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Parallel Ant Colony Optimization for Real World Problems

Parallel Ant Colony Optimization for Real World Problems. Brandon Phelps and Daniel White. Topics to be covered:. Traveling Salesman Problem(TSP) Sequential TSP Solution Ant Colony Optimization(ACO) Parallelization of ACO Time Complexity Comparison. Introduction to TSP.

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Parallel Ant Colony Optimization for Real World Problems

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  1. Parallel Ant Colony Optimization for Real World Problems Brandon Phelps and Daniel White

  2. Topics to be covered: Traveling Salesman Problem(TSP) Sequential TSP Solution Ant Colony Optimization(ACO) Parallelization of ACO Time Complexity Comparison

  3. Introduction to TSP Traveling Salesman Problem- Given a list of cities and distance between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city? For a number of cities N, the number of permutations of cycles is N factorial. The time complexity for an exact algorithm with brute force search is O(N!) because all possible cycles must be considered. This will produce the optimal path, but becomes almost unusable for anything past a couple dozen vertices. NP-Hard - Nondeterministic Polynomial Time

  4. Why TSP is Important Circuit Boards When drilling circuit boards, different sizes of bits are used to drill and the TSP is used to find the fastest path to decrease production time.

  5. Sequential Algorithm for TSP Nearest Neighbor - also known as the greedy algorithm. Doesn't return an exact answer, but rather just a relatively short cycle. (Averages 25% longer than optimal) O( n2 ) - Similar to Prim's algorithm, nearest neighbor goes along each vertex and chooses the next vertex to visit by the shortest edge. Choose a starting pointing V V = starting vertex while (all vertices have not been visited) set V as visited for all vertices connected to V return edge values and compare to find nearest unvisited vertex V = nearest vertex

  6. What is ACO? Ant Colony Optimization - an algorithm to find “good” paths through graphs ACO is based on the generalized behavior of an ant colony seeking a path between the colony and a source of food. So how do ant colonies work?

  7. Ant Colony Behavior Initially, ants wander in random directions until food is found Once food is found, the ants return to the colony, laying down pheromone trails for other ants to follow and find the food. - If an ant finds an existing pheromone trail, it is likely to follow it - The trail is reinforced if other ants find the food as well

  8. Colony S G

  9. How ACO works on TSP At each node, or “city”, the ant chooses the next node according to some parameters: 1) The ant must visit every node only once. 2) The distance of the next node. Distant nodes are not as likely to be chosen. 3) The pheromone value of the path between nodes. The higher the value, the more likely the path will be chosen. 4) The cost of the tour. After all the ants in the iteration have completed a loop, the ant with the shortest tour places pheromones on the path with the lowest cost.

  10. S

  11. How ACO works on TSP cont. Ant memory - Each ant has a visited set for traversing through the graph - Each ant also has a local pheromone “map” used to record it’s route. Global Pheromone Map - Updated after all ants have traversed the graph with the lowest path cost found.

  12. How ACO relates to parallel processing Two types - Multiple ants - Multiple colonies Distributed Memory vs Shared Memory - Contrast

  13. Multiple ants Each processor acts like a single ant, which generates a local pheromone map. This is then sent to a master processor.

  14. Multiple ants cont. The master processor then updates the global pheromone map. Which is then sent back to the slave processors. This then completes the cycle and is repeated for N generations.

  15. P0 P3 P2 P1

  16. Multiple Colonies Each processor runs an entire colony. After which information is sent across processors about each colony’s best solution so far.

  17. Multiple Colonies Modifications By taking advantage of the parallel processing and the multiple amount of parameters. Each processor can be given different parameters which can cause an increase in diversity of the solutions.

  18. Comparison of Sequential Time Complexity Nearest neighbor O(n^2) Ant colony Optimization O(G*A*n^2) G = number of generations A = number of ants

  19. Parallel vs Sequential Time Complexity Multiple Ants O(G(lg(n)*P + n^2)) where P is the number of processors Multiple Colonies - same as Sequential, except has a greater convergence rate, as well as search space.

  20. DEMO

  21. Our Results - Computation Time Average of 20 runs Constant: 50 generations, 30 cities

  22. Our Results - Path Length Average over 20 runs Constant: 40 ants, 50 generations

  23. Conclusion ACO, due to it’s nature, is easy to implement on a parallel system. Using multiple processors, good solutions to the TSP can be found.

  24. Citations Ant colonies for the traveling salesman problem, Marco Dorigo and Luca Maria Gambardella A Parallel Implementation of Ant Colony Optimization, Marcus Randall and Andrew Lewis

  25. Questions?

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