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  1. Swarm Intelligence
  2. Swarm Intelligence : Volume 7
  3. Swarm Intelligence : Volume 7, Issue 1, March 2013
  4. Ants find the shortest path: a mathematical proof
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Swarm Intelligence : Volume 11
Swarm Intelligence : Volume 10
Swarm Intelligence : Volume 9
Swarm Intelligence : Volume 8
Swarm Intelligence : Volume 7
Swarm Intelligence : Volume 7, Issue 4, December 2013
Swarm Intelligence : Volume 7, Issue 2-3, September 2013
Swarm Intelligence : Volume 7, Issue 1, March 2013
Swarm robotics: a review from the swarm engineering perspective
Ants find the shortest path: a mathematical proof
ACOHAP: an efficient ant colony optimization for the haplotype inference by pure parsimony problem
Swarm Intelligence : Volume 6
Swarm Intelligence : Volume 5
Swarm Intelligence : Volume 4
Swarm Intelligence : Volume 3
Swarm Intelligence : Volume 2
Swarm Intelligence : Volume 1

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Ants find the shortest path: a mathematical proof

Content Provider SpringerLink
Author Shah, Sameena Bhaya, Amit Kothari, Ravi Chandra, Suresh
Copyright Year 2013
Abstract In the most basic application of Ant Colony Optimization (ACO), a set of artificial ants find the shortest path between a source and a destination. Ants deposit pheromone on paths they take, preferring paths that have more pheromone on them. Since shorter paths are traversed faster, more pheromone accumulates on them in a given time, attracting more ants and leading to reinforcement of the pheromone trail on shorter paths. This is a positive feedback process that can also cause trails to persist on longer paths, even when a shorter path becomes available. To counteract this persistence on a longer path, ACO algorithms employ remedial measures, such as using negative feedback in the form of uniform evaporation on all paths. Obtaining high performance in ACO algorithms typically requires fine tuning several parameters that govern pheromone deposition and removal. This paper proposes a new ACO algorithm, called EigenAnt, for finding the shortest path between a source and a destination, based on selective pheromone removal that occurs only on the path that is actually chosen for each trip. We prove that the shortest path is the only stable equilibrium for EigenAnt, which means that it is maintained for arbitrary initial pheromone concentrations on paths, and even when path lengths change with time. The EigenAnt algorithm uses only two parameters and does not require them to be finely tuned. Simulations that illustrate these properties are provided.
Starting Page 43
Ending Page 62
Page Count 20
File Format PDF
ISSN 19353812
Journal Swarm Intelligence
Volume Number 7
Issue Number 1
e-ISSN 19353820
Language English
Publisher Springer US
Publisher Date 2013-02-08
Publisher Place Boston
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Ant Colony Optimization Stability analysis Pheromone Collective foraging Stagnation Self-organization Selective removal of pheromone Distributed optimization Optimization Swarm intelligence Artificial Intelligence (incl. Robotics) Computer Systems Organization and Communication Networks ApplicationMathematics/Computational Methods of Engineering Communications Engineering, Networks Computer Communication Networks
Content Type Text
Resource Type Article
Subject Artificial Intelligence
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