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

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 (...

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Bibliographic Details
Published in:Information processing letters Vol. 105; no. 3; pp. 88 - 92
Main Authors: Attiratanasunthron, Nattapat, Fakcharoenphol, Jittat
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 31.01.2008
Elsevier Science
Elsevier Sequoia S.A
Subjects:
Algorithmics. Computability. Computer arithmetics
Algorithms
Analysis of algorithms
Ant Colony Optimization
Applied sciences
Calculus of variations and optimal control
Computer science; control theory; systems
Exact sciences and technology
Graph algorithms
Graphs
Mathematical analysis
Mathematics
Miscellaneous
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in mathematical programming, optimization and calculus of variations
Optimization algorithms
Polynomials
Sciences and techniques of general use
Shortest paths
Studies
Theoretical computing
Ant Colony Optimization
Graph algorithms
Analysis of algorithms
Shortest paths
Polynomial
Graph path
Computer theory
Graph node
Optimization method
Shortest path
Iteration
Optimization
Polynomial time
Information processing
Digraph
Time analysis
Acyclic graph
Algorithm analysis
Directed graph
Graph algorithm
ISSN:0020-0190, 1872-6119
Online Access:Get full text
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Summary: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 ρ n 2 m log n ) for graphs with n nodes and m edges, where ρ 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 ρ n 2 log n ) 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 ρ = O ( n − 1 − ε ) for any ε > 0 .
Bibliography:SourceType-Scholarly Journals-1
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ISSN:0020-0190
1872-6119
DOI:10.1016/j.ipl.2007.08.013