Travelling and salesman problem using ant colony optimization
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This document discusses using ant colony optimization to solve the travelling salesman problem. It first defines the travelling salesman problem as finding the shortest route for a salesman to visit all cities exactly once and return to the starting city with the minimum cost. It then explains that ant colony optimization is a probabilistic technique inspired by how real ants find food sources, and involves artificial ants laying pheromone trails between cities to probabilistically build solutions. The document provides pseudocode of the ant colony optimization algorithm and shows its results are faster than brute force solutions for solving the travelling salesman problem, with runtime scaling better as the number of cities increases.
Travelling and salesman problem using ant colony optimization
- 1. Travelling and Salesman Problem Using Ant colony optimization AKASH SETHIYA ALGORITHMS FOR ARTIFICIAL INTELLIGENCE (SPRING 2017) COMPUTER SCIENCE GRADUATE MISSISSIPPI STATE UNIVERSITY
- 2. TSP (Travelling and Salesman) One salesman, visiting all cities in a route exactly once and come back to same city where he started. Problem to find the path for salesman in which cost is minimum. TSP can be modelled as an undirected weighted graph, in which cities are represent by vertices and path’s are graph edges and distance between cities are edge weights. The goal in TSP is to find a minimum length Hamiltonian circuit of the graph NP-hard problem (Permutation problem)
- 3. ACO (Ant colony optimization) Probabilistic technique for solving computation problem which can be reduced to finding shortest path through graphs. Initially proposed by Marco Dorigo in 1992 in his PhD thesis. Inspired by the approach of real ants to find the shortest path from nest to food source. Ants communicate with each other via a chemical substance called Pheromone. Trail which has high amount of pheromone, other ants follow the same trail to find food otherwise use a random path to search for food source.
- 4. Ant Colony Optimization Natural behaviors of Ants https://www.slideshare.net/MeenakshiDevi/ant-colony-optimization-11696728
- 5. Pseudocode of ACO Loop Randomly position m artificial ants on n cities for city=1 to n for ant=1 to m {Each ant builds a solution by adding one city after other} Select probabilistically the next city Apply local trail updating rule end for end for Apply the global trail updating rule using best ant Until end condition
- 6. Flow chart of ACO for TSP Initialize Place each ant in a randomly chosen city Choose NextCity(For Each Ant) more cities to visit For Each Ant Return to the initial cities Update pheromone level using the tour cost for each ant Print Best tour yes No Stopping criteria yes No Image credit: Ant colony optimization by Ahmad Elshamli, Daniel Asmar, Fadi Elmasri
- 7. Results No of Cities Brute Force (TSP) (ms) ACO (TSP) (ms) 10 95.2 20 2407 30 2888.4 40 2609.4 50 4328.8 60 6880.6 70 10345 80 14706 90 20704 100 28313
- 8. Result Analysis 0 5000 10000 15000 20000 25000 30000 0 20 40 60 80 100 120 TIME(MS) NUMBER OF CITIES ACO RUNTIME ANALYSIS - CITY VS
- 9. Complexities TSP – Brute force – O(n!) TSP – Dynamic Programming – O(2n n2) TSP – ACO - O(mn3)
- 10. References The Ant System: Optimization by a colony of cooperating agents by Marco Dorigo, Member, IEEE, Vittorio Maniezzo and Alberto Colorni An Ant colony optimization Algorithm for Solving Travelling Salesman Problem, Krishna H. Hingrajiya, Ravindra Kumar Gupta, Gajendra Singh Chandel https://github.com/lukedodd/ant-tsp https://en.wikipedia.org/wiki/Ant_colony_optimization_algorithms http://www.geeksforgeeks.org/travelling-salesman-problem-set-1/ https://en.wikipedia.org/wiki/Travelling_salesman_problem
- 11. THANK YOU