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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| Vydáno v: | IEEE transactions on evolutionary computation Ročník 13; číslo 5; s. 1083 - 1092 |
|---|---|
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| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
New York, NY
IEEE
01.10.2009
Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 1089-778X, 1941-0026 |
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| Abstract | 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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| AbstractList | 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. |
| Author | Yuren Zhou |
| Author_xml | – sequence: 1 givenname: Yuren Zhou surname: Yuren Zhou fullname: Yuren Zhou, Yuren Zhou |
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| Keywords | 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) |
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| SubjectTerms | 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 |
| Title | Runtime Analysis of an Ant Colony Optimization Algorithm for TSP Instances |
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