPTIMIZATION ( ACO )

2 5

3 4

1

P12P15

P54P23

P24P35

P34

ANT COLONY OPTIMIZATION ( ACO )

2 5

3 4

1

P12P15

P54

P24P35

ANT COLONY OPTIMIZATION ( ACO )

2 5

3 4

1

P12P15

P54

P24P35

ANT COLONY OPTIMIZATION ( ACO )

2 5

3 4

1

P12P15

P54

P24P35

ANT COLONY OPTIMIZATION ( ACO )

2 5

3 4

1

P12P15

P54

P24P35

ANT COLONY OPTIMIZATION ( ACO )

2 5

3 4

1

P12P15

P54

P24P35

ACO CONCEPT

UpdatePheromones:- When all ants comleted a solution

pheromones updated by Is amount phermones deposited for a

state transion xy.  ρ is evaporation coefficient and is the

amount of pheromone deposited. DaemonActions:- DaemonAction is

procedure to implement centralized action which cannot be performed by single ant.example –decide whether deposit additional pheromone to bias the search process.

ANT COLONY OPTIMIZATION ( ACO )

2 5

3 4

1

P12P15

P54

P24P35

PARRALLEL IMPLEMENTATION OF ACO

Our target is to parrallize the sequential algorithm.

On large instances sequential algorithm does not use full resources.Ex:- if we have 6-processors sequential algorithm works as one process.

To make better use of available resources parrallel process work concurrently on system.

Ant speed up process of finding solution.

PARRALLEL IMPLEMENTATION OF ACO

start

Fork

Join

End

Parrallel threads

PARRALLEL IMPLEMENTATION OF ACO

start

Fork

Join

End

Parrallel threads

SHARED MEMORY MODEL FOR CONCURREMT ACCESS TO DATA

Memory

Reead only access

Reead only access

Reead only access

For update of data by ant. Lock data and uadate by single ant

PARRALLEL ALGORITHM OF ACO

Algorithm:- Procedure ACOMetaheuristic

Set parameters, initialize pheromone trails

While( termination condition not met ) Do

Parrallel DoConstruct Solution

Update pheromone daemon Action

endend

RESULT OF PARRELLEL ALGORITHM

Instances:- Intance :- eli51

51 citiesBest known solution:- 426Best known solution by Our implementat:- 426

Intance :- eli76 76 citiesBest known solution:- 540Best known solution by Our implementat:- 538

PERFOMANCE GRAPH BETWEEN THREAD AND TIME

2 4 6 8 10 120

0.5

1

1.5

2

2.5

3

3.5

4

4.5

time

Number of Thread

GRAPH BETWEEN PARRALLEL IMPLEMENTATION AND SEQUENTIAL IMPLEMENTATION

itera

tion

50

itera

tion1

00

itera

tion

300

itera

tion

500

itera

tion

100

itera

tion

2000

02468

10121416

sequentialparrallel

Time

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