A running time analysis of an Ant Colony Optimization algorithm for shortest paths in directed acyclic graphs

  • Authors:

  • Nattapat Attiratanasunthron;Jittat Fakcharoenphol

  • Affiliations:

  • Department of Computer Engineering, Kasetsart University, Bangkok 10900, Thailand;Department of Computer Engineering, Kasetsart University, Bangkok 10900, Thailand

  • Venue:
  • Information Processing Letters
  • Year:
  • 2008

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Abstract

In this paper, we prove polynomial running time bounds for an Ant Colony Optimization (ACO) algorithm for the single-destination shortest path problem on directed acyclic graphs. More specifically, we show that the expected number of iterations required for an ACO-based algorithm with n ants is O(1@rn^2mlogn) for graphs with n nodes and m edges, where @r is an evaporation rate. This result can be modified to show that an ACO-based algorithm for One-Max with multiple ants converges in expected O(1@rn^2logn) iterations, where n is the number of variables. This result stands in sharp contrast with that of Neumann and Witt, where a single-ant algorithm is shown to require an exponential running time if @r=O(n^-^1^-^@e) for any @e0.