Runtime Analysis of a Simple Ant Colony Optimization Algorithm

Ant Colony Optimization (ACO) has become quite popular in recent years. In contrast to many successful applications, the theoretical foundation of this randomized search heuristic is rather weak. Building up such a theory is demanded to understand how these heuristics work as well as to come up with...

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Veröffentlicht in:Algorithmica Jg. 54; H. 2; S. 243 - 255
Hauptverfasser: Neumann, Frank, Witt, Carsten
Format: Journal Article Tagungsbericht
Sprache:Englisch
Veröffentlicht: New York Springer-Verlag 01.06.2009
Springer
Schlagworte:
Algorithm Analysis and Problem Complexity
Algorithmics. Computability. Computer arithmetics
Algorithms
Applied sciences
Computer Science
Computer science; control theory; systems
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Exact sciences and technology
Mathematics of Computing
Theoretical computing
Theory of Computation
Runtime analysis
Randomized search heuristics
Ant colony optimization
Lower bound
Insecta
Evolutionary algorithm
Evaporation
Randomized algorithm
Social insect
Formicoidea
Phase transitions
Search algorithm
Arthropoda
Optimal solution
Heuristic method
Swarm intelligence
Hymenoptera
Invertebrata
Algorithm analysis
Aculeata
ISSN:0178-4617, 1432-0541
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Beschreibung
Zusammenfassung:Ant Colony Optimization (ACO) has become quite popular in recent years. In contrast to many successful applications, the theoretical foundation of this randomized search heuristic is rather weak. Building up such a theory is demanded to understand how these heuristics work as well as to come up with better algorithms for certain problems. Up to now, only convergence results have been achieved showing that optimal solutions can be obtained in finite time. We present the first runtime analysis of an ACO algorithm, which transfers many rigorous results with respect to the runtime of a simple evolutionary algorithm to our algorithm. Moreover, we examine the choice of the evaporation factor, a crucial parameter in ACO algorithms, in detail. By deriving new lower bounds on the tails of sums of independent Poisson trials, we determine the effect of the evaporation factor almost completely and prove a phase transition from exponential to polynomial runtime.
ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-007-9134-2