parallel implementation of ant colony optimization on traveling salesman problem
DESCRIPTION
Parallel Implementation of Ant Colony Optimization on Traveling Salesman problem. Under the supervision of Dr.K.P.Singh. Yogesh sharma IIT2009175 Ankur mangal IIT2009176. Traveling Salesman Problem (TSP). - PowerPoint PPT PresentationTRANSCRIPT
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
THANK YOU