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Ants find the shortest path: a mathematical proof

Content Provider	Springer Nature Link
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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