Ant colony optimization
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Ant Colony Optimization (ACO) is a heuristic optimization technique inspired by the behavior of real ant colonies. It is used to find solutions to optimization and shortest path problems. The technique works by simulating ants walking between points, such as between their nest and food sources. As artificial ants walk, they lay down and follow pheromone trails. Over time, the shortest paths become more desirable as they have the most pheromone accumulated on them. The algorithm iteratively improves the solutions found via the probabilistic decisions of many agents (the artificial ants) based on local information and global pheromone trails.
Ant colony optimization
- 1. Ant Colony Optimization By: Sachin Agarwalla Regd. No-0911012065 C.S.E(A) Under Guidance Of: Mr. Swadhin Ku. Barisal B.E., M.Tech., CSE (IIT, Kharagpur) Assistant Professor 1 I.T.E.R
- 2. Optimization General optimization problem: given f:Xℝ, find xεX such that f(x) is minimum • Given a graph with two specified vertices A and B, find a shortest path from A to B. shortest path problem, polynomial 2
- 3. Ant colony food 3 nest
- 4. Ant Colony Optimization (ACO): a heuristic optimization method for shortest path and other optimization problems which borrows ideas from biological ants 4
- 5. Ant Colony Optimization Outline • History: ACO for shortest paths • ACO for shortest paths I: directed • ACO for shortest paths II: general • Advantages and Disadvantages • Summary • References 5
- 6. History: ACO for shortest paths … 6
- 7. History: ACO for shortest paths Goss et al. 1989, Deneuborg et al. 1990 food experiments with Argentine ants: • ants go from the nest to the food source and backwards • after a while, the ants prefer the shortest path from the nest to the food source • stigmercy: • the ants communicate indirectly laying pheromone trails and following trails with higher pheromone • length gradient pheromone will accumulate on the shortest path nest 7
- 8. ACO for shortest paths I:directed A first ACO for a simple shortest path problem: directed acyclic graph (V={0,...,N}, E={ij}), ant hill: 0, food source: N for all i: pi:=0; /*ant position init*/ si:=hungry; /*ant state init*/ for all i j: τij:=const; /*pheromone init*/ repeat for all i: ant_step(i); /*ant step*/ 8 for all i j: τij := (1-ρ) τij ; /*evaporate pheromone*/
- 9. ACO for shortest paths I:directed ant_step(i): if pi=N: si:=satisfied; if pi=0: si:=hungry; /*collect food/deliver food*/ if si=hungry: choose j with pij with probability τpi j/Σpij’τpij’ /*choose next step*/ update Δτpi j := ε; pi:=j; /*update pheromone*/ if si=satisfied: choose j with jpi with probability τjpi/Σj’piτj’pi update Δτjpi:= ε; pj:=i; /* reversed directions*/ 9
- 10. ACO for shortest paths II:general ...a more complex undirected cyclic graph ... WC4 WC5 Barbara Marc 449a Anja Dagmar Espresso 322 339 WC3 Friedhelm Fachschaft WC2 Rechner Astrid Zeitschriften WC Bibo RZ-Sekretariat Mensa Cafete Getraenke- RZ Toiletten automat 10
- 11. ACO for shortest paths II:general ... Marc was not so happy with the result ... 449a 449a 11
- 12. ACO for shortest paths II:general for all i: pi:=0; /*ant position init*/ si:=hungry si:=( ); /*ant brain is empty*/ minibrain for all i-j: τi-j:=const; /*pheromone init*/ repeat for all i: construct_solution(i); repeat for all i: ant_step(i); for all i: global_pheromone_update(i); for all i-j: τi-j := (1-ρ) τi-j; /*evaporate*/ construct_solution(i): while pi≠N /*no solution*/ choose j with pi-j with probability τpi-j / Σpi-j’τpi-j’; pi:=j; minibrain append j to si; /*remember the trail*/ global_pheromone_update(i): update according for all j-j’ in si: Δτj-j’:= 1/length of the path stored in si; 12 to the quality
- 13. ACO for shortest paths II:general WC4 WC5 Barbara Marc Anja Dagmar Espresso 449a 339 WC3 Friedhelm 322 Fachschaft WC2 Rechner Astrid Zeitschriften WC Bibo RZ-Sekretariat Mensa Cafete Getraenke RZ Toiletten 13
- 14. ACO for shortest paths init pheromone ti-j ; repeat for all ants i: construct_solution(i); for all ants i: global_pheromone_update(i); for all edges: evaporate pheromone; construct_solution(i): init ant; while not yet a solution: expand the solution by one edge probabilistically according to the pheromone; global_pheromone_update(i): for all edges in the solution: increase the pheromone according to the quality; 14
- 15. Advantages and Disadvantages Advantages : 1) Positive feedback accounts for rapid discovery of good solution. 2) Efficient for Travels salesman problem and other similar problem. 3) Can be use in dynamic application. Disadvantages : 1) Theoretical analysis is difficult. 2) Probability distribution changes by iteration. 3) Time to convergence is uncertian. 15
- 16. Summary • Artificial Intelligence technique used to develop a new method to solve problems unsolvable since last many years • ACO is a recently proposed metaheuristic approach for solving hard combinatorial optimization problems. • Artificial ants implement a randomized construction heuristic which makes probabilistic decisions • ACO shows great performance with the “ill-structured” problems like network routing 16
- 17. References • M. Dorigo, M. Birattari, T. Stützle, “Ant Colony Optimization – Artificial Ants as a Computational Intelligence Technique”, IEEE Computational Intelligence Magazine, 2006 • C. Blum, Theoretical and Practical Aspects of Ant Colony Optimization, Dissertations in Artificial Intelligence, Vol. 282, Akademische Verlagsgesellschaft Aka GmbH, Berlin, Germany, 2004. • Wikipedia.com 17
- 18. Questions ? 18
- 19. Thank You ! 19