Ant colony optimization algorithms Mykulska Eugenia
[email protected]
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1. Summary 2. Detailed 3. Common extensions 4. Convergence 5.
Pheromone update 6. Applications 7. Some problem 8. Definition
difficulty 9. Stigmergy algorithms 10. Related methods
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ant colony optimization algorithm In computer science and
operations research, the ant colony optimization algorithm (ACO) is
a probabilistic technique for solving computational problems which
can be reduced to finding good paths through graphs.
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This algorithm is a member of ant colony algorithms family, in
swarm intelligence methods, and it constitutes some metaheuristic
optimizations..
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Initially proposed by Marco Dorigo in 1992 in his PhD thesis,
the first algorithm was aiming to search for an optimal path in a
graph, based on the behavior of ants seeking a path between their
colony and a source of food.
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A little from biology A little from biology The original idea
comes from observing the exploitation of food resources among ants,
in which ants individually limited cognitive abilities have
collectively been able to find the shortest path between a food
source and the nest.
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An ant (called "blitz") runs more or less at random around the
colony; If it discovers a food source, it returns more or less
directly to the nest, leaving in its path a trail of pheromone;
These pheromones are attractive, nearby ants will be inclined to
follow, more or less directly, the track; Returning to the colony,
these ants will strengthen the route; If there are two routes to
reach the same food source then, in a given amount of time, the
shorter one will be traveled by more ants than the long route; The
short route will be increasingly enhanced, and therefore become
more attractive; The long route will eventually disappear because
pheromones are volatile; Eventually, all the ants have determined
and therefore "chosen" the shortest route.
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The basic philosophy of the algorithm involves the movement of
a colony of ants through the different states of the problem
influenced by two local decision policies, viz., trails and
attractiveness.
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Thereby, each such ant incrementally constructs a solution to
the problem. When an ant completes a solution, or during the
construction phase, the ant evaluates the solution and modifies the
trail value on the components used in its solution. This pheromone
information will direct the search of the future ants
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Furthermore, the algorithm also includes two more mechanisms,
viz., trailevaporation and daemon actions. Trail evaporation
reduces all trail values over time thereby avoiding any
possibilities of getting stuck in local optima. The daemon actions
are used to bias the search process from a non-local
perspective.
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Elitist ant system Max-Min ant system (MMAS) Ant Colony System
Rank-based ant system (ASrank) Continuous orthogonal ant colony
(COAC)
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Example pseudo-code and formulae procedure ACO_MetaHeuristic
while(not_termination) generateSolutions() daemonActions()
pheromoneUpdate() end while end procedure
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In general, the kth ant moves from state x to state y with
probability where xy is the amount of pheromone deposited for
transition from state x to y, 0 is a parameter to control the
influence of xy, xy is the desirability of state transition xy (a
priori knowledge, typically1 / d xy, where d is the distance) and 1
is a parameter to control the influence of xy.
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Pheromone update When all the ants have completed a solution,
the trails are updated by where is the amount of pheromone
deposited for a state transition xy, is the pheromone evaporation
coefficient and is the amount of pheromone deposited, typically
given for a TSP problem (with moves corresponding to arcs of the
graph) by where L k is the cost of the kth ant's tour (typically
length) and Q is a constant.
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It must visit each city exactly once; A distant city has less
chance of being chosen (the visibility); The more intense the
pheromone trail laid out on an edge between two cities, the greater
the probability that that edge will be chosen; Having completed its
journey, the ant deposits more pheromones on all edges it
traversed, if the journey is short; After each iteration, trails of
pheromones evaporate.
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Scheduling problem Vehicle routing problem Assignment problem
Set problem Others
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Initialization: chromosomes are randomly created. At this
point, it is very important that the population is diverse.
Otherwise, the algorithm may not produce good solutions.
Evaluation: each chromosome is rated on how well the chromosome
solves the problem at hand. A fitness value is assigned to each
chromosome. Selection: the fittest chromosomes are selected for
propagation into the future generation based on how fit they are.
Recombination: individual chromosomes and pairs of chromosomes are
recombined, modified and then put back into the population.
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