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this slide is about the algorithm which is design using ant colony optimization
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Ant Colony Optimization
By:Sachin AgarwallaRegd. No-0911012065C.S.E(A)
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Under Guidance Of:Mr. Swadhin Ku. BarisalB.E., M.Tech., CSE (IIT, Kharagpur)Assistant ProfessorI.T.E.R
Optimization
• Given a graph with two specified vertices A and B, find a shortest path from A to B.
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General optimization problem:
given f:X ,ℝfind xεX such that f(x) is minimum
shortest path problem, polynomial
Ant colony
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food
nest
Ant Colony Optimization (ACO):a heuristic optimization method for shortest path
and other optimization problems which borrows ideas from biological ants
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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
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History: ACO for shortest paths …
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History: ACO for shortest paths
Goss et al. 1989, Deneuborg et al. 1990experiments 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
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nest
food
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
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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*/
for all i j: τij := (1-ρ) τij ; /*evaporate pheromone*/
ACO for shortest paths I:directed
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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*/
ACO for shortest paths II:general
...a more complex undirected cyclic graph ...
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WC4 WC5 Barbara Marc
449a Anja Dagmar Espresso
322 339 WC3 Friedhelm
Fachschaft WC2 Rechner Astrid
Zeitschriften WC Bibo RZ-Sekretariat
ToilettenCafete RZGetraenke-automat
Mensa
ACO for shortest paths II:general
11449a
449a
... Marc was not so happy with the result ...
ACO for shortest paths II:general
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for all i: pi:=0; /*ant position init*/
si:=( ); /*ant brain is empty*/
for all i-j: τi-j:=const; /*pheromone init*/
repeat for all i: construct_solution(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;
append j to si; /*remember the trail*/
global_pheromone_update(i):
for all j-j’ in si: Δτj-j’:= 1/length of the path stored in si;
minibrain
update according
to the quality
minibrain
si:=hungry
repeat for all i: ant_step(i);
ACO for shortest paths II:general
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WC4 WC5 Barbara Marc
449a Anja Dagmar Espresso
322 339 WC3 Friedhelm
Fachschaft WC2 Rechner Astrid
Zeitschriften WC Bibo RZ-Sekretariat
ToilettenCafete RZGetraenkeMensa
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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;
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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.
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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
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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
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Questions ?
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Thank You !