Parallel%20Implementation%20of%20Ant%20Colony%20Optimization%20on%20%20Traveling%20Salesman%20problem

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Parallel Implementation of Ant Colony
Optimization on Traveling Salesman problem

• Yogesh sharma IIT2009175
• Ankur mangal IIT2009176

Under the supervision of Dr.K.P.Singh
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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.

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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.
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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.

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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.

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Ant colony optimization ( ACO )
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Ant colony optimization ( ACO )

• Algorithm-
• Procedure ACOMetaheuristic
• Set parameters, initialize pheromone trails
• While( termination condition not met ) Do
• Construct Solution
• Update pheromone
• daemon Action
• end
• end

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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.

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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.

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Ant colony optimization ( ACO )
1
P15
P12
2
5
P24
P35
P54
P23
3
4
P34
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Ant colony optimization ( ACO )
1
P15
P12
2
5
P24
P35
P54
3
4
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Ant colony optimization ( ACO )
1
P15
P12
2
5
P24
P35
P54
3
4
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Ant colony optimization ( ACO )
1
P15
P12
2
5
P24
P35
P54
3
4
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Ant colony optimization ( ACO )
1
P15
P12
2
5
P24
P35
P54
3
4
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Ant colony optimization ( ACO )
1
P15
P12
2
5
P24
P35
P54
3
4
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ACO Concept

• UpdatePheromones-
• When all ants comleted a solution pheromones
  updated by
• Is amount phermones deposited for a state
  transion xy.
•  ? 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.

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Ant colony optimization ( ACO )
1
P15
P12
2
5
P24
P35
P54
3
4
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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.

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Parrallel implementation of ACO
start
Fork
Parrallel threads
Join
End
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Parrallel implementation of ACO
start
Fork
Parrallel threads
Join
End
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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
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Parrallel Algorithm Of ACo

• Algorithm-
• Procedure ACOMetaheuristic
• Set parameters, initialize pheromone trails
• While( termination condition not met ) Do
• Parrallel Do
• Construct Solution
• Update pheromone
• daemon Action
• end
• end

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Result of parrellel Algorithm

• Instances-
• Intance - eli51
• 51 cities
• Best known solution- 426
• Best known solution by Our implementat- 426
• Intance - eli76
• 76 cities
• Best known solution- 540
• Best known solution by Our implementat- 538

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Perfomance graph between thread and time
time
Number of Thread
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Graph between Parrallel implementation and
sequential implementation
Time
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Thank You