Ant colony optimization (aco)
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This document discusses ant colony optimization (ACO), a metaheuristic technique for finding optimal paths or solutions. ACO is inspired by how ants find the shortest path to food. It can be used to solve complex optimization problems like routing parcels between cities. The algorithm works by simulating "pheromone trails" that ants leave to mark paths, and determining the next steps probabilistically based on the pheromone levels. Over multiple iterations, the paths with higher pheromone become more desirable, until the optimal solution emerges. As an example, the document outlines how ACO can be applied to solve the traveling salesman problem of finding the shortest route between multiple cities.
Ant colony optimization (aco)
- 1. ANT COLONY OPTIMIZATION (ACO) DESIGN OPTIMIZATION TECHNIQUES Presented by K. Magesh 17ME325 I yr M.Tech. PDM PONDICHERRY ENGINEERING COLLEGE Subject handling Staff Dr. V. Anandhan Professor Mechanical Engineering
- 2. WHY ACO IS DEVELOPED? • We take an example of a courier company in Germany which has to dispatch parcels in various cities Let no. of Parcels to be delivered = 40 • To save time, we need to find the fastest routes between the cities 2
- 3. • No. of possible routes interconnecting these 40 cities is found to be 815 Quattuordocillion possibilities, i.e., numerically equal to one 8 followed by 47 zeros (8 x 1047) • ACO serves as the best optimization tool to find the optimum in these complex situations 3
- 4. BIOLOGY BEHIND ACO • Ants are blind • Every ant has some liquid in their body, which is called as a pheromone, similar to harmones and enzymes in human body • Ant secrete one type of pheromone when they go in search of food 4
- 5. CHARACTERISTICS OF PHEROMONE • Pheromone evaporates as time goes on • It grows in density if ants travel repeatedly in same path • After finding the minimum distant path, the pheromone in the other trails evaporate completely 5
- 6. TYPICAL EXAMPLE Image courtesy : www.stuartreid.co.za 6
- 7. ANT COLONY OPTIMIZATION • ACO was first developed by Marco Dorigo in 1992 • ACO is a probabilistic technique for solving highly computational problems • It is based on foraging behaviour of ants (Swarm Intelligence) 7
- 8. SOLVING A TRAVELLING SALESMAN PROBLEM USING ACO
- 9. ASSUMPTIONS • All the cities should be visited by the ants, but only once., no repetition is allowed • Initial Pheromone level is assumed to be constant for every path HOME DESTINATION ONE TOUR (ONE ITERATION) 9
- 10. ACO ALGORITHM FOR TSP I. Randomly place all the ants in the cities. Let m = no.of cities and n = no. of ants. ‘m’ may or may not be equal to n II. Assume initial pheromone level and problem constants α, β. Let the initial pheromone level τij =1 10 A B C 1 2 3 1 1 1 A B C
- 11. III. (i) For ant 1, choose an optimum ‘not yet visited’ city until one tour is completed ηij – Visibility (1/distance) pk ij – Probability of choosing a city ( for kth ant ) (ii) Calculate the cumulative probabilities and compare with a random number ‘r’. (iii) The path with immediately greater probability than ‘r’ is chosen (iv) Repeat the step III until the tour of ant 1 is completed 11 B A 1 C
- 12. IV.Find the total length of the tour Lk for ant 1 Evaporate the pheromone level after ant 1 completes its tour V. Update the pheromone level after ant 1 completes its tour Where Δτk = Q/Lk Q – constant ,usually equals to 1 12
- 13. VI.Repeat all the steps for ant 2,3,…n. Find the optimum path and update the pheromone levels. The path with highest pheromone level is the optimum path 13
- 14. REFERENCES • ‘Tutorial On Ant Colony Optimization’ by Budi Santosa, Professor, Industrial Engineering, Institut Teknologi Sepuluh Nopember, ITS, Surabaya • Engineering Optimization – theory and Practice by Singaresu S Rao – 4th Edition • Solving travelling salesman problem by Ant Colony Algorithm by Jayathra Majumdar, Barrackpore Rastraguru Sundaranath College • Practical Genetic algorithms by Randy L Haupt and Sue Ellen Haupt • Jinhui Yang, Xiaohu Shi, Mariso Marchese, Yanchun, ‘LiangAn ant colony optimization method for generalized TSP problem’ Progress in Natural Science ( Elsevier) – 2008 14
- 15. THANK YOU 15
Editor's Notes
- #8: Foraging – search of food Swarm Intelligence – decentralization, collective effort. Metaheuristics – An algorithm to find near optimum solution Stochastic - Random