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Ant Colony Optimization
in Multiple Travelling
Salesman Problem
Ant Colony Optimization
• Ant colony optimization is a population-based
metaheuristic that can be used to find
approximate solutions to difficult optimization
problems.
• It studies artificial systems that take
inspiration from the behavior of real ant
colonies and which are used to solve discrete
optimization problems.
Multiple Traveling Salesman Problem
• The Multiple Travelling Salesman Problem (mTSP) is a
generalization of Travelling Salesman Problem (TSP) in
which more than one salesman is allowed.
• Given a set of cities, one depot where m salesman are
located, and a cost metric, the objective of mTSP is to
determine a set of routes for m salesman so as to
minimize the total cost of the m routes. The cost metric
can represent cost, distance or time. The requirements
on the set of routes are:
 All the routes must start and end at the same point.
 Each city must be visited exactly once by only one
salesman.
Characteristics of Ants
• Almost blind.
• Incapable of achieving complex tasks alone.
• Rely on the phenomena of swarm intelligence for survival.
• Capable of establishing shortest-route paths from their colony to feeding
sources and back.
• Use stigmergic communication via pheromone trails.
• Follow existing pheromone trails with high probability.
• What emerges is a form of autocatalytic behavior: the more ants follow
a trail, the more attractive that trail becomes for being followed.
• The process is thus characterized by a positive feedback loop, where the
probability of a discrete path choice increases with the number of times
the same path was chosen before.
Natural Behaviour of Ants
Ants as Agents
Each ant is a simple agent with the following
characteristics:
• It chooses the town to go to with a probability
that is a function of the town distance and of the
amount of trail present on the connecting edge.
• To force the ant to make legal tours, transitions
to already visited towns are disallowed until a
tour is complete.
• When it completes a tour, it lays a substance
called trail on each edge (i, j) visited.
New Modified Ant Colony Optimization (NMACO)
Steps of the proposed algorithm
• Step 1: Build n solutions of the MTSP by using
a new transition rule and a candidate list.
• Step 2: Use insert, swap and 2-opt moves for
the current best solution and the best solution
until now in order to improve them more.
• Step 3: Update the global pheromone
information.
Pseudo code for NMACO for solving MSTP
1) Set the parameters.
2) Place all ants at the depot.
3) Select a nest node for each ant based on a new proposed formula
and efficient candidate list.
4) Deposit pheromone.
5) if there is a node that has not been visited, go to step 3.
6) Save the best solution and its value obtained in current iteration.
7) Update the best solution and its value obtained until now.
8) Apply the local searches for two best solutions in current iteration
and obtained until now.
9) Update global pheromone on each edge.
10) If the best solution till now is improved within ten iterations, go to
step 2.
11) Print the best solution and its value.
Applications of ACO
• Traveling salesman
• Quadratic assignment
• Graph coloring
• Multiple knapsack
• Set covering
• Maximum clique
• Bin packing
Questions?

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Ant colony optimization in multiple travelling salesman problem

  • 1. Ant Colony Optimization in Multiple Travelling Salesman Problem
  • 2. Ant Colony Optimization • Ant colony optimization is a population-based metaheuristic that can be used to find approximate solutions to difficult optimization problems. • It studies artificial systems that take inspiration from the behavior of real ant colonies and which are used to solve discrete optimization problems.
  • 3. Multiple Traveling Salesman Problem • The Multiple Travelling Salesman Problem (mTSP) is a generalization of Travelling Salesman Problem (TSP) in which more than one salesman is allowed. • Given a set of cities, one depot where m salesman are located, and a cost metric, the objective of mTSP is to determine a set of routes for m salesman so as to minimize the total cost of the m routes. The cost metric can represent cost, distance or time. The requirements on the set of routes are:  All the routes must start and end at the same point.  Each city must be visited exactly once by only one salesman.
  • 4. Characteristics of Ants • Almost blind. • Incapable of achieving complex tasks alone. • Rely on the phenomena of swarm intelligence for survival. • Capable of establishing shortest-route paths from their colony to feeding sources and back. • Use stigmergic communication via pheromone trails. • Follow existing pheromone trails with high probability. • What emerges is a form of autocatalytic behavior: the more ants follow a trail, the more attractive that trail becomes for being followed. • The process is thus characterized by a positive feedback loop, where the probability of a discrete path choice increases with the number of times the same path was chosen before.
  • 6. Ants as Agents Each ant is a simple agent with the following characteristics: • It chooses the town to go to with a probability that is a function of the town distance and of the amount of trail present on the connecting edge. • To force the ant to make legal tours, transitions to already visited towns are disallowed until a tour is complete. • When it completes a tour, it lays a substance called trail on each edge (i, j) visited.
  • 7. New Modified Ant Colony Optimization (NMACO) Steps of the proposed algorithm • Step 1: Build n solutions of the MTSP by using a new transition rule and a candidate list. • Step 2: Use insert, swap and 2-opt moves for the current best solution and the best solution until now in order to improve them more. • Step 3: Update the global pheromone information.
  • 8. Pseudo code for NMACO for solving MSTP 1) Set the parameters. 2) Place all ants at the depot. 3) Select a nest node for each ant based on a new proposed formula and efficient candidate list. 4) Deposit pheromone. 5) if there is a node that has not been visited, go to step 3. 6) Save the best solution and its value obtained in current iteration. 7) Update the best solution and its value obtained until now. 8) Apply the local searches for two best solutions in current iteration and obtained until now. 9) Update global pheromone on each edge. 10) If the best solution till now is improved within ten iterations, go to step 2. 11) Print the best solution and its value.
  • 9. Applications of ACO • Traveling salesman • Quadratic assignment • Graph coloring • Multiple knapsack • Set covering • Maximum clique • Bin packing