Runtime Analysis of an Ant Colony Optimization Algorithm for TSP Instances

Ant colony optimization (ACO) is a relatively new random heuristic approach for solving optimization problems. The main application of the ACO algorithm lies in the field of combinatorial optimization, and the traveling salesman problem (TSP) is the first benchmark problem to which the ACO algorithm...

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Bibliographic Details
Published in:IEEE transactions on evolutionary computation Vol. 13; no. 5; pp. 1083 - 1092
Main Author: Yuren Zhou, Yuren Zhou
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.10.2009
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithm design and analysis
Algorithmics. Computability. Computer arithmetics
Algorithms
Ant colony optimization
Ant colony optimization (ACO)
Applied sciences
Artificial intelligence
Benchmarking
Biological system modeling
Colonies
Combinatorial analysis
Computer science; control theory; systems
Evolution (biology)
Evolutionary algorithms
Evolutionary computation
Exact sciences and technology
Flows in networks. Combinatorial problems
Graphs
heuristic algorithm
Heuristic algorithms
Learning and adaptive systems
Logistics
Operational research and scientific management
Operational research. Management science
Optimization
Particle swarm optimization
Partitioning algorithms
Runtime
runtime analysis
Theoretical computing
Traveling salesman problem
traveling salesman problem (TSP)
Traveling salesman problems
Insecta
Evolutionary algorithm
Travelling salesman problem
Combinatorial optimization
Formicoidea
heuristic algorithm
Swarm intelligence
Ant colony optimization (ACO)
Aculeata
Mathematical programming
Probabilistic approach
Complete graph
Pheromone
Social insect
Particle swarm optimization
Arthropoda
Heuristic method
Minimax method
Problem solving
runtime analysis
Visibility
Hymenoptera
Invertebrata
Algorithm analysis
traveling salesman problem (TSP)
ISSN:1089-778X, 1941-0026
Online Access:Get full text
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Summary:Ant colony optimization (ACO) is a relatively new random heuristic approach for solving optimization problems. The main application of the ACO algorithm lies in the field of combinatorial optimization, and the traveling salesman problem (TSP) is the first benchmark problem to which the ACO algorithm has been applied. However, relatively few results on the runtime analysis of the ACO on the TSP are available. This paper presents the first rigorous analysis of a simple ACO algorithm called (1 + 1) MMAA (Max-Min ant algorithm) on the TSP. The expected runtime bounds for (1 + 1) MMAA on two TSP instances of complete and non-complete graphs are obtained. The influence of the parameters controlling the relative importance of pheromone trail versus visibility is also analyzed, and their choice is shown to have an impact on the expected runtime.
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ISSN:1089-778X
1941-0026
DOI:10.1109/TEVC.2009.2016570